Sequences with ultrashort echo times enable new applications of MRI, including bone, tendon, ligament, and dental imaging. In this article, a sequence is presented that achieves the shortest possible encoding time for each k-space point, limited by pulse length, hardware switching times, and gradient performance of the scanner. In pointwise encoding time reduction with radial acquisition (PETRA), outer k-space is filled with radial half-projections, whereas the centre is measured single point- In MR experiments, the transversal magnetization decays with T * 2 . Standard MR sequences offer echo times (TEs) in the range of a few milliseconds for spin-echo sequences and down to 1 ms for gradient-echo sequences. Signals arising from tissues with a very short T 2 , well below 1 ms, are therefore not visible using standard sequences, as the signal has already decayed by the time of acquisition. In the image, these tissues appear dark, similar to air cavities or noise. A short T 2 can usually be found in tissue with strong couplings of solid materials like teeth, ligaments, tendons, and bones in the human body.Many regions of the human body have already been investigated with ultrashort echo time sequences. Clinical applications of sequences with ultrashort TE are used in orthopedics, dental imaging, and many other special applications. Studies not only of the knee (1), Achilles

X-ray attenuation measurements are widely used in medical and industrial applications. The usual results are one-to three-dimensional representations of the attenuation coefficient ͑r͒. In this paper, we present the Z projection algorithm for obtaining the density ͑r͒ and atomic number Z(r) with an energy-resolving x-ray method. As input data the algorithm uses at least two measurements 1 , 2 ,... with different spectral weightings of the source spectrum S(E) and/or detector sensitivity D(E). Analytically, is a function of 1 Ϫc 2 , cϭconst, and Z is a function of 1 / 2. The full numerical treatment yields (1 , 2) and Z(1 , 2) with S(E) and D(E) as commutative parametric functions. We tested the method with dual-energy computed tomography measurements of an organic sample and a set of chemical solutions with predefined and Z. The resulting images show and Z as complementary information: The density reflects the morphology of the objects, whereas the atomic number Zϭnumber of electrons/atom describes the material distribution. For our experimental setup we obtain an absolute precision of 0.1 for Z and 20 mg/cm 3 for. The Z projection can potentially lead to these classes of quantitative information for various scientific, industrial, and medical applications.

No abstract