T1 mapping in cardiac MRI

Quantitative myocardial and blood T1 have recently achieved clinical utility in numerous pathologies, as they provide non-invasive tissue characterization with the potential to replace invasive biopsy. Native T1 time (no contrast agent), changes with myocardial extracellular water (edema, focal or diffuse fibrosis), fat, iron, and amyloid protein content. After contrast, the extracellular volume fraction (ECV) estimates the size of the extracellular space and identifies interstitial disease. Spatially resolved quantification of these biomarkers (so-called T1 mapping and ECV mapping) are steadily becoming diagnostic and prognostically useful tests for several heart muscle diseases, influencing clinical decision-making with a pending second consensus statement due mid-2017. This review outlines the physics involved in estimating T1 times and summarizes the disease-specific clinical and research impacts of T1 and ECV to date. We conclude by highlighting some of the remaining challenges such as their community-wide delivery, quality control, and standardization for clinical practice

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach numbe

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number

Robust reliability-based aerodynamic shape optimization

This paper presents a methodology for robust and reliable shape optimization of aerodynamic bodies under uncertainties. The mean value and standard deviation of the drag coefficient objective function with respect to flow related uncertain parameters are computed using sparse grid quadrature rules. On the other hand the lift coefficient inequality constraint is dealt with a probabilistic manner based on the reliability index approach by not allowing the probability of unacceptable performance to be larger than a predefined value. The sensitivity derivatives of the two statistical moments and the probability of unacceptable performance with respect to the shape controlling design parameters are computed using the adjoint approach and an augmented Lagrangian method is used to obtain the robust and reliable optimal shape. The methodology is applied to pure aerodynamic shape optimization, comparing the robust solutions with the single-point optimum. © 2015 Taylor & Francis Group, London