scholarly journals Nonparametric Estimation of Time-Variant Parametric Models with Application to Cross-Sectional Data

2017 ◽  
Vol 47 (2) ◽  
pp. 197-220
Author(s):  
Mohammed Chowdhury
Keyword(s):  
Nonparametric Estimation ◽  
Parametric Models ◽  
Cross Sectional ◽  
Estimation Of Time

Estimation from cross-sectional data under a semiparametric truncation model

Biometrika ◽  
2020 ◽  
Vol 107 (2) ◽  
pp. 449-465
Author(s):  
C Heuchenne ◽  
J De Uña-Álvarez ◽  
G Laurent
Keyword(s):  
Mean Squared Error ◽  
Disease Onset ◽  
Lifetime Distribution ◽  
Parametric Models ◽  
Parametric Family ◽  
Cross Sectional ◽  
Right Censored Data ◽  
Lifetime Distributions ◽  
Likelihood Approach ◽  
Event Times

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang’s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer’s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.

Motion-Based Shape Deformation of Solid Models

2007 ◽  
Author(s):  
Nier Wu ◽  
Horea T. Ilies¸
Keyword(s):  
Parametric Modeling ◽  
Parametric Models ◽  
Shape Deformation ◽  
Cross Sectional ◽  
New Approach ◽  
Geometric Invariants ◽  
Solid Models ◽  
Modeling Systems ◽  
Geometric Changes ◽  
Near Future

Mechanical designs undergo numerous geometric changes throughout the design process. Performing these changes relies, whenever possible, on the parametric models used to create the initial geometry. However, a number of open issues prevent the current parametric modeling systems to support many practical design situations, which, in turn, forces the geometry to evolve independently of the original parametric model. The fact that every parametric update can be expressed in terms of a sequence of shape deformations implies that the same geometric updates could be obtained, at least in principle, via shape deformation procedures that parameterize the deformation itself. In this paper we propose a new approach to create and edit solid models by introducing a geometric deformation procedure that relies on motion interpolation. We show that the proposed approach induces a parametrization of the deformation that allows direct control and editing of the deformation, is capable of preserving important geometric invariants such as constant cross-sectional properties of the deformed models, and maintains the ability to perform parametric optimization of the associated solid models. We conclude by discussing advantages and limitations of this approach as well as a number of important research directions that we will pursue in the near future.

Vortex formation and associated aneurysmogenic transverse rotational shear stress near the apex of wide-angle cerebral bifurcations

2021 ◽  
pp. 1-12
Author(s):  
Adel M. Malek ◽  
James E. Hippelheuser ◽  
Alexandra Lauric
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Vortex Formation ◽  
Parametric Models ◽  
Wide Angle ◽  
Cross Sectional ◽  
Bifurcation Angle ◽  
Aneurysm Formation ◽  
Narrow Angle ◽  
Wall Shear

OBJECTIVE Aneurysm formation preferentially occurs at the site of wide-angle cerebral arterial bifurcations, which were recently shown to have a high longitudinal positive wall shear stress (WSS) gradient that promotes aneurysm formation. The authors sought to explore the other components of the hemodynamic environment that are altered with increasing bifurcation angle in the apical region and the effects of these components on WSS patterns on the vessel wall that may modulate aneurysm genesis and progression. METHODS Parametric models of symmetrical and asymmetrical bifurcations were created with increasing bifurcation angles (45°–240°), and 3D rotational angiography models of 13 middle cerebral artery (MCA) bifurcations (7 aneurysmal, 6 controls) were analyzed using computational fluid dynamics. For aneurysmal bifurcations, the aneurysm was digitally removed to uncover hemodynamics at the apex. WSS vectors along cross-sectional planes distal to the bifurcation apex were decomposed as orthogonal projections to the cut plane into longitudinal and transverse (tangential to the cross-sectional plane) components. Transverse rotational WSS (TRWSS) and TRWSS gradients (TRWSSGs) were sampled and evaluated at the apex and immediately distal from the apex. RESULTS In parametric models, increased bifurcation angle was associated with transverse flow vortex formation with emergence of an associated apical high TRWSS with highly aneurysmogenic positive TRWSSGs. While TRWSS decayed rapidly away from the apex in narrow-angle bifurcations, it remained greatly elevated for many radii downstream in aneurysm-prone wider bifurcations. In asymmetrical bifurcations, TRWSS was higher on the aneurysm-prone daughter vessel associated with the wider angle. Patient-derived models with aneurysmal bifurcations had wider angles (149.33° ± 12.56° vs 98.17° ± 8.67°, p < 0.001), with significantly higher maximum TRWSS (1.37 ± 0.67 vs 0.48 ± 0.23 Pa, p = 0.01) and TRWSSG (1.78 ± 0.92 vs 0.76 ± 0.50 Pa/mm, p = 0.03) compared to control nonaneurysmal bifurcations. CONCLUSIONS Wider vascular bifurcations are associated with a novel and to the authors’ knowledge previously undescribed transverse component rotational wall shear stress associated with a positive (aneurysmogenic) spatial gradient. The resulting hemodynamic insult, demonstrated in both parametric models and patient-based anatomy, is noted to decay rapidly away from the protection of the medial pad in healthy narrow-angle bifurcations but remain elevated distally downstream of wide-angle aneurysm-prone bifurcations. This TRWSS serves as a new contribution to the hemodynamic environment favoring aneurysm formation and progression at wide cerebral bifurcations and may have clinical implications favoring interventions that reduce bifurcation angle.

Aneurysm presence at the anterior communicating artery bifurcation is associated with caliber tapering of the A1 segment

2021 ◽  
pp. 1-11
Author(s):  
Alexandra Lauric ◽  
Luke Silveira ◽  
Emal Lesha ◽  
Jeffrey M. Breton ◽  
Adel M. Malek
Keyword(s):  
Three Dimensional ◽  
Parametric Models ◽  
Anterior Communicating Artery ◽  
Predisposing Factor ◽  
Cross Sectional ◽  
Flow Acceleration ◽  
Significant Difference ◽  
Healthy Control ◽  
Mca Aneurysm

OBJECTIVE Vessel tapering results in blood flow acceleration at downstream bifurcations (firehose nozzle effect), induces hemodynamics predisposing to aneurysm initiation, and has been associated with middle cerebral artery (MCA) aneurysm presence and rupture status. The authors sought to determine if vessel caliber tapering is a generalizable predisposing factor by evaluating upstream A1 segment profiles in association with aneurysm presence in the anterior communicating artery (ACoA) complex, the most prevalent cerebral aneurysm location associated with a high rupture risk. METHODS Three-dimensional rotational angiographic studies were analyzed for 68 patients with ACoA aneurysms, 37 nonaneurysmal contralaterals, and 53 healthy bilateral controls (211 samples total). A1 segments were determined to be dominant, codominant, or nondominant based on flow and size. Equidistant cross-sectional orthogonal cuts were generated along the A1 centerline, and cross-sectional area (CSA) was evaluated proximally and distally, using intensity-invariant edge detection filtering. The relative tapering of the A1 segment was evaluated as the tapering ratio (distal/proximal CSA). Computational fluid dynamics was simulated on ACoA parametric models with and without tapering. RESULTS Aneurysms occurred predominantly on dominant (79%) and codominant (17%) A1 segments. A1 segments leading to unruptured ACoA aneurysms had significantly greater tapering compared to nonaneurysmal contralaterals (0.69 ± 0.13 vs 0.80 ± 0.17, p = 0.001) and healthy controls (0.69 ± 0.13 vs 0.83 ± 0.16, p < 0.001), regardless of dominance labeling. There was no statistically significant difference in tapering values between contralateral A1 and healthy A1 controls (0.80 ± 0.17 vs 0.83 ± 0.16, p = 0.56). Hemodynamically, A1 segment tapering induces high focal pressure, high wall shear stress, and high velocity at the ACoA bifurcation. CONCLUSIONS Aneurysmal, but not contralateral or healthy control, A1 segments demonstrated significant progressive vascular tapering, which is associated with aneurysmogenic hemodynamic conditions at the ACoA complex. Demonstration of the upstream tapering effect in the communicating ACoA segment is consistent with its prior detection in the noncommunicating MCA bifurcation, which together form more than 50% of intracranial aneurysms. The mechanistic characterization of this upstream vascular tapering phenomenon is warranted to understand its clinical relevance and devise potential therapeutic strategies.

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