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The development of ultrafast dynamic contrast‐enhanced (UF‐DCE) MRI has occurred in tandem with fast MRI scan techniques, particularly view‐sharing and compressed sensing. Understanding the strengths of each technique and optimizing the relevant parameters are essential to their implementation. UF‐DCE MRI has now shifted from research protocols to becoming a part of clinical scan protocols for breast cancer. UF‐DCE MRI is expected to compensate for the low specificity of abbreviated MRI by adding kinetic information from the upslope of the time‐intensity curve. Because kinetic information from UF‐DCE MRI is obtained from the shape and timing of the initial upslope, various new kinetic parameters have been proposed. These parameters may be associated with receptor status or prognostic markers for breast cancer. In addition to the diagnosis of malignant lesions, more emphasis has been placed on predicting and evaluating treatment response because hyper‐vascularity is linked to the aggressiveness of breast cancers. In clinical practice, it is important to note that breast lesion images obtained from UF‐DCE MRI are slightly different from those obtained by conventional DCE MRI in terms of morphology. A major benefit of using UF‐DCE MRI is avoidance of the marked or moderate background parenchymal enhancement (BPE) that can obscure the target enhancing lesions. BPE is less prominent in the earlier phases of UF‐DCE MRI, which offers better lesion‐to‐noise contrast. The excellent contrast of early‐enhancing vessels provides a key to understanding the detailed pathological structure of tumor‐associated vessels. UF‐DCE MRI is normally accompanied by a large volume of image data for which automated/artificial intelligence‐based processing is expected to be useful. In this review, both the theoretical and practical aspects of UF‐DCE MRI are summarized. Evidence Level: 5 Technical Efficacy: Stage 2 [ABSTRACT FROM AUTHOR]

This paper addresses the probabilistic analysis of the deflection of a cantilever beam by means of a randomization of the classical governing fourth-order differential equation with null boundary conditions. The probabilistic study is based on the calculation of the first probability density function of the solution, which is a stochastic process, as well as the density function of further quantities of interest associated with this engineering problem such as the maximum slope and deflection at the free end of the cantilever beam, that are treated as random variables. In addition, the probability density function of the bending moment and the shear force will also be computed. The study takes extensive advantage of the so called Random Variable Transformation method, also known as Probability Transformation Method, that allows us to fully unify the probabilistic analysis in three relevant cases commonly studied in the deterministic setting. All the theoretical findings are illustrated via detailed numerical examples corresponding to each one of the three scenarios. [ABSTRACT FROM AUTHOR]