Hydraulic fracturing has been widely applied to stimulate the natural gas and oil production from unconventional reservoirs. To optimize the design of hydraulic fracturing in this application, an accurate estimation of the initiation and propagation of hydraulic fractures is indispensable. However, it still remains challenging as a result of the complex stress state and geological conditions. On account of their ability to complete control some significant factors and efficient observation of fracture geometry, laboratory-scale hydraulic fracturing experiments have received abundant research attention in recent years. This paper presents a review of the state of the art of laboratory-scale hydraulic fracturing experiments, focusing on the scaling analysis, experimental setup, fracturing fluids, and sample preparation. A discussion of the directions for future research is also provided with the intention of stimulating the development of the experimental technique for investigating hydraulic fracturing.
Maximal intensity projection (MIP) is routinely used to view MRA and other volumetric angiographic data. The straightforward implementation of MIP is ray casting that traces a volumetric data set in a computationally expensive manner. This article reports a fast MIP algorithm using shear warp factorization and reduced resampling that drastically reduced the redundancy in the computations for projection, thereby speeding up MIP by more than 10 times. Maximum intensity projection (MIP) is the most widely used algorithm for displaying volumetric angiographic data in MRI and CT (1-6). A brute force method for implementing MIP is ray casting and searching for the maximal intensity in that ray (7). The computation cost consists of addressing the data storage and resampling data along a ray. Because addressing arithmetic has to be performed for each ray, the computation becomes expensive for the large datasets typically associated with high-resolution angiographic data. The shear warp factorization method has been developed to minimize the amount of addressing arithmetic required for ray casting in volume rendering (8 -11). Recently, this shear warp factorization has also been adapted to speed up projections in MIP based on nearest neighbor approximation (12). In this study, we developed the shear warp factorized MIP using linear interpolation, which is more accurate than the nearest neighbor approximation (13). We also introduced a reduced resampling method to further reduce the redundancy in computation. We evaluated our fast MIP algorithm on volumetric time of flight and contrast-enhanced magnetic resonance angiography (MRA) data. METHODS Ray Casting and Shear WarpFor reference, the ray casting method is illustrated in Fig. 1. The shear warp factorization method is illustrated in Fig. 2. The shear warp factorization method operates by factorizing the viewing transformation matrix into a 3D shear parallel to the data slices to form an intermediate but distorted projection image and then applying a 2D warp to form an undistorted final image (11). For affine viewing transformation matrix (M view ) concerned in this study, the shear warp factorization includes a permutation (represented by matrix P), a 3D shear (represented by matrix M shear ), and a 2D warp (represented by matrix M warp ): M view ϭ M warp M shear P. The permutation matrix P is associated with the choice of the principal viewing axis. The geometry specified by the viewing matrix M view determines the shear matrix M shear and the warp matrix M warp (only a 2D warp matrix is needed). The details for the calculation of M shear and M warp from a given M view can be found in Ref. 11 and are summarized in the Appendix.This shear warp factorization allows substantial reduction of computation cost, which we demonstrate here for the case of linear interpolation. The computation for trilinear resampling in ray casting (Fig. 1b) is:
A801drug manufacturers and the decision makers. This study reports the findings from a survey of pricing and reimbursement experts in Australia to gain insight into their attitude/opinions of RSAs from their own personal experience. Methods: Senior-level health economists and consultants were targeted. The survey included questions about responder's demographics, the number and type of RSAs they have personally been involved with, and their experience and opinions about RSAs. A general overview of RSAs is also provided to better contextualise the survey findings. Results: Ten experts participated on an anonymous basis. They in total have been involved in 403 submissions, and 56 RSAs of various types. Capped cost agreements were most frequently employed (> 70% of all RSAs). 'Hidden price' is also frequently agreed. Respondents generally had positive attitude towards RSA (mean of 3 using a 1-5 scale) mainly because it can potentially benefit timeline and address global pricing issues. Concerns were however raised about the fact that the 'risk' is entirely borne by the industry in many cases and RSA has now become an integral element in the PBAC's decision making process. ConClusions: RSA is generally well perceived among industry experts in Australia, whilst an increasing role of PBAC in defining clauses in the agreement is seen as a hurdle against productive involvement from the industry. The Australian model of RSA may offer a useful template for other jurisdictions.
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