Dynamic estimation of three-dimensional cerebrovascular deformation from rotational angiography

Purpose: The objective of this study is to investigate the feasibility of detecting and quantifying 3D cerebrovascular wall motion from a single 3D rotational x-ray angiography (3DRA) acquisition within a clinically acceptable time and computing from the estimated motion field for the further biomechanical modeling of the cerebrovascular wall. Methods: The whole motion cycle of the cerebral vasculature is modeled using a 4D B-spline transformation, which is estimated from a 4D to 2D + t image registration framework. The registration is performed by optimizing a single similarity metric between the entire 2D + t measured projection sequence and the corresponding forward projections of the deformed volume at their exact time instants. The joint use of two acceleration strategies, together with their implementation on graphics processing units, is also proposed so as to reach computation times close to clinical requirements. For further characterizing vessel wall properties, an approximation of the wall thickness changes is obtained through a strain calculation. Results: Evaluation on in silico and in vitro pulsating phantom aneurysms demonstrated an accurate estimation of wall motion curves. In general, the error was below 10% of the maximum pulsation, even in the situation when substantial inhomogeneous intensity pattern was present. Experiments on in vivo data provided realistic aneurysm and vessel wall motion estimates, whereas in regions where motion was neither visible nor anatomically possible, no motion was detected. The use of the acceleration strategies enabled completing the estimation process for one entire cycle in 5-10 min without degrading the overall performance. The strain map extracted from our motion estimation provided a realistic deformation measure of the vessel wall. Conclusions: The authors' technique has demonstrated that it can provide accurate and robust 4D estimates of cerebrovascular wall motion within a clinically acceptable time, although it has to be applied to a larger patient population prior to possible wide application to routine endovascular procedures. In particular, for the first time, this feasibility study has shown that in vivo cerebrovascular motion can be obtained intraprocedurally from a 3DRA acquisition. Results have also shown the potential of performing strain analysis using this imaging modality, thus making possible for the future modeling of biomechanical properties of the vascular wall.

Limit Cycles for a class of three dimensional polynomial differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

A three dimensional signed small ball inequality

"Vegeu el resum a l'inici del document del fitxer adjunt."

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

Three-dimensional morphological analysis of intracranial aneurysms: a fully automated method for aneurysm sac isolation and quantification

Morphological descriptors are practical and essential biomarkers for diagnosis andtreatment selection for intracranial aneurysm management according to the current guidelinesin use. Nevertheless, relatively little work has been dedicated to improve the three-dimensionalquanti cation of aneurysmal morphology, automate the analysis, and hence reduce the inherentintra- and inter-observer variability of manual analysis. In this paper we propose a methodologyfor the automated isolation and morphological quanti cation of saccular intracranial aneurysmsbased on a 3D representation of the vascular anatomy.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Multislice CT for assessing in-stent dimensions after left main coronary artery stenting: a comparison with three dimensional intravascular ultrasound

Objective: To evaluate the agreement between multislice CT (MSCT) and intravascular ultrasound (IVUS) to assess the in-stent lumen diameters and lumen areas of left main coronary artery (LMCA) stents. Design: Prospective, observational single centre study. Setting: A single tertiary referral centre. Patients: Consecutive patients with LMCA stenting excluding patients with atrial fibrillation and chronic renal failure. Interventions: MSCT and IVUS imaging at 912 months follow-up were performed for all patients. Main outcome measures: Agreement between MSCT and IVUS minimum luminal area (MLA) and minimum luminal diameter (MLD). A receiver operating characteristic (ROC) curve was plotted to find the MSCT cut-off point to diagnose binary restenosis equivalent to 6 mm2 by IVUS. Results: 52 patients were analysed. PassingBablok regression analysis obtained a β coefficient of 0.786 (0.586 to 1.071) for MLA and 1.250 (0.936 to 1.667) for MLD, ruling out proportional bias. The α coefficient was −3.588 (−8.686 to −0.178) for MLA and −1.713 (−3.583 to −0.257) for MLD, indicating an underestimation trend of MSCT. The ROC curve identified an MLA ≤4.7 mm2 as the best threshold to assess in-stent restenosis by MSCT. Conclusions: Agreement between MSCT and IVUS to assess in-stent MLA and MLD for LMCA stenting is good. An MLA of 4.7 mm2 by MSCT is the best threshold to assess binary restenosis. MSCT imaging can be considered in selected patients to assess LMCA in-stent restenosis