Magnetic fields associated with a nuclear magnetic resonance medical imaging system

Measurements were made of magnetic and electric field levels in and around a nuclear magnetic resonance imaging system undergoing a clinical trial. Magnetic field levels ranged from 0.04 tesla (T) in the imaging volume down to about 0.0006 T at the end of the patient table. The peak radio-frequency magnetic field level was 15 amperes per meter (A/m) in the imaging volume, while the rms value was 4.6 A/m. The specific absorption rate resulting from the radio-frequency magnetic field was calculated to be no more than 0.017 watts per kilogram (W/kg). The radio-frequency electric field was detectable only within a few centimeters of the coil assembly, and does not significantly contribute to the specific absorption rate. These exposure levels were much lower than existing guidelines for clinical NMR procedures.     

On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set

LetT be a nonexpansive self-mapping of a closed convex subsetC of a real Hilbert space. In this paper we deal with the structure of the weak ω-limit set of iterates {T ⁿx}, establish conditions under which it is invariant underT, and show that {T ⁿx} converges weakly iffT has a fixed-point andT ⁿx-Tⁿ⁺¹x→0 weakly. Dedicated to the memory of my father Supported by NSF Grant MCS 76-08217.     

Orderly algorithms for generating restricted classes of graphs

Orderly algorithms for the generation of exhaustive lists of nonisomorphic graphs are discussed. The existence of orderly methods to generate the graphs with a given subgraph and without a given subgraph is established. This method can be used to list all the nonisomorphic subgraphs of a given graph, as well as to produce catalogs of Hamiltonian graphs, pancyclic graphs, degree-constrained graphs, and other classes. A generalization of this method is given that can be used to generate lists of graphs with given girth, planar graphs, k-colorable graphs, and k-connected graphs, for example. Finally, these observations are employed to generate restricted classes of digraphs, notably acyclic digraphs and poset digraphs. The generation of poset digraphs is shown to supply a practical orderly method for producing a catalog of lattices. Similar observations concerning vertex addition generation methods allow one to improve on existing methods for the generation of catalog of interval and circle graphs.     

Finding the convex hull of a simple polygon

It is well known that the convex hull of a set of n points in the plane can be found by an algorithm having worst-case complexity O(n log n). A short linear-time algorithm for finding the convex hull when the points form the (ordered) vertices of a simple (i.e., non-self-intersecting) polygon is given.     

Divergence of the Bethe-Salpeter wave function at the origin

We point out an error in the proof of Nishijima et al. that the Bethe-Salpeter wave function for composite particles, lying on Regge trajectories, is finite. We describe a simple counter-example drawn from non-relativistic quantum mechanics and cite others from field theory.     

Endocyclic vs exocyclic olefin formation from 4-piperidones via the wittig reaction

The reaction of 1-methyl-4-piperidone and 1-benzoyl-4-piperidone with triethyl phosphono-acetate in the presence of excess base yields both the endocyclic and exocyclic olefins. However, treatment of 1-methyl-4-piperidone with diethyl cyanomethylphosphonate, even in the presence of excess base, yielded only the exocyclic olefin. Factors affecting isomer distribution during the course of the reaction are presented. The isolation of an exocyclic tetrahydropyridine from the sodium borohydride reduction of the methiodide of 4-pyridylacetonitrile is reported.     

Quantitative pharmacokinetic analysis of DCE-MRI data without an arterial input function: a reference region model

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assess tumor perfusion, microvascular vessel wall permeability and extravascular-extracellular volume fraction. Analysis of DCE-MRI data is usually based on indicator dilution theory that requires knowledge of the concentration of the contrast agent in the blood plasma, the arterial input function (AIF). A method is presented that compares the tissues of interest (TOI) curve shape to that of a reference region (RR), thereby eliminating the need for direct AIF measurement. By assigning literature values for Ktrans (the blood perfusion-vessel permeability product) and v(e) (extravascular-extracellular volume fraction) in a reference tissue, it is possible to extract the Ktrans and v(e) values for a TOI without knowledge of the AIF. The operational RR equation for DCE-MRI analysis is derived, and its sensitivity to noise and incorrect assignment of the RR parameters is tested via simulations. The method is robust at noise levels of 10%, returning accurate (+/-20% in the worst case) and precise (+/-15% in the worst case) values. Errors in the TOI Ktrans and v(e) values scale approximately linearly with the errors in the assigned RR Ktrans and v(e) values. The methodology is then applied to a Lewis Lung Carcinoma mouse tumor model. A slowly enhancing TOI yielded Ktrans=0.039+/-0.002 min-1 and v(e)=0.46+/-0.01, while a rapidly enhancing region yielded Ktrans=0.35+/-0.05 min-1 and v(e)=0.31+/-0.01. Parametric Ktrans and v(e) mappings manifested a tumor periphery with elevated Ktrans (>0.30 min-1) and v(e) (>0.30) values. The main advantage of the RR approach is that it allows for quantitative assessment of tissue properties without having to obtain high temporal resolution images to characterize an AIF. This allows for acquiring images with higher spatial resolution and/or SNR, and therefore, increased ability to probe tissue heterogeneity.     

Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner

Acousto-optic sensing (AOS) is a dual-wave sensing technique based on the ultrasound modulation of diffuse light in a turbid medium. We experimentally demonstrate the feasibility of combining AOS and conventional ultrasound imaging by use of a commercially available pulsed-ultrasound scanner coupled with a photorefractive crystal-based optical interferometry system. Optically absorbing targets embedded in highly diffusive phantoms (mus'= 10 cm(-1)) are imaged through a thickness of 27 mm with millimeter resolution. The acousto-optic images are intrinsically coregistered with the ultrasound images.