Utility of magnetic resonance imaging-based finite element analysis for the biomechanical stress analysis of hemorrhagic and non-hemorrhagic carotid plaques

Background: Biomechanical stress analysis has been used for plaque vulnerability assessment. The presence of plaque hemorrhage (PH) is a feature of plaque vulnerability and is associated with thromboembolic ischemic events. The purpose of the present study was to use finite element analysis (FEA) to compare the stress profiles of hemorrhagic and non-hemorrhagic profiles. Methods and Results: Forty-five consecutive patients who had suffered a cerebrovascular ischemic event with an underlying carotid artery disease underwent high-resolution magnetic resonance imaging (MRI) of their symptomatic carotid artery in a 1.5-T MRI system. Axial images were manually segmented for various plaque components and used for FEA. Maximum critical stress (M-CstressSL) for each slice was determined. Within a plaque, the maximum M-CstressSL for each slice of a plaque was selected to represent the maximum critical stress of that plaque (M-CstressPL) and used to compare hemorrhagic and non-hemorrhagic plaques. A total of 62% of plaques had hemorrhage. It was observed that plaques with hemorrhage had significantly higher stress (M-CstressPL) than plaques without PH (median [interquartile range]: 315 kPa [247-434] vs. 200 kPa [171-282], P=0.003). Conclusions: Hemorrhagic plaques have higher biomechanical stresses than non-hemorrhagic plaques. MRI-based FEA seems to have the potential to assess plaque vulnerability.

Arterial luminal curvature and fibrous-cap thickness affect critical stress conditions within atherosclerotic plaque: An in vivo MRI-based 2D finite-element study

High mechanical stress in atherosclerotic plaques at vulnerable sites, called critical stress, contributes to plaque rupture. The site of minimum fibrous cap (FC) thickness (FCMIN) and plaque shoulder are well-documented vulnerable sites. The inherent weakness of the FC material at the thinnest point increases the stress, making it vulnerable, and it is the big curvature of the lumen contour over FC which may result in increased plaque stress. We aimed to assess critical stresses at FCMIN and the maximum lumen curvature over FC (LCMAX) and quantify the difference to see which vulnerable site had the highest critical stress and was, therefore, at highest risk of rupture. One hundred patients underwent high resolution carotid magnetic resonance (MR) imaging. We used 352 MR slices with delineated atherosclerotic components for the simulation study. Stresses at all the integral nodes along the lumen surface were calculated using the finite-element method. FCMIN and LCMAX were identified, and critical stresses at these sites were assessed and compared. Critical stress at FC MIN was significantly lower than that at LCMAX (median: 121.55 kPa; inter quartile range (IQR) = [60.70-180.32] kPa vs. 150.80 kPa; IQR = [91.39-235.75] kPa, p < 0.0001). If critical stress at FCMIN was only used, then the stress condition of 238 of 352 MR slices would be underestimated, while if the critical stress at LCMAX only was used, then 112 out of 352 would be underestimated. Stress analysis at FCMIN and LCMAX should be used for a refined mechanical risk assessment of atherosclerotic plaques, since material failure at either site may result in rupture.

Association between biomechanical structural stresses of atherosclerotic carotid plaques and subsequent ischaemic cerebrovascular events - A longitudinal in vivo magnetic resonance imaging-based finite element study

Background: High-resolution magnetic resonance (MR) imaging has been used for MR imaging-based structural stress analysis of atherosclerotic plaques. The biomechanical stress profile of stable plaques has been observed to differ from that of unstable plaques; however, the role that structural stresses play in determining plaque vulnerability remains speculative. Methods: A total of 61 patients with previous history of symptomatic carotid artery disease underwent carotid plaque MR imaging. Plaque components of the index artery such as fibrous tissue, lipid content and plaque haemorrhage (PH) were delineated and used for finite element analysis-based maximum structural stress (M-C Stress) quantification. These patients were followed up for 2 years. The clinical end point was occurrence of an ischaemic cerebrovascular event. The association of the time to the clinical end point with plaque morphology and M-C Stress was analysed. Results: During a median follow-up duration of 514 days, 20% of patients (n=12) experienced an ischaemic event in the territory of the index carotid artery. Cox regression analysis indicated that M-C Stress (hazard ratio (HR): 12.98 (95% confidence interval (CI): 1.32-26.67, pZ0.02), fibrous cap (FC) disruption (HR: 7.39 (95% CI: 1.61e33.82), p Z 0.009) and PH (HR: 5.85 (95% CI: 1.27e26.77), p Z 0.02) are associated with the development of subsequent cerebrovascular events. Plaques associated with future events had higher M-C Stress than those which had remained asymptomatic (median (interquartile range, IQR): 330 kPa (229e494) vs. 254 kPa (166-290), p Z0.04). Conclusions: High biomechanical structural stresses, in addition to FC rupture and PH, are associated with subsequent cerebrovascular events.

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.

A Doubly curved Quadrilateral finite-element for the analysis of laminated anisotropic thin shells of revoution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.

Correlation of carotid atheromatous plaque inflammation with biomechanical stress: Utility of USPIO enhanced MR imaging and finite element analysis

Objective: The aim of this study was to explore whether there is a relationship between the degree of MR-defined inflammation using ultra small super-paramagnetic iron oxide (USPIO) particles, and biomechanical stress using finite element analysis (FEA) techniques, in carotid atheromatous plaques. Methods and Results: 18 patients with angiographically proven carotid stenoses underwent multi-sequence MR imaging before and 36 h after USPIO infusion. T2 * weighted images were manually segmented into quadrants and the signal change in each quadrant normalised to adjacent muscle was calculated after USPIO administration. Plaque geometry was obtained from the rest of the multi-sequence dataset and used within a FEA model to predict maximal stress concentration within each slice. Subsequently, a new statistical model was developed to explicitly investigate the form of the relationship between biomechanical stress and signal change. The Spearman's rank correlation coefficient for USPIO enhanced signal change and maximal biomechanical stress was -0.60 (p = 0.009). Conclusions: There is an association between biomechanical stress and USPIO enhanced MR-defined inflammation within carotid atheroma, both known risk factors for plaque vulnerability. This underlines the complex interaction between physiological processes and biomechanical mechanisms in the development of carotid atheroma. However, this is preliminary data that will need validation in a larger cohort of patients.

Identifying vulnerable carotid plaques in vivo using high resolution magnetic resonance imaging-based finite element analysis

Object. Individuals with carotid atherosclerosis develop symptoms following rupture of vulnerable plaques. Biomechanical stresses within this plaque may increase vulnerability to rupture. In this report the authors describe the use of in vivo carotid plaque imaging and computational mechanics to document the magnitude and distribution of intrinsic plaque stresses. Methods. Ten (five symptomatic and five asymptomatic) individuals underwent plaque characterization magnetic resonance (MR) imaging. Plaque geometry and composition were determined by multisequence review. Intrinsic plaque stress profiles were generated from 3D meshes by using finite element computational analysis. Differences in principal (shear) stress between normal and diseased sections of the carotid artery and between symptomatic and asymptomatic plaques were noted. Results. There was a significant difference in peak principal stress between diseased and nondiseased segments of the artery (mean difference 537.65 kPa, p < 0.05). Symptomatic plaques had higher mean stresses than asymptomatic plaques (627.6 kPa compared with 370.2 kPa, p = 0.05), which were independent of luminal stenosis and plaque composition. Conclusions. Significant differences in plaque stress exist between plaques from symptomatic individuals and those from asymptomatic individuals. The MR imaging-based computational analysis may therefore be a useful aid to identification of vulnerable plaques in vivo.

Buoyant Jet Discharges into Finite Ambient Waters

The paper presents the results of an experimental study regarding the effect of the lateral dimension of the receiving water on the spreading, mixing, and temperature decay of a horizontal buoyant surface jet. The widths of the ambient water in the experiments have been 240, 120, 90 and 60 times the diameter of the jet nozzle. Based on the experimental data, correlations are carried out and empirical equations for prediction of jet width, thickness in vertical direction and longitudinal temperature decay are obtained. The available data of earlier investigators are included to obtain generalized equations for the spreading and temperature decay. Similarity of temperature profiles in the lateral and vertical directions is observed. The longitudinal temperature decay is found to vary inversely with distance in the flow direction and ¼th power of the densimetric Froude number.

On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars