Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models

Nonlinear 3-D models with fluid-structure interactions (FSI) based on in vitro experiments are introduced and solved by ADINA to perform flow and stress/strain analysis for stenotic arteries with lipid cores. Navier-Stokes equations are used as the governing equations for the fluid. Hyperelastic Mooney-Rivlin models are used for both the arteries and lipid cores. Our results indicate that critical plaque stress/strain conditions are affected considerably by stenosis severity, eccentricity, lipid pool size, shape and position, plaque cap thickness, axial stretch, pressure, and fluid-structure interactions, and may be used for possible plaque rupture predictions.     

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

Changes in the mechanical environment of stenotic arteries during interaction with stents: computational assessment of parametric stent designs

Clinical studies have identified factors such as the stent design and the deployment technique that are one cause for the success or failure of angioplasty treatments. In addition, the success rate may also depend on the stenosis type. Hence, for a particular stenotic artery, the optimal intervention can only be identified by studying the influence of factors such as stent type, strut thickness, geometry of the stent cell, and stent-artery radial mismatch with the wall. We propose a methodology that allows a set of stent parameters to be varied, with the aim of evaluating the difference in the mechanical environment within the wall before and after angioplasty with stenting. Novel scalar quantities attempt to characterize the wall changes inform of the contact pressure caused by the stent struts, and the stresses within the individual components of the wall caused by the stent. These quantities are derived numerically and serve as indicators, which allow the determination of the correct size and type of the stent for each individual stenosis. In addition, the luminal change due to angioplasty may be computed as well. The methodology is demonstrated by using a full three-dimensional geometrical model of a postmortem specimen of a human iliac artery with a stenosis using imaging data. To describe the material behavior of the artery, we considered mechanical data of eight different vascular tissues, which formed the stenosis. The constitutive models for the tissue components capture the typical anisotropic, nonlinear and dissipative characteristics under supra-physiological loading conditions. Three-dimensional stent models were parametrized in such a way as to enable new designs to be generated simply with regard to variations in their geometric structure. For the three-dimensional stent-artery interaction we use a contact algorithm based on smooth contact surfaces of at least C-continuity, which prevents numerical problems known from standard facet-based contact algorithm. The proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures and stent geometries and materials, to help stent designers examine new stent designs "virtually," and to assist clinicians in choosing the most suitable stent for a particular stenosis.     

Conductance catheter measurements of lumen area of stenotic coronary arteries: theory and experiment

An injection of saline solution is required for the measurement of vessel lumen area using a conductance catheter. The injection of room temperature saline to displace blood in a vessel inevitably involves mass and heat transport and electric field conductance. The objective of the present study is to understand the accuracy of conductance method based on the phenomena associated with the saline injection into a stenotic blood vessel. Computational fluid dynamics were performed to simulate flow and its relation to transport and electric field in a stenotic artery for two different sized conductance catheters (0.9 and 0.35 mm diameter) over a range of occlusions [56-84% cross-sectional area (CSA) stenosis]. The results suggest that the performance of conductance catheter is dependent on catheter size and severity of stenosis more significantly for 0.9 mm than for 0.35 mm catheter. Specifically, the time of detection of 95% of injected saline solution at the detection electrodes was shown to range from 0.67 to 3.7 s and 0.82 to 0.94 s for 0.9 mm and 0.35 mm catheter, respectively. The results also suggest that the detection electrodes of conductance catheter should be placed outside of flow recirculation region distal to the stenosis to minimize the detection time. Finally, the simulations show that the accuracy in distal CSA measurements, however, is not significantly altered by whether the position of detection electrodes is inside or outside of recirculation zone (error was within 12% regardless of detection electrodes position). The results were experimentally validated for one lesion geometry and the simulation results are within 8% of actual measurements. The simulation of conductance catheter injection method may lead to further optimization of device and method for accurate sizing of diseased coronary arteries, which has clinical relevance to percutaneous intervention.     

Ventricular mechanics in diastole: material parameter sensitivity

Models of ventricular mechanics have been developed over the last 20 years to include finite deformation theory, anisotropic and inhomogeneous material properties and an accurate representation of ventricular geometry. As computer performance and the computational efficiency of the models improve, clinical application of these heart mechanics models is becoming feasible. One such application is to estimate myocardial material properties by adjusting the constitutive parameters to match wall deformation from MRI or ultrasound measurements, together with a measurement (or estimate) of ventricular pressure. Pigs are now the principal large animal model for these studies and in this paper we present the development of a new three-dimensional finite element model of the heart based on measurements of the geometry and the fibre and sheet orientations of pig hearts. The end-diastolic deformation of the model is computed using the "pole-zero" constitutive law which we have previously used to model the mechanics of passive myocardial tissue specimens. The sensitivities of end-diastolic fibre-sheet material strains and heart shape to changes in the material parameters are computed for the parameters of the pole-zero law in order to assess the utility of the models for inverse material property determination.     

The importance of assessing parameter sensitivity when using biophysical models: a case study using plethodontid salamanders

Landscapes are continually changing due to numerous assaults, including habitat alteration, anthropogenic disturbances, and climate change. Understanding how species will respond to these changes is of critical importance for conservation and management. Mechanistic models, such as biophysical models (BPMs), are an increasingly popular tool to predict how local population dynamics or species’ distributions may be altered in response to environmental and climate changes. By mechanistically modeling relationships between environmental conditions, physiology and behavior, it is possible to make accurate predictions about how species may respond. However, BPMs are often difficult to implement due to lack of appropriate, species-specific data that is biologically realistic or relevant. In this study, we present a BPM for the salamander Plethodon jordani and assess how adding more biological realism has potential to alter model predictions about annual energy budgets. Additionally, we conducted local and global sensitivity analyses to evaluate the importance of accurately specifying model parameter values and functional relationships. We found that the addition of biological realism resulted in greater model complexity as well as substantially different estimates of energy balance. Correct parameterization of biophysical models is also critical, as small changes in parameter values can result in disproportionately large changes in downstream model estimates. Our model highlights the overall importance of using ecologically relevant and specific data for input parameters, as well as careful assessment of parameter sensitivity. We encourage researchers to be aware of the data they are using to parameterize BPMs, and urge the collection of system-specific data that is relevant in spatial and temporal scale. We also recommend greater and more transparent use of sensitivity analyses to provide a better understanding of the model, as well as greater confidence in model predictions.     

Numerical sensitivity modeling for the detection of skin tumors by using tetrapolar probe

The measurement of electrical impedance of skin using surface electrodes permits the assessment of changes in local properties of the skin and can be used in the detection of tumors. The sensitivity of this technique depends mainly on the geometry of the probe and the size of the tumor. In this article, the impedance method was used to estimate the sensitivity of a tetrapolar probe in detecting small regions of increased conductivity in a stratified model of human skin. The impedance method was used to model the potential distribution using fasorial analysis to solve the node equations of the equivalent circuit. Interpolation was applied to reduce discretization error. The skin was modeled as a three-layer structure with different conductivity and permittivity obtained from the literature. A tumor was modeled as a small volume with admittivity four times higher than the normal tissue. Sensitivity calculation was made as a function of electrode diameter and separation, tumor size, and excitation frequency. The simulations indicated that by inserting a one square millimeter tumor in the epidermis, the load impedance to the current source varies about 1% while the transfer impedance varied 8%. The sensitivity also increases nonlinearly with increasing tumor area and thickness. Additionally, it was found that the sensitivity of the transfer impedance has a maximum value when the electrodes are separated by 1.8 mm. The results show that transfer impedance measurements of the skin may detect small skin tumors with a reasonable sensitivity by using an appropriate tetrapolar probe.     

Numerical sensitivity modeling for the detection of skin tumors by using tetrapolar probe

The measurement of electrical impedance of skin using surface electrodes permits the assessment of changes in local properties of the skin and can be used in the detection of tumors. The sensitivity of this technique depends mainly on the geometry of the probe and the size of the tumor. In this article, the impedance method was used to estimate the sensitivity of a tetrapolar probe in detecting small regions of increased conductivity in a stratified model of human skin. The impedance method was used to model the potential distribution using fasorial analysis to solve the node equations of the equivalent circuit. Interpolation was applied to reduce discretization error. The skin was modeled as a three-layer structure with different conductivity and permittivity obtained from the literature. A tumor was modeled as a small volume with admittivity four times higher than the normal tissue. Sensitivity calculation was made as a function of electrode diameter and separation, tumor size, and excitation frequency. The simulations indicated that by inserting a one square millimeter tumor in the epidermis, the load impedance to the current source varies about 1% while the transfer impedance varied 8%. The sensitivity also increases nonlinearly with increasing tumor area and thickness. Additionally, it was found that the sensitivity of the transfer impedance has a maximum value when the electrodes are separated by 1.8?mm. The results show that transfer impedance measurements of the skin may detect small skin tumors with a reasonable sensitivity by using an appropriate tetrapolar probe.     

Interaction of cardiotoxins with membranes: a molecular modeling study

Incorporation of beta-sheet proteins into membrane is studied theoretically for the first time, and the results are validated by the direct experimental data. Using Monte Carlo simulations with implicit membrane, we explore spatial structure, energetics, polarity, and mode of insertion of two cardiotoxins with different membrane-destabilizing activity. Both proteins, classified as P- and S-type cardiotoxins, are found to retain the overall "three-finger" fold interacting with membrane core and lipid/water interface by the tips of the "fingers" (loops). The insertion critically depends upon the structure, hydrophobicity, and electrostatics of certain regions. The simulations reveal apparently distinct binding modes for S- and P-type cardiotoxins via the first loop or through all three loops, respectively. This rationalizes an earlier empirical classification of cardiotoxins into S- and P-type, and provides a basis for the analysis of experimental data on their membrane affinities. Accomplished with our previous simulations of membrane alpha-helices, the computational method may be used to study partitioning of proteins with diverse folds into lipid bilayers.     

The importance of blood rheology in patient-specific computational fluid dynamics simulation of stenotic carotid arteries

Biomechanics and Modeling in Mechanobiology - The initiation and progression of atherosclerosis, which is the main cause of cardiovascular diseases, correlate with local haemodynamic factors such...     

Comparative study of parameter sensitivity analyses of the TCR-activated Erk-MAPK signalling pathway

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.     

Agent-based modelling and parameter sensitivity analysis with a finite-element method for skin contraction

In this paper, we extend the model of wound healing by Boon et al. (J Biomech 49(8):1388–1401, 2016). In addition to explaining the model explicitly regarding every component, namely cells, signalling molecules and tissue bundles, we categorized fibroblasts as regular fibroblasts and myofibroblasts. We do so since it is widely documented that myofibroblasts play a significant role during wound healing and skin contraction and that they are the main phenotype of cells that is responsible for the permanent deformations. Furthermore, we carried out some sensitivity tests of the model by modifying certain parameter values, and we observe that the model shows some consistency with several biological phenomena. Using Monte Carlo simulations, we found that there is a significant strong positive correlation between the final wound area and the minimal wound area. The high correlation between the wound area after 4 days and the final/minimal wound area makes it possible for physicians to predict the most probable time evolution of the wound of the patient. However, the collagen density ratio at the time when the wound area reaches its equilibrium and minimum, cannot indicate the degree of wound contractions, whereas at the 4th day post-wounding, when the collagen is accumulating from null, there is a strong negative correlation between the area and the collagen density ratio. Further, under the circumstances that we modelled, the probability that patients will end up with 5% contraction is about 0.627.

     

Temporal adaptability and the inverse relationship to sensitivity: a parameter identification model

Following a prolonged period of visual adaptation to a temporally modulated sinusoidal luminance pattern, the threshold contrast of a similar visual pattern is elevated. The adaptive elevation in threshold contrast is selective for spatial frequency, may saturate at low adaptor contrast, and increases as a function of the spatio-temporal frequency of the adapting signal. A model for signal extraction that is capable of explaining these threshold contrast effects of adaptation is proposed. Contrast adaptation in the model is explained by the identification of the parameters of an environmental model: the autocorrelation function of the visualized signal. The proposed model predicts that the adaptability of threshold contrast is governed by unpredicted signal variations present in the visual signal, and thus represents an internal adjustment by the visual system that takes into account these unpredicted signal variations given the additional possibility for signal corruption by additive noise.     

Calculations of protein volumes: sensitivity analysis and parameter database

MOTIVATION: The precise sizes of protein atoms in terms of occupied packing volume are of great importance. We have previously presented standard volumes for protein residues based on calculations with Voronoi-like polyhedra. To understand the applicability and limitations of our set, we investigated, in detail, the sensitivity of the volume calculations to a number of factors: (i) the van der Waals radii set, (ii) the criteria for including buried atoms in the calculations or atom selection, (iii) the method of positioning the dividing plane in polyhedra construction, and (iv) the set of structures used in the averaging. RESULTS: We find that different radii sets have only moderate affects to the distribution and mean of volumes. Atom selection and dividing plane methods cause larger changes in protein atoms volumes. More significantly, we show how the variation in volumes appears to be clearly related to the quality of the structures analyzed, with higher quality structures giving consistently smaller average volumes with less variance.     

A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk

Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller components, whose parameters can then be estimated independently. This leads to significant improvements in computational efficiency. We present our approach in the context of Hybrid Functional Petri Net modeling and evolutionary search for parameter value estimation. However, the approach can be easily extended to other modeling frameworks and is independent of the search method used. We have tested our approach on a detailed model of the Akt and MAPK pathways with two known and one hypothesized crosstalk mechanisms. The entire model contains 84 unknown parameters. Our simulation results exhibit good correlation with experimental data, and they yield positive evidence in support of the hypothesized crosstalk between the two pathways.     

Response to oxidative stress as a welfare parameter in swine

In pigs, the genetic selection for lean, large muscle blocks and fast growth has been linked to an increased prevalence of metabolic diseases such as porcine stress syndrome and mulberry heart disease. These diseases are associated with cardiovascular inadequacy, which may lead to oxidative stress. In the present study, reactive oxygen metabolites (ROMs) and the anti-oxidant power (OXY) in sera of different swine groups were investigated. The following groups were selected (each around 80 kg body weight): wild boars (WB), Cinta Senese (CS), and Landrace x Large White (LxLW), the latter as both specific pathogen-free (SPF) and intensively farmed animals. In addition, a group of LxLW agonic sows (AS) was also investigated; this group is known to be under oxidative stress. Two colorimetric micro-methods were used to measure ROMs and OXY; ROMs were expressed as mM H(2)O(2) and OXY as microM HOCl neutralised. Between groups, average ROM and OXY values were found to be significantly different by one-way ANOVA (P < 0.001). ROM levels were lower in WB (13.41 +/- 1.85) and CS (19.27 +/- 1.68), and highest in LxLW (42.00 +/- 1.36). OXY values ranged from 260.10 +/- 22.13 (WB) to 396.90 +/- 9.83 (LxLW). Only one swine group (the CS group) showed a significant, positive correlation between ROM and OXY values. The AS group even showed a negative correlation between ROM and OXY values. These results imply satisfactory environmental coping occurred only within the CS group. Results are discussed in the light of animal welfare legislation, food safety and consumers' protection.