ERK-Mediated Mechanochemical Waves Direct Collective Cell Polarization

During collective migration of epithelial cells, the migration direction is aligned over a tissue-scale expanse. Although the collective cell migration is known to be directed by mechanical forces transmitted via cell-cell junctions, it remains elusive how the intercellular force transmission is coordinated with intracellular biochemical signaling to achieve collective movements. Here, we show that intercellular coupling of extracellular signal-regulated kinase (ERK)-mediated mechanochemical feedback yields long-distance transmission of guidance cues. Mechanical stretch activates ERK through epidermal growth factor receptor (EGFR) activation, and ERK activation triggers cell contraction. The contraction of the activated cell pulls neighboring cells, evoking another round of ERK activation and contraction in the neighbors. Furthermore, anisotropic contraction based on front-rear polarization guarantees unidirectional propagation of ERK activation, and in turn, the ERK activation waves direct multicellular alignment of the polarity, leading to long-range ordered migration. Our findings reveal that mechanical forces mediate intercellular signaling underlying sustained transmission of guidance cues for collective cell migration.

Ability of magnetic resonance elastography to assess taut bands

BACKGROUND

Myofascial taut bands are central to diagnosis of myofascial pain. Despite their importance, we still lack either a laboratory test or imaging technique capable of objectively confirming either their nature or location. This study explores the ability of magnetic resonance elastography to localize and investigate the mechanical properties of myofascial taut bands on the basis of their effects on shear wave propagation.

METHODS

This study was conducted in three phases. The first involved the imaging of taut bands in gel phantoms, the second a finite element modeling of the phantom experiment, and the third a preliminary evaluation involving eight human subjects-four of whom had, and four of whom did not have myofascial pain. Experiments were performed with a 1.5 T magnetic resonance imaging scanner. Shear wave propagation was imaged and shear stiffness was reconstructed using matched filtering stiffness inversion algorithms.

FINDINGS

The gel phantom imaging and finite element calculation experiments supported our hypothesis that taut bands can be imaged based on its outstanding shear stiffness. The preliminary human study showed a statistically significant 50-100% (P=0.01) increase of shear stiffness in the taut band regions of the involved subjects relative to that of the controls or in nearby uninvolved muscle.

INTERPRETATION

This study suggests that magnetic resonance elastography may have a potential for objectively characterizing myofascial taut bands that have been up to now detectable only by the clinician's fingers.

Shape-Adaptive Metastructures with Variable Bandgap Regions by 4D Printing

This article shows how four-dimensional (4D) printing technology can engineer adaptive metastructures that exploit resonating self-bending elements to filter vibrational and acoustic noises and change filtering ranges. Fused deposition modeling (FDM) is implemented to fabricate temperature-responsive shape-memory polymer (SMP) elements with self-bending features. Experiments are conducted to reveal how the speed of the 4D printer head can affect functionally graded prestrain regime, shape recovery and self-bending characteristics of the active elements. A 3D constitutive model, along with an in-house finite element (FE) method, is developed to replicate the shape recovery and self-bending of SMP beams 4D-printed at different speeds. Furthermore, a simple approach of prestrain modeling is introduced into the commercial FE software package to simulate material tailoring and self-bending mechanism. The accuracy of the straightforward FE approach is validated against experimental observations and computational results from the in-house FE MATLAB-based code. Two periodic architected temperature-sensitive metastructures with adaptive dynamical characteristics are proposed to use bandgap engineering to forbid specific frequencies from propagating through the material. The developed computational tool is finally implemented to numerically examine how bandgap size and frequency range can be controlled and broadened. It is found out that the size and frequency range of the bandgaps are linked to changes in the geometry of self-bending elements printed at different speeds. This research is likely to advance the state-of-the-art 4D printing and unlock potentials in the design of functional metastructures for a broad range of applications in acoustic and structural engineering, including sound wave filters and waveguides.

High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle

Beta (β)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units were classified as excitatory and inhibitory cells. We find that γ-oscillations in human and β-oscillations in monkey are characterized by a strong implication of inhibitory neurons, both in terms of their firing rate and their phasic firing with the oscillation cycle. The β- and γ-waves systematically propagate across the array, with similar velocities, during both wake and sleep. However, only in slow-wave sleep (SWS) β- and γ-oscillations are associated with highly coherent and functional interactions across several millimeters of the neocortex. This interaction is specifically pronounced between inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of β- and γ-oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain. The highest oscillation coherence found during SWS suggests that fast oscillations implement a highly coherent reactivation of wake patterns that may support memory consolidation during SWS.

Neural circuits for peristaltic wave propagation in crawling Drosophila larvae: analysis and modeling

Drosophila larvae crawl by peristaltic waves of muscle contractions, which propagate along the animal body and involve the simultaneous contraction of the left and right side of each segment. Coordinated propagation of contraction does not require sensory input, suggesting that movement is generated by a central pattern generator (CPG). We characterized crawling behavior of newly hatched Drosophila larvae by quantifying timing and duration of segmental boundary contractions. We developed a CPG network model that recapitulates these patterns based on segmentally repeated units of excitatory and inhibitory (EI) neuronal populations coupled with immediate neighboring segments. A single network with symmetric coupling between neighboring segments succeeded in generating both forward and backward propagation of activity. The CPG network was robust to changes in amplitude and variability of connectivity strength. Introducing sensory feedback via "stretch-sensitive" neurons improved wave propagation properties such as speed of propagation and segmental contraction duration as observed experimentally. Sensory feedback also restored propagating activity patterns when an inappropriately tuned CPG network failed to generate waves. Finally, in a two-sided CPG model we demonstrated that two types of connectivity could synchronize the activity of two independent networks: connections from excitatory neurons on one side to excitatory contralateral neurons (E to E), and connections from inhibitory neurons on one side to excitatory contralateral neurons (I to E). To our knowledge, such I to E connectivity has not yet been found in any experimental system; however, it provides the most robust mechanism to synchronize activity between contralateral CPGs in our model. Our model provides a general framework for studying the conditions under which a single locally coupled network generates bilaterally synchronized and longitudinally propagating waves in either direction.

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.

Wave Propagation of Porous Nanoshells

This study aims at investigating the wave propagation of porous nanoshells. The Bi-Helmholtz non-local strain gradient theory is employed in conjunction with a higher-order shear deformation shell theory, in order to include the size-dependent effects. The nanoshells are made of a porous functionally graded material (P-FGM), whose properties vary continuously along the thickness direction. A variational approach is here applied to handle the governing equations of the problem, which are solved analytically to compute the wave frequencies and phase velocities as function of the wave numbers. The sensitivity of the wave response is analyzed for a varying porosity volume fraction, material properties, non-local parameters, strain gradient length scales, temperature, humidity, and wave numbers. Based on the results, it is verified that the size-dependence of the response is almost the same to the one of plates, beams and tubes.

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Traditionally, astrocytes have been considered to couple via gap-junctions into a syncytium with only rudimentary spatial organization. However, this view is challenged by growing experimental evidence that astrocytes organize as a proper gap-junction mediated network with more complex region-dependent properties. On the other hand, the propagation range of intercellular calcium waves (ICW) within astrocyte populations is as well highly variable, depending on the brain region considered. This suggests that the variability of the topology of gap-junction couplings could play a role in the variability of the ICW propagation range. Since this hypothesis is very difficult to investigate with current experimental approaches, we explore it here using a biophysically realistic model of three-dimensional astrocyte networks in which we varied the topology of the astrocyte network, while keeping intracellular properties and spatial cell distribution and density constant. Computer simulations of the model suggest that changing the topology of the network is indeed sufficient to reproduce the distinct ranges of ICW propagation reported experimentally. Unexpectedly, our simulations also predict that sparse connectivity and restriction of gap-junction couplings to short distances should favor propagation while long–distance or dense connectivity should impair it. Altogether, our results provide support to recent experimental findings that point toward a significant functional role of the organization of gap-junction couplings into proper astroglial networks. Dynamic control of this topology by neurons and signaling molecules could thus constitute a new type of regulation of neuron-glia and glia-glia interactions.

Applications of Piezoelectric Materials in Structural Health Monitoring and Repair: Selected Research Examples

The paper reviews the recent applications of piezoelectric materials in structural health monitoring and repair conducted by the authors. First, commonly used piezoelectric materials in structural health monitoring and structure repair are introduced. The analysis of plain piezoelectric sensors and actuators and interdigital transducer and their applications in beam, plate and pipe structures for damage detection are reviewed in detail. Second, an overview is presented on the recent advances in the applications of piezoelectric materials in structural repair. In addition, the basic principle and the current development of the technique are examined.

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric-a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

Functional Genetic Screen to Identify Interneurons Governing Behaviorally Distinct Aspects of Drosophila Larval Motor Programs

Drosophila larval crawling is an attractive system to study rhythmic motor output at the level of animal behavior. Larval crawling consists of waves of muscle contractions generating forward or reverse locomotion. In addition, larvae undergo additional behaviors, including head casts, turning, and feeding. It is likely that some neurons (e.g., motor neurons) are used in all these behaviors, but the identity (or even existence) of neurons dedicated to specific aspects of behavior is unclear. To identify neurons that regulate specific aspects of larval locomotion, we performed a genetic screen to identify neurons that, when activated, could elicit distinct motor programs. We used 165 Janelia CRM-Gal4 lines—chosen for sparse neuronal expression—to ectopically express the warmth-inducible neuronal activator TrpA1, and screened for locomotor defects. The primary screen measured forward locomotion velocity, and we identified 63 lines that had locomotion velocities significantly slower than controls following TrpA1 activation (28°). A secondary screen was performed on these lines, revealing multiple discrete behavioral phenotypes, including slow forward locomotion, excessive reverse locomotion, excessive turning, excessive feeding, immobile, rigid paralysis, and delayed paralysis. While many of the Gal4 lines had motor, sensory, or muscle expression that may account for some or all of the phenotype, some lines showed specific expression in a sparse pattern of interneurons. Our results show that distinct motor programs utilize distinct subsets of interneurons, and provide an entry point for characterizing interneurons governing different elements of the larval motor program.

Rapid, parallel path planning by propagating wavefronts of spiking neural activity

Efficient path planning and navigation is critical for animals, robotics, logistics and transportation. We study a model in which spatial navigation problems can rapidly be solved in the brain by parallel mental exploration of alternative routes using propagating waves of neural activity. A wave of spiking activity propagates through a hippocampus-like network, altering the synaptic connectivity. The resulting vector field of synaptic change then guides a simulated animal to the appropriate selected target locations. We demonstrate that the navigation problem can be solved using realistic, local synaptic plasticity rules during a single passage of a wavefront. Our model can find optimal solutions for competing possible targets or learn and navigate in multiple environments. The model provides a hypothesis on the possible computational mechanisms for optimal path planning in the brain, at the same time it is useful for neuromorphic implementations, where the parallelism of information processing proposed here can fully be harnessed in hardware.

Becoming Multicellular by Aggregation; The Morphogenesis of the Social Amoebae Dicyostelium discoideum

The organisation and form of most organisms is generated during theirembryonic development and involves precise spatial and temporal controlof cell division, cell death, cell differentiation and cell movement.Differential cell movement is a particularly important mechanism in thegeneration of form. Arguably the best understood mechanism of directedmovement is chemotaxis. Chemotaxis plays a major role in the starvationinduced multicellular development of the social amoebae Dictyostelium.Upon starvation up to 10(5) individual amoebae aggregate to form afruiting body. In this paper we review the evidence that the movement ofthe cells during all stages of Dictyostelium development is controlled bypropagating waves of cAMP which control the chemotactic movement ofthe cells. We analyse the complex interactions between cell-cell signallingresulting in cAMP waves of various geometries and cell movement whichresults in a redistribution of the signalling sources and therefore changes thegeometry of the waves. We proceed to show how the morphogenesis,including aggregation stream and mound formation, slug formation andmigration, of this relatively simple organism is beginning to be understoodat the level of rules for cell behaviour, which can be tested experimentallyand theoretically by model calculations.

Mechanics of Mineralized Collagen Fibrils upon Transient Loads

Collagen is a key structural protein in the human body, which undergoes mineralization during the formation of hard tissues. Earlier studies have described the mechanical behavior of bone at different scales, highlighting material features across hierarchical structures. Here we present a study that aims to understand the mechanical properties of mineralized collagen fibrils upon tensile/compressive transient loads, investigating how the kinetic energy propagates and it is dissipated at the molecular scale, thus filling a gap of knowledge in this area. These specific features are the mechanisms that nature has developed to passively dissipate stress and prevent structural failures. In addition to the mechanical properties of the mineralized fibrils, we observe distinct nanomechanical behaviors for the two regions (i.e., overlap and gap) of the D-period to highlight the effect of the mineralization. We notice decreasing trends for both wave speeds and Young's moduli over input velocity with a marked strengthening effect in the gap region due to the accumulation of the hydroxyapatite. In contrast, the dissipative behavior is not affected by either loading conditions or the mineral percentage, showing a stronger damping effect upon faster inputs compatible to the bone behavior at the macroscale. Our results offer insights into the dissipative behavior of mineralized collagen composites to design and characterize bioinspired composites for replacement devices (e.g., prostheses for sound transmission or conduction) or optimized structures able to bear transient loads, for example, impact, fatigue, in structural applications.

Wave Propagation and Energy Dissipation in Collagen Molecules

Collagen is the key protein of connective tissue (i.e., skin, tendons and ligaments, and cartilage, among others), accounting for 25-35% of the whole-body protein content and conferring mechanical stability. This protein is also a fundamental building block of bone because of its excellent mechanical properties together with carbonated hydroxyapatite minerals. Although the mechanical resilience and viscoelasticity have been studied both in vitro and in vivo from the molecular to tissue level, wave propagation properties and energy dissipation have not yet been deeply explored, in spite of being crucial to understanding the vibration dynamics of collagenous structures (e.g., eardrum, cochlear membranes) upon impulsive loads. By using a bottom-up atomistic modeling approach, here we study a collagen peptide under two distinct impulsive displacement loads, including longitudinal and transversal inputs. Using a one-dimensional string model as a model system, we investigate the roles of hydration and load direction on wave propagation along the collagen peptide and the related energy dissipation. We find that wave transmission and energy-dissipation strongly depend on the loading direction. Also, the hydrated collagen peptide can dissipate five times more energy than dehydrated one. Our work suggests a distinct role of collagen in term of wave transmission of different tissues such as tendon and eardrum. This study can step toward understanding the mechanical behavior of collagen upon transient loads, impact loading and fatigue, and designing biomimetic and bioinspired materials to replace specific native tissues such as the tympanic membrane.

Poro-elastic modeling of Syringomyelia - a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

Syringomyelia, fluid-filled cavities within the spinal cord, occurs frequently in association with a Chiari I malformation and produces some of its most severe neurological symptoms. The exact mechanism causing syringomyelia remains unknown. Since syringomyelia occurs frequently in association with obstructed cerebrospinal fluid (CSF) flow, it has been hypothesized that syrinx formation is mechanically driven. In this study we model the spinal cord tissue either as a poro-elastic medium or as a solid linear elastic medium, and simulate the propagation of pressure waves through an anatomically plausible 3D geometry, with boundary conditions based on in vivo CSF pressure measurements. Then various anatomic and tissue properties are modified, resulting in a total of 11 variations of the model that are compared. The results show that an open segment of the central canal and a stiff pia (relative to the cord) both increase the radial pressure gradients and enhance interstitial fluid flow in the central canal. The anterior median fissure, anisotropic permeability of the white matter, and Poisson ratio play minor roles.

Direct observation of impact propagation and absorption in dense colloidal monolayers

Single-particle characterization of the impact response has unveiled design principles to focus and control stress propagation in macroscopic granular crystalline arrays. We demonstrate that similar principles apply to aqueous monolayers of microparticles excited by localized mechanical pulses. By inducing extreme local deformation rates and tracking the motion of each particle with velocities that reach up to few meters per second, we reveal that a regime of elastic collisions, typically forbidden due to overdamping, becomes accessible. This provides insights on the stress propagation and energy absorption of dense suspensions upon fast deformation rates.

Dense colloidal suspensions can propagate and absorb large mechanical stresses, including impacts and shocks. The wave transport stems from the delicate interplay between the spatial arrangement of the structural units and solvent-mediated effects. For dynamic microscopic systems, elastic deformations of the colloids are usually disregarded due to the damping imposed by the surrounding fluid. Here, we study the propagation of localized mechanical pulses in aqueous monolayers of micron-sized particles of controlled microstructure. We generate extreme localized deformation rates by exciting a target particle via pulsed-laser ablation. In crystalline monolayers, stress propagation fronts take place, where fast-moving particles (V approximately a few meters per second) are aligned along the symmetry axes of the lattice. Conversely, more viscous solvents and disordered structures lead to faster and isotropic energy absorption. Our results demonstrate the accessibility of a regime where elastic collisions also become relevant for suspensions of microscopic particles, behaving as “billiard balls” in a liquid, in analogy with regular packings of macroscopic spheres. We furthermore quantify the scattering of an impact as a function of the local structural disorder.

A multiscale model of vascular function in chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) is caused by recurrent or unresolved pulmonary thromboemboli, leading to perfusion defects and increased arterial wave reflections. CTEPH treatment aims to reduce pulmonary arterial pressure and reestablish adequate lung perfusion, yet patients with distal lesions are inoperable by standard surgical intervention. Instead, these patients undergo balloon pulmonary angioplasty (BPA), a multisession, minimally invasive surgery that disrupts the thromboembolic material within the vessel lumen using a catheter balloon. However, there still lacks an integrative, holistic tool for identifying optimal target lesions for treatment. To address this insufficiency, we simulate CTEPH hemodynamics and BPA therapy using a multiscale fluid dynamics model. The large pulmonary arterial geometry is derived from a computed tomography (CT) image, whereas a fractal tree represents the small vessels. We model ring- and web-like lesions, common in CTEPH, and simulate normotensive conditions and four CTEPH disease scenarios; the latter includes both large artery lesions and vascular remodeling. BPA therapy is simulated by simultaneously reducing lesion severity in three locations. Our predictions mimic severe CTEPH, manifested by an increase in mean proximal pulmonary arterial pressure above 20 mmHg and prominent wave reflections. Both flow and pressure decrease in vessels distal to the lesions and increase in unobstructed vascular regions. We use the main pulmonary artery (MPA) pressure, a wave reflection index, and a measure of flow heterogeneity to select optimal target lesions for BPA. In summary, this study provides a multiscale, image-to-hemodynamics pipeline for BPA therapy planning for patients with inoperable CTEPH. NEW & NOTEWORTHY This article presents novel computational framework for predicting pulmonary hemodynamics in chronic thromboembolic pulmonary hypertension. The mathematical model is used to identify the optimal target lesions for balloon pulmonary angioplasty, combining simulated pulmonary artery pressure, wave intensity analysis, and a new quantitative metric of flow heterogeneity.

Detection of Defects in Reinforced Concrete Structures Using Ultrasonic Nondestructive Evaluation with Piezoceramic Transducers and the Time Reversal Method

Reinforced concrete is of vital importance in many civil and industrial structural applications. The effective bonding between steel and concrete is the core guarantee of the safe operation of the structures. Corrosion or other interface debonding in steel-concrete is a typical failure mode during the long service period of the structures, which can severely reduce the load-bearing capacity. The Non-destructive Evaluation technique has been applied to civil engineering structures in recent years. This paper investigates the evaluation of reinforced concrete structures that have interface defects, including the cross-sectional loss and cracks, by using the piezoceramic induced ultrasonic wave and time reversal method. Ultrasonic wave is used as actuating wave to obtain the signals with defect information. Time reversal method is applied to localize and characterize defect along the interface of the steel-concrete and to image the defect through the cross-sectional scanning. Experiments were conducted to perform Nondestructive Evaluation by using six reinforced concrete components with different levels of defects. The invisible damages were made by the cutting part of the steel and embedding a table tennis ball inside concrete structures. The results show that the time reversed method can locate and evaluate the defects along the steel reinforced concrete, and the obtained defect images at the cross-section of the concrete structure are accurate.

Peri-Elastodynamic Simulations of Guided Ultrasonic Waves in Plate-Like Structure with Surface Mounted PZT

Peridynamic based elastodynamic computation tool named Peri-elastodynamics is proposed herein to simulate the three-dimensional (3D) Lamb wave modes in materials for the first time. Peri-elastodynamics is a nonlocal meshless approach which is a scale-independent generalized technique to visualize the acoustic and ultrasonic waves in plate-like structure, micro-electro-mechanical systems (MEMS) and nanodevices for their respective characterization. In this article, the characteristics of the fundamental Lamb wave modes are simulated in a sample plate-like structure. Lamb wave modes are generated using a surface mounted piezoelectric (PZT) transducer which is actuated from the top surface. The proposed generalized Peri-elastodynamics method is not only capable of simulating two dimensional (2D) in plane wave under plane strain condition formulated previously but also capable of accurately simulating the out of plane Symmetric and Antisymmetric Lamb wave modes in plate like structures in 3D. For structural health monitoring (SHM) of plate-like structures and nondestructive evaluation (NDE) of MEMS devices, it is necessary to simulate the 3D wave-damage interaction scenarios and visualize the different wave features due to damages. Hence, in addition, to simulating the guided ultrasonic wave modes in pristine material, Lamb waves were also simulated in a damaged plate. The accuracy of the proposed technique is verified by comparing the modes generated in the plate and the mode shapes across the thickness of the plate with theoretical wave analysis.

Stochastic sensitivity analysis for timing and amplitude of pressure waves in the arterial system

In the field of computational hemodynamics, sensitivity quantification of pressure and flow wave dynamics has received little attention. This work presents a novel study of the sensitivity of pressure-wave timing and amplitude in the arterial system with respect to arterial stiffness. Arterial pressure and flow waves were simulated with a one-dimensional distributed wave propagation model for compliant arterial networks. Sensitivity analysis of this model was based on a generalized polynomial chaos expansion evaluated by a stochastic collocation method. First-order statistical sensitivity indices were formulated to assess the effect of arterial stiffening on timing and amplitude of the pressure wave and backward-propagating pressure wave in the ascending aorta, at the maximum pressure and inflection point in the systolic phase. Only the stiffness of aortic arteries was found to significantly influence timing and amplitude of the backward-propagating pressure wave, whereas other large arteries in the systemic tree showed marginal impact. Furthermore, the ascending aorta, aortic arch, thoracic aorta, and infrarenal abdominal aorta had the largest influence on amplitude, whereas only the thoracic aorta influenced timing. Our results showed that the non-intrusive polynomial chaos expansion is an efficient method to compute statistical sensitivity measures for wave propagation models. These sensitivities provide new knowledge in the relative importance of arterial stiffness at various locations in the arterial network. Moreover, they will significantly influence clinical data collection and effective composition of the arterial tree for in-silico clinical studies.

Structural Monitoring of Underground Structures in Multi-Layer Media by Dynamic Methods

The actual problem of structural monitoring and modeling of dynamic response from buried building is considered in the framework of arbitrary dynamic load. The results can be used for designing underground transport constructions, crossings, buried reservoirs and foundations. In existing methods, the system of sensors that register the response to a dynamic action does not allow for effective interpretation of the signal without understanding the dynamic features and resonance phenomena. The analytical and numerical solution of the problem of the dynamics of a buried object in a layered medium is considered. A multilayer half-space is a set of rigidly interconnected layers characterized by elastic properties. At a distance, an arbitrary dynamic load acts on the half-space, which causes oscillations in the embedded structure, and the sensor system registers the response. The problem of assessing the dynamic stress-strain state (DSSS) is solved using Fourier transforms with the principle of limiting absorption. As an example, the behavior of an embedded massive structure of an underground pedestrian crossing under the influence of a dynamic surface source on a multilayer medium is considered, as well as instrumental support of the sensor system. The solution in the form of stress, strain and displacement fields is obtained and compared with the experimental data. The frequency-dependent characteristics of the system are determined and the possibility of determining the DSSS by a shock pulse is shown.

A proof that multiple waves propagate in ensemble-averaged particulate materials

Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterize wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber. For this reason, there are many published studies on how to calculate a single effective wavenumber. Here, we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half-space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener-Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method.

Numerical Method of Characteristics for One-Dimensional Blood Flow

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

Role of structural anisotropy of biological tissues in poroelastic wave propagation

Ultrasound waves have a broad range of clinical applications as a non-destructive testing approach in imaging and in the diagnoses of medical conditions. Generally, biological tissues are modeled as an homogenized equivalent medium with an apparent density through which a single wave propagates. Only the first wave arriving at the ultrasound probe is used for the measurement of the speed of sound. However, the existence of a second wave in tissues such as cancellous bone has been reported and its existence is an unequivocal signature of Biot type poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as density, a fabric-dependent anisotropic poroelastic ultrasound (PEU) propagation theory was recently developed. Key to this development was the inclusion of the fabric tensor - a quantitative stereological measure of the degree of structural anisotropy of bone - into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of waves in several soft and hard tissues. It was found that collagen fibers in soft tissues and the mineralized matrix in hard tissues are responsible for the anisotropy of the solid tissue constituent through the fabric tensor in the model.