scholarly journals Subject-specific multiscale modeling of aortic valve biomechanics

2021 ◽  
Author(s):  
G. Rossini ◽  
A. Caimi ◽  
A. Redaelli ◽  
E. Votta
Keyword(s):  
Aortic Valve ◽  
Boundary Conditions ◽  
Narrow Range ◽  
Radial Strain ◽  
Length Scale ◽  
Length Scales ◽  
Anatomical Features ◽  
Wide Range ◽  
Subject Specific ◽  
Cell Strains

AbstractA Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range ($$0.36-0.87$$ 0.36 - 0.87 ) with a strong correlation with the organ length-scale radial strain ($$R^{2}= 0.95$$ R 2 = 0.95 ); conversely, circumferential cell strains spanned a very narrow range ($$0.75-0.88$$ 0.75 - 0.88 ) showing no correlation with the circumferential strain at the organ level ($$R^{2}= 0.02$$ R 2 = 0.02 ). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

scholarly journals Derivation of Canopy Resistance in Turbulent Flow from First-Order Closure Models

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1782 ◽  
Author(s):  
Wei-Jie Wang ◽  
Wen-Qi Peng ◽  
Wen-Xin Huai ◽  
Gabriel Katul ◽  
Xiao-Bo Liu ◽  
...  
Keyword(s):  
Friction Factor ◽  
Free Surface Flows ◽  
Hydrodynamic Resistance ◽  
Small Scale ◽  
Length Scale ◽  
Length Scales ◽  
First Order ◽  
Closure Models ◽  
Wide Range ◽  
The Mean

Quantification of roughness effects on free surface flows is unquestionably necessary when describing water and material transport within ecosystems. The conventional hydrodynamic resistance formula empirically shows that the Darcy–Weisbach friction factor f~(r/hw)1/3 describes the energy loss of flowing water caused by small-scale roughness elements characterized by size r (<<hw), where hw is the water depth. When the roughness obstacle size becomes large (but <hw) as may be encountered in flow within canopies covering wetlands or river ecosystem, the f becomes far more complicated. The presence of a canopy introduces additional length scales above and beyond r/hw such as canopy height hv, arrangement density m, frontal element width D, and an adjustment length scale that varies with the canopy drag coefficient Cd. Linking those length scales to the friction factor f frames the scope of this work. By adopting a scaling analysis on the mean momentum equation and closing the turbulent stress with a first-order closure model, the mean velocity profile, its depth-integrated value defining the bulk velocity, as well as f can be determined. The work here showed that f varies with two dimensionless groups that depend on the canopy submergence depth and a canopy length scale. The relation between f and these two length scales was quantified using first-order closure models for a wide range of canopy and depth configurations that span much of the published experiments. Evaluation through experiments suggests that the proposed model can be imminently employed in eco-hydrology or eco-hydraulics when using the De Saint-Venant equations.

Numerical modeling of multiple length scales in thermal transport processes

2014 ◽  
Vol 24 (4) ◽  
pp. 781-796 ◽  
Author(s):  
Yogesh Jaluria
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Time Scales ◽  
Transport Processes ◽  
Thermal Processes ◽  
Length Scales ◽  
Content Type ◽  
Multiple Length Scales ◽  
Wide Range ◽  
Simulation Results

Purpose – Multiple length and time scales arise in a wide variety of practical and fundamental problems. It is important to obtain accurate and validated numerical simulation results, considering the different scales that exist, in order to predict, design and optimize the behavior of practical thermal processes and systems. The purpose of this paper is to present modeling at the different length scales and then addresses the question of coupling the different models to obtain the overall model for the system or process. Design/methodology/approach – Both numerical and experimental methods to obtain results at the different length scales, particularly at micro and nanoscales, are considered. Even though the paper focusses on length scales, multiple time scales lead to similar concerns and are also considered. The two circumstances considered in detail are multiple length scales in different domains and those in the same domain. These two cases have to be modeled quite differently in order to obtain a model for the overall process or system. The basic considerations involved in such a modeling are discussed. A wide range of thermal processes are considered and the methods that may be used are presented. The models employed must be validated and the accuracy of the simulation results established if the simulation results are to be used for prediction, control and design. Findings – Of particular interest are concerns like verification and validation, imposition of appropriate boundary conditions, and modeling of complex, multimode transport phenomena in multiple scales. Additional effects such as viscous dissipation, surface tension, buoyancy and rarefaction that could arise and complicate the modeling are discussed. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. Large variations in the geometry and coupled multiple regions are also discussed. Research limitations/implications – The paper is largely focussed on multiple-scale considerations in thermal processes. Both numerical modeling/simulation and experimentation are considered, with the latter being used for validation and physical insight. Practical implications – Several examples from materials processing, environmental flows and electronic systems, including data centers, are given to present the different techniques that may be used to achieve the desired level of accuracy and predictability. Originality/value – Present state of the art and future needs in this interesting and challenging area are discussed, providing the impetus for further work. Different methods for treating multiscale problems are presented.

Experiments on turbulence in a rotating fluid

1975 ◽  
Vol 68 (4) ◽  
pp. 639-672 ◽  
Author(s):  
A. Ibbetson ◽  
D. J. Tritton
Keyword(s):  
Rotation Rate ◽  
Rotation Axis ◽  
Turbulence Energy ◽  
Length Scale ◽  
Grid Turbulence ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Length Scales ◽  
Wide Range ◽  
Energy Sink

Experiments have been carried out to investigate the effect of rotation of the whole system on decaying turbulence, generally similar to grid turbulence, generated in air in an annular container on a rotating table. Measurements to determine the structure of the turbulence were made during its decay, mean quantities being determined by a mixture of time and ensemble averaging. Quantities measured (as functions of time after the turbulence generation) were turbulence intensities perpendicular to and parallel to the rotation axis, spectra of these two components with respect to a wavenumber perpendicular to the rotation axis, and some correlation coefficients, selected to detect differences in length scales perpendicular and parallel to the rotation axis. The intensity measurements were made for a wide range of rotation rates; the other measurements were made at a single rotation rate (selected to give a Rossby number varying during the decay from about 1 to small values) and, for comparison, at zero rotation. Subsidiary experiments were carried out to measure the spin-up time of the system, and to determine whether the turbulence produced any mean flow relative to the container.A principal result is that increasing the rotation rate produces faster decay of the turbulence; the nature of the additional energy sink is an important part of the interpretation. Other features of the results are as follows: the measurements with-outrotation can be satisfactorily related to wind-tunnel measurements; even with rotation, the ratio of the intensities in the two directions remains substantially constant; the normalized spectra for the rotating and the non-rotating cases show surprising similarity but do contain slight systematic differences, consistent with the length scales indicated by the correlations; rotation produces a large increase in the length scale parallel to the rotation axis and a smaller increase in that perpendicular to it; the turbulence produces no measurable mean flow.A model for the interpretation of the results is developed in terms of the action of inertial waves in carrying energy to the boundaries of the enclosure, where it is dissipated in viscous boundary layers. The model provides satisfactory explanations of the overall decay of the turbulence and of the decay of individual spectral components. Transfer of energy between wavenumbers plays a much less significant role in the dynamics of decay than in a non-rotating fluid. The relationship of the model to the interpretation of the length-scale difference in terms of the Taylor-Proudman theorem is discussed.The model implies that the overall dimensions of the system enter in an important way into the dynamics. This imposes a serious limitation on the application of the results to the geophysical situations at which experiments of this type are aimed.The paper includes some discussion of the possibility of energy transfer from the turbulence to a mean motion (the ‘vorticity expulsion’ hypothesis). It is possible, on the basis of the observations, to exclude this process as the additional turbulence energy sink. But this does not provide any evidence either for or against the hypothesis in the conditions for which it has been postulated.

Constraints on glacier bedrock roughness from spectral analysis of glacier forefields

2020 ◽  
Author(s):  
Jacob Woodard ◽  
Lucas Zoet ◽  
Neal Iverson ◽  
Christian Helanow
Keyword(s):  
Narrow Range ◽  
Ice Sheet ◽  
Length Scale ◽  
Fault Rocks ◽  
Length Scales ◽  
Aspect Ratios ◽  
Digital Elevation ◽  
Valley Glacier ◽  
Glacier Flow ◽  
Spectral Patterns

&lt;p&gt;The slip of hard bedded glaciers partly depends on the morphology of their beds. Thus, constraints on subglacial bedrock morphology are imperative for accurate forecasting of glacier flow rates. Digital elevation models (DEMs) from ten valley glacier and ice-sheet forefields were used to analyze the spectral patterns of recently deglaciated bedrock. Valley glacier DEM length scales are 0.1 m - 100 m, while ice sheet DEM length scales are 10 m -1000 m. We observe a higher spectral roughness and aspect ratio (i.e. bump height/wavelength) for valley glaciers than ice-sheet forefields. However, forefield aspect ratios span a narrow range and decrease with increasing length scale at a consistent rate despite a range of bedrock lithologies analyzed. This implies that bedrock shear strength (&amp;#964;) scales with length scale (L), as &amp;#964; ~ L&lt;sup&gt;-0.37&lt;/sup&gt;, closely matching the bulk strength scaling relation seen in fault rocks (Brodsky et al., 2016). These morphological constraints of forefields allow extrapolation of bedrock roughness beneath active glaciers that can help predict sliding rates.&lt;/p&gt;

scholarly journals A Workflow for Rapid Unbiased Quantification of Fibrillar Feature Alignment in Biological Images

2021 ◽  
Vol 3 ◽  
Author(s):  
Stefania Marcotti ◽  
Deandra Belo de Freitas ◽  
Lee D Troughton ◽  
Fiona N Kenny ◽  
Tanya J Shaw ◽  
...  
Keyword(s):  
Fourier Transforms ◽  
Image Feature ◽  
Global Alignment ◽  
Length Scale ◽  
Desktop Computer ◽  
Length Scales ◽  
Advantages And Disadvantages ◽  
Segmentation Methods ◽  
Wide Range ◽  
Feature Alignment

Measuring the organization of the cellular cytoskeleton and the surrounding extracellular matrix (ECM) is currently of wide interest as changes in both local and global alignment can highlight alterations in cellular functions and material properties of the extracellular environment. Different approaches have been developed to quantify these structures, typically based on fiber segmentation or on matrix representation and transformation of the image, each with its own advantages and disadvantages. Here we present AFT − Alignment by Fourier Transform, a workflow to quantify the alignment of fibrillar features in microscopy images exploiting 2D Fast Fourier Transforms (FFT). Using pre-existing datasets of cell and ECM images, we demonstrate our approach and compare and contrast this workflow with two other well-known ImageJ algorithms to quantify image feature alignment. These comparisons reveal that AFT has a number of advantages due to its grid-based FFT approach. 1) Flexibility in defining the window and neighborhood sizes allows for performing a parameter search to determine an optimal length scale to carry out alignment metrics. This approach can thus easily accommodate different image resolutions and biological systems. 2) The length scale of decay in alignment can be extracted by comparing neighborhood sizes, revealing the overall distance that features remain anisotropic. 3) The approach is ambivalent to the signal source, thus making it applicable for a wide range of imaging modalities and is dependent on fewer input parameters than segmentation methods. 4) Finally, compared to segmentation methods, this algorithm is computationally inexpensive, as high-resolution images can be evaluated in less than a second on a standard desktop computer. This makes it feasible to screen numerous experimental perturbations or examine large images over long length scales. Implementation is made available in both MATLAB and Python for wider accessibility, with example datasets for single images and batch processing. Additionally, we include an approach to automatically search parameters for optimum window and neighborhood sizes, as well as to measure the decay in alignment over progressively increasing length scales.

scholarly journals A Workflow for Rapid Unbiased Quantification of Fibrillar Feature Alignment in Biological Images

2021 ◽  
Author(s):  
Stefania Marcotti ◽  
Deandra Belo de Freitas ◽  
Lee D Troughton ◽  
Fiona N Kenny ◽  
Tanya J Shaw ◽  
...  
Keyword(s):  
Fourier Transforms ◽  
Image Feature ◽  
Global Alignment ◽  
Length Scale ◽  
Desktop Computer ◽  
Length Scales ◽  
Advantages And Disadvantages ◽  
Segmentation Methods ◽  
Wide Range ◽  
Feature Alignment

Measuring the organisation of the cellular cytoskeleton and the surrounding extracellular matrix (ECM) is currently of wide interest as changes in both local and global alignment can highlight alterations in cellular functions and material properties of the extracellular environment. Different approaches have been developed to quantify these structures, typically based on fibre segmentation or on matrix representation and transformation of the image, each with its own advantages and disadvantages. Here we present AFT −Alignment by Fourier Transform, a workflow to quantify the alignment of fibrillar features in microscopy images exploiting 2D Fast Fourier Transforms (FFT). Using pre- existing datasets of cell and ECM images, we demonstrate our approach and compare and contrast this workflow with two other well-known ImageJ algorithms to quantify image feature alignment. These comparisons reveal that AF T has a number of advantages due to its grid-based FFT approach. 1) Flexibility in defining the window and neighbourhood sizes allows for performing a parameter search to determine an optimal length scale to carry out alignment metrics. This approach can thus easily accommodate different image resolutions and biological systems. 2) The length scale of decay in alignment can be extracted by comparing neighbourhood sizes, revealing the overall distance that features remain anisotropic. 3) The approach is ambivalent to the signal source, thus making it applicable for a wide range of imaging modalities and is dependent on fewer input parameters than segmentation methods. 4) Finally, compared to segmentation methods, this algorithm is computationally inexpensive, as high-resolution images can be evaluated in less than a second on a standard desktop computer. This makes it feasible to screen numerous experimental perturbations or examine large images over long length scales. Implementation is made available in both MATLAB and Python for wider accessibility, with example datasets for single images and batch processing. Additionally, we include an approach to automatically search parameters for optimum window and neighbourhood sizes, as well as to measure the decay in alignment over progressively increasing length scales.

Fluctuations above a burning heterogeneous propellant

2007 ◽  
Vol 581 ◽  
pp. 1-32 ◽  
Author(s):  
L. MASSA ◽  
T. L. JACKSON ◽  
J. BUCKMASTER ◽  
F. NAJJAR
Keyword(s):  
Boundary Conditions ◽  
Characteristic Length ◽  
Mesh Point ◽  
Length Scale ◽  
Normal Velocity ◽  
Length Scales ◽  
Propellant Combustion ◽  
Temporal Correlations ◽  
Flow Domain ◽  
Relevant Length Scale

A numerical description of heterogeneous propellant combustion enables us to examine the spatial and temporal fluctuations in the flow field arising from the heterogeneity. Particular focus is placed on the fluctuations in a zone intermediate between the combustion field (where reaction is important) and the chamber flow domain, for these define boundary conditions for simulations of the turbulent chamber flow. The statistics of the temperature field and the normal velocity field are described, and characteristic length scales and time scales are identified. The length scales are small compared to any relevant length scale of the chamber flow, and so the boundary conditions for this flow at any mesh point are statistically independent of those at any other mesh point. But the temporal correlations at a fixed point are significant, and affect the nature of the chamber flow in a variety of ways. We describe the fluctuations in the head-end pressure that arise because of them, and contrast these results with those calculated using a white-noise assumption.

Length scale-dependent natural frequencies of piezoelectric microplates

2017 ◽  
Vol 24 (13) ◽  
pp. 2749-2759 ◽  
Author(s):  
M Jafari ◽  
E Jomehzadeh ◽  
M Rezaeizadeh
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Length Scale ◽  
Governing Equations ◽  
Classical Plate Theory ◽  
Wide Range ◽  
Piezoelectric Layers

The length-scale free vibration analysis of a rectangular microplate coupled with piezoelectric layers is presented. The modified couple stress theory is used to describe the size effect of the system. The governing equations of motion are obtained using Hamilton’s principle based on the classical plate theory. The transverse part of the electric potential for the piezoelectric layers is considered to satisfy the Maxwell’s equation and the electrical boundary conditions. A new procedure is introduced to decouple the governing equations and then an analytical Levy-type solution is obtained. The exact natural frequencies are established for a wide range of length scales, various plate dimensions, several piezoelectric layer thicknesses, and different boundary conditions. The results show that the effect of length scale parameter is decreased by the piezoelectric electrical field.

scholarly journals Size-adjusted aortic valve area: refining the definition of severe aortic stenosis

2020 ◽  
Author(s):  
Branka Vulesevic ◽  
Naozumi Kubota ◽  
Ian G Burwash ◽  
Claire Cimadevilla ◽  
Sarah Tubiana ◽  
...  
Keyword(s):  
Aortic Valve ◽  
Predictive Accuracy ◽  
Severe Aortic Stenosis ◽  
Aortic Valve Area ◽  
Obese Patients ◽  
Derivation Cohort ◽  
Wide Range ◽  
Definition Of ◽  
Diagnostic And Prognostic Value ◽  
Valve Area

Abstract Aims Severe aortic valve stenosis (AS) is defined by an aortic valve area (AVA) &lt;1 cm2 or an AVA indexed to body surface area (BSA) &lt;0.6 cm/m2, despite little evidence supporting the latter approach and important intrinsic limitations of BSA indexation. We hypothesized that AVA indexed to height (H) might be more applicable to a wide range of populations and body morphologies and might provide a better predictive accuracy. Methods and results In 1298 patients with degenerative AS and preserved ejection fraction from three different countries and continents (derivation cohort), we aimed to establish an AVA/H threshold that would be equivalent to 1.0 cm2 for defining severe AS. In a distinct prospective validation cohort of 395 patients, we compared the predictive accuracy of AVA/BSA and AVA/H. Correlations between AVA and AVA/BSA or AVA/H were excellent (all R2 &gt; 0.79) but greater with AVA/H. Regressions lines were markedly different in obese and non-obese patients with AVA/BSA (P &lt; 0.0001) but almost identical with AVA/H (P = 0.16). AVA/BSA values that corresponded to an AVA of 1.0 cm2 were markedly different in obese and non-obese patients (0.48 and 0.59 cm2/m2) but not with AVA/H (0.61 cm2/m for both). Agreement for the diagnosis of severe AS (AVA &lt; 1 cm2) was significantly higher with AVA/H than with AVA/BSA (P &lt; 0.05). Similar results were observed across the three countries. An AVA/H cut-off value of 0.6 cm2/m [HR = 8.2(5.6–12.1)] provided the best predictive value for the occurrence of AS-related events [absolute AVA of 1 cm2: HR = 7.3(5.0–10.7); AVA/BSA of 0.6 cm2/m2 HR = 6.7(4.4–10.0)]. Conclusion In a large multinational/multiracial cohort, AVA/H was better correlated with AVA than AVA/BSA and a cut-off value of 0.6 cm2/m provided a better diagnostic and prognostic value than 0.6 cm2/m2. Our results suggest that severe AS should be defined as an AVA &lt; 1 cm2 or an AVA/H &lt; 0.6 cm2/m rather than a BSA-indexed value of 0.6 cm2/m2.

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