Finite element analysis of vulnerable atherosclerotic plaques: A comparison of mechanical stresses within carotid plaques of acute and recently symptomatic patients with carotid artery disease

Objectives: There is considerable evidence that patients with carotid artery stenosis treated immediately after the ischaemic cerebrovascular event have a better clinical outcome than those who have delayed treatment. Biomechanical assessment of carotid plaques using high-resolution MRI can help examine the relationship between the timing of carotid plaque symptomology and maximum simulated plaque stress concentration. Methods: Fifty patients underwent high-resolution multisequence in vivo MRI of their carotid arteries. Patients with acute symptoms (n=25) underwent MRI within 72 h of the onset of ischaemic cerebrovascular symptoms, whereas recently symptomatic patients (n=25) underwent MRI from 2 to 6 weeks after the onset of symptoms. Stress analysis was performed based on the geometry derived from in vivo MRI of the symptomatic carotid artery at the point of maximum stenosis. The peak stresses within the plaques of the two groups were compared. Results: Patient demographics were comparable for both groups. All the patients in the recently symptomatic group had severe carotid stenosis in contrast to patients with acute symptoms who had predominantly mild to moderate carotid stenosis. The simulated maximum stresses in patients with acute symptoms was significantly higher than in recently symptomatic patients (median (IQR): 313310 4 dynes/cm 2 (295 to 382) vs 2523104 dynes/cm 2 (236 to 311), p=0.02). Conclusions: Patients have extremely unstable, high-risk plaques, with high stresses, immediately after an acute cerebrovascular event, even at lower degrees of carotid stenoses. Biomechanical stress analysis may help us refine our risk-stratification criteria for the management of patients with carotid artery disease in future.

Study on tracheal collapsibility, compliance, and stress by considering nonlinear mechanical property of cartilage

Tracheal cartilage has been widely regarded as a linear elastic material either in experimental studies or in analytic and numerical models. However, it has been recently demonstrated that, like other fiber-oriented biological tissues, tracheal cartilage is a nonlinear material, which displays higher strength in compression than in extension. Considering the nonlinearity requires a more complex theoretical frame work and costs more to simulate. This study aims to quantify the deviation due to the simplified treatment of the tracheal cartilage as a linear material. It also evaluates the improved accuracy gained by considering the nonlinearity. Pig tracheal rings were used to exam the mechanical properties of cartilage and muscular membrane. By taking into account the asymmetric shape of tracheal cartilage, the collapse behavior of complete rings was simulated, and the compliance of airway and stress in the muscular membrane were discussed. The results obtained were compared with those assuming linear mechanical properties. The following results were found: (1) Models based on both types of material properties give a small difference in representing collapse behavior; (2) regarding compliance, the relative difference is big, ranging from 10 to 40% under negative pressure conditions; and (3) the difference in determining stress in the muscular membrane is small too: <5%. In conclusion, treating tracheal cartilage as a linear material will not cause big deviations in representing the collapse behavior, and mechanical stress in the muscular part, but it will induce a big deviation in predicting the compliance, particularly when the transmural pressure is lower than -0.5 kPa. The results obtained in this study may be useful in both understanding the collapse behavior of trachea and in evaluating the error induced by the simplification of treating the tracheal cartilage as a linear elastic material.

MRI-based measurement of carotid mechanical properties in asymptomatic patients

Arterial mechanical property may be a potential variable for risk stratification. Large artery and central arterial compliance have been shown not only to correlate well with overall cardiovascular outcome in large epidemiological studies [1, 2] but also to correlate with coronary atherosclerotic burden as measured by conventional angiography [3]. Until recently, real-time B-mode ultrasound combined with simultaneous blood pressure measurements have been used to assess large artery compliance [4]. These techniques have an excellent temporal resolution but are unable to provide adequate spatial resolution to determine changes in vessel area as opposed to diameter and make the assumption that the vessel is perfectly round. Attempts to use MR imaging to measure large artery compliance have been published previously [5]. However, they have not utilised simultaneous blood pressure measurements during sequence acquisition. We report a technique using regular and simultaneous blood pressure measurement during 2 dimensional phase contrast magnetic resonance imaging 2DPC-MRI to determine local carotid compliance.

Utility of USPIO-enhanced MR imaging to identify inflammation and the fibrous cap: A comparison of symptomatic and asymptomatic individuals

Background and purpose: Inflammation is a risk factor the vulnerable atheromatous plaque. This can be detected in vivo on high-resolution magnetic resonance (MR) imaging using a contrast agent, Sinerem™, an ultra-small super-paramagnetic iron oxide (USPIO). The aim of this study was to explore whether there is a difference in the degree of MR defined inflammation using USPIO particles, between symptomatic and asymptomatic carotid plaques. We report further on its T1 effect of enhancing the fibrous cap, which may allow dual contrast resolution of carotid atheroma. Methods: Twenty patients with carotid stenosis (10 symptomatic and 10 asymptomatic) underwent multi-sequence MR imaging before and 36 h post-USPIO infusion. Images were manually segmented into quadrants and signal change in each quadrant was calculated following USPIO administration. Mean signal change across all quadrants were compared between the two groups. Results: Symptomatic patients had significantly more quadrants with a signal drop than asymptomatic individuals (75% vs. 32%, p < 0.01). Asymptomatic plaques had more quadrants with signal enhancement than symptomatic ones (68% vs. 25%, p < 0.05); their mean signal change was also higher (46% vs. 15%, p < 0.01) and this appeared to correlate with a thicker fibrous cap on histology. Conclusions: Symptomatic patients had more quadrants with signal drop suggesting larger inflammatory infiltrates. Asymptomatic individuals showed significantly more enhancement possibly suggesting greater stability as a result of thicker fibrous caps. However, some asymptomatic plaques also had focal areas of signal drop, suggesting an occult macrophage burden. If validated by larger studies, USPIO may be a useful dual contrast agent able to improve risk stratification of patients with carotid stenosis and inform selection for intervention.

Carotid arterial plaque stress analysis using fluid-structure interactive simulation based on in-vivo magnetic resonance images of four patients

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress (WTS) is usually recognized as a primary trigger for the rupture of vulnerable plaque. The present study used the in-vivo high-resolution multi-spectral magnetic resonance imaging (MRI) for carotid arterial plaque morphology reconstruction. Image segmentation of different plaque components was based on the multi-spectral MRI and co-registered with different sequences for the patient. Stress analysis was performed on totally four subjects with different plaque burden by fluid-structure interaction (FSI) simulations. Wall shear stress distributions are highly related to the degree of stenosis, while the level of its magnitude is much lower than the WTS in the fibrous cap. WTS is higher in the luminal wall and lower at the outer wall, with the lowest stress at the lipid region. Local stress concentrations are well confined in the thinner fibrous cap region, and usually locating in the plaque shoulder; the introduction of relative stress variation during a cycle in the fibrous cap can be a potential indicator for plaque fatigue process in the thin fibrous cap. According to stress analysis of the four subjects, a risk assessment in terms of mechanical factors could be made, which may be helpful in clinical practice. However, more subjects with patient specific analysis are desirable for plaque-stability study.

Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap

Eleven carotid atherothrombotic plaque samples were harvested from patients. Three samples that were highly calcified were discarded, while eight yielded results. The elastic properties of the material were estimated by fitting the measured indentation response to finite element simulations. The methodology was refined and its accuracy quantified using a synthetic rubber. The neo-Hookean form of the material model gave a good fit to the measured response of the tissue. The inferred shear modulus μ was found to be in the range 7-100 kPa, with a median value of 11 kPa. A review of published materials data showed a wide range of material properties for human atherothrombotic tissue. The effects of anisotropy and time dependency in these published results were highlighted. The present measurements were comparable to the static radial compression tests of Lee et al, 1991 [Structure-dependent dynamic behaviour of fibrous caps from human atherosclerotic plaques. Circulation 83, 1764-1770].

Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm

Background: Increased biomechanical stresses within the abdominal aortic aneurysm (AAA) wall contribute to its rupture. Calcification and intraluminal thrombus can be commonly found in AAAs, but the relationship between calcification/intraluminal thrombus and AAA wall stress is not completely described. Methods: Patient-specific three-dimensional AAA geometries were reconstructed from computed tomographic images of 20 patients. Structural analysis was performed to calculate the wall stresses of the 20 AAA models and their altered models when calcification or intraluminal thrombus was not considered. A nonlinear large-strain finite element method was used to compute the wall stress distribution. The relationships between wall stresses and volumes of calcification and intraluminal thrombus were sought. Results: Maximum stress was not correlated with the percentage of calcification, and was negatively correlated with the percentage of intraluminal thrombus (r = -0.56; P = .011). Exclusion of calcification from analysis led to a significant decrease in maximum stress by a median of 14% (range, 2%-27%; P < .01). When intraluminal thrombus was eliminated, maximum stress increased significantly by a median of 24% (range, 5%-43%; P < .01). Conclusion: The presence of calcification increases AAA peak wall stress, suggesting that calcification decrease the biomechanical stability of AAA. In contrast, intraluminal thrombus reduces the maximum stress in AAA. Calcification and intraluminal thrombus should both be considered in the evaluation of wall stress for risk assessment of AAA rupture.

Simulation of the interaction between blood flow and atherosclerotic plaque

It has been well accepted that over 50% of cerebral ischemic events are the result of rupture of vulnerable carotid atheroma and subsequent thrombosis. Such strokes are potentially preventable by carotid interventions. Selection of patients for intervention is currently based on the severity of carotid luminal stenosis. It has been, however, widely accepted that luminal stenosis alone may not be an adequate predictor of risk. To evaluate the effects of degree of luminal stenosis and plaque morphology on plaque stability, we used a coupled nonlinear time-dependent model with flow-plaque interaction simulation to perform flow and stress/strain analysis for stenotic artery with a plaque. The Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the fluid. The Ogden strain energy function was used for both the fibrous cap and the lipid pool. The plaque Principal stresses and flow conditions were calculated for every case when varying the fibrous cap thickness from 0.1 to 2mm and the degree of luminal stenosis from 10% to 90%. Severe stenosis led to high flow velocities and high shear stresses, but a low or even negative pressure at the throat of the stenosis. Higher degree of stenosis and thinner fibrous cap led to larger plaque stresses, and a 50% decrease of fibrous cap thickness resulted in a 200% increase of maximum stress. This model suggests that fibrous cap thickness is critically related to plaque vulnerability and that, even within presence of moderate stenosis, may play an important role in the future risk stratification of those patients when identified in vivo using high resolution MR imaging.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Characterization of Ion-Exchange Fibers for Controlled Drug Delivery

Increasing attention has been focused on methods that deliver pharmacologically active compounds (e.g. drugs, peptides and proteins) in a controlled fashion, so that constant, sustained, site-specific or pulsatile action can be attained. Ion-exchange resins have been widely studied in medical and pharmaceutical applications, including controlled drug delivery, leading to commercialisation of some resin based formulations. Ion-exchangers provide an efficient means to adjust and control drug delivery, as the electrostatic interactions enable precise control of the ion-exchange process and, thus, a more uniform and accurate control of drug release compared to systems that are based only on physical interactions. Unlike the resins, only few studies have been reported on ion-exchange fibers in drug delivery. However, the ion-exchange fibers have many advantageous properties compared to the conventional ion-exchange resins, such as more efficient compound loading into and release from the ion-exchanger, easier incorporation of drug-sized compounds, enhanced control of the ion-exchange process, better mechanical, chemical and thermal stability, and good formulation properties, which make the fibers attractive materials for controlled drug delivery systems. In this study, the factors affecting the nature and strength of the binding/loading of drug-sized model compounds into the ion-exchange fibers was evaluated comprehensively and, moreover, the controllability of subsequent drug release/delivery from the fibers was assessed by modifying the conditions of external solutions. Also the feasibility of ion-exchange fibers for simultaneous delivery of two drugs in combination was studied by dual loading. Donnan theory and theoretical modelling were applied to gain mechanistic understanding on these factors. The experimental results imply that incorporation of model compounds into the ion-exchange fibers was attained mainly as a result of ionic bonding, with additional contribution of non-specific interactions. Increasing the ion-exchange capacity of the fiber or decreasing the valence of loaded compounds increased the molar loading, while more efficient release of the compounds was observed consistently at conditions where the valence or concentration of the extracting counter-ion was increased. Donnan theory was capable of fully interpreting the ion-exchange equilibria and the theoretical modelling supported precisely the experimental observations. The physico-chemical characteristics (lipophilicity, hydrogen bonding ability) of the model compounds and the framework of the fibrous ion-exchanger influenced the affinity of the drugs towards the fibers and may, thus, affect both drug loading and release. It was concluded that precisely controlled drug delivery may be tailored for each compound, in particularly, by choosing a suitable ion-exchange fiber and optimizing the delivery system to take into account the external conditions, also when delivering two drugs simultaneously.

Thermal Stability of Polystyrene Peroxide

It has been observed that poly(styrene peroxide) with a high molecular weight is thermally less stable than the same polymer with a low molecular weight. This has been explained as being due to the strain on the O-O bond due to the greater polymer chain length.

Stability of Fe3+ -VO defect pairs in polycrystalline Pb(Ti,Zr)O3

The intensity of the EPR signal with g = 5.985 arising from a ferric ion â oxygen vacancy defect pair (Fe3+ â VO) in PbTiO3, varies with the extent of PbO nonstoichiometry at constant Fe3+ content due to an increased oxygen vacancy concentration. In PZT solid solutions, the signal intensity decreases with an increase in Zr. A lower intensity is also noticed for Fe3+ â VO signals in PbZrO3. This behaviour is explained on the basis of PbO nonstoichiometry arising from independent Pb- and O-vacancies as well as the randomly distributed crystallographic shear (CS) plane defects. The contribution to PbO nonstoichiometry from CS planes is larger in high zirconium compositions of PZT.

Biophysical response of living cells to boron nitride nanoparticles: Uptake mechanism and bio-mechanical characterization

Boron nitride nanomaterials have attracted significant interest due to their superior chemical and physical properties. Despite these novel properties, investigation on the interaction between boron nitride nanoparticle (BN NP) and living systems has been limited. In this study, BN NP (100–250 nm) is assessed as a promising biomaterial for medical applications. The toxicity of BN NP is evaluated by assessing the cells behaviours both biologically (MTT assay, ROS detection etc.) and physically (atomic force microscopy). The uptake mechanism of BN NP is studied by analysing the alternations in cellular morphology based on cell imaging techniques. The results demonstrate in vitro cytocompatibility of BN NP with immense potential for use as an effective nanoparticle for various bio-medical applications.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.