We propose new approaches to ray tracing that greatly reduce the required number of operations while strictly preserving the geometrical correctness of the solution. A hierarchical "beam" structure serves as a proxy for a collection of rays. It is tested against a kd-tree representing the overall scene in order to discard from consideration the sub-set of the kd-tree (and hence the scene) that is guaranteed not to intersect with any possible ray inside the beam. This allows for all the rays inside the beam to start traversing the tree from some node deep inside thus eliminating unnecessary operations. The original beam can be further sub-divided, and we can either continue looking for new optimal entry points for the sub-beams, or we can decompose the beam into individual rays. This is a hierarchical process that can be adapted to the geometrical complexity of a particular view direction allowing for efficient geometric anti-aliasing. By amortizing the cost of partially traversing the tree for all the rays in a beam, up to an order of magnitude performance improvement can be achieved enabling interactivity for complex scenes on ordinary desktop machines.
A kinetic model of the citric acid cycle for calculating oxygen consumption from (13)C nuclear magnetic resonance (NMR) multiplet data has been developed. Measured oxygen consumption (MVO(2)) was compared with MVO(2) predicted by the model with (13)C NMR data obtained from rat hearts perfused with glucose and either [2-(13)C]acetate or [3-(13)C]pyruvate. The accuracy of MVO(2) measured from three subsets of NMR data was compared: glutamate C-4 and C-3 resonance areas; the doublet C4D34 (expressed as a fraction of C-4 area); and C-4 and C-3 areas plus several multiplets of C-2, C-3, and C-4. MVO(2) determined by set 2 (C4D34 only) gave the same degree of accuracy as set 3 (complete data); both were superior to set 1 (C-4 and C-3 areas). Analysis of the latter suffers from the correlation between citric acid cycle flux and exchange between alpha-ketoglutarate and glutamate, resulting in greater error in estimating MVO(2). Analysis of C4D34 is less influenced by correlation between parameters, and this single measurement provides the best opportunity for a noninvasive measurement of oxygen consumption.
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