On the area of the intersection of disks in the plane

Let C₁,…, C_n and C′₁,…, C′_n be two collections of equal disks in the plane, with centers c₁,…, c_n and c′₁,…, c′_n. According to a well-known conjecture of Klee and Wagon (1991), if |c_i − c_j| ≥ |c′_i − c′_j| for all i, j, then Area(∩_i C_i) ≤ Area(∩_i C′_i).

We prove this statement in the special case when there is a continuous contraction of {c₁,…, c_n} onto {c′₁,…, c′_n}.     

Would near-infrared fluorescence signals propagate through large human organs for clinical studies?

We predict the capacity of near-infrared fluorescent signals to propagate through human tissue for non-invasive medical imaging. This analysis employs experimental measurements of a biologically relevant local fluorochrome embedded in tissuelike media and predicts the equivalent photon counts expected from breast, lung, brain, and muscle as a function of diameter by use of an analytical solution of the diffusion equation that can take into account large arbitrary geometries. The findings address feasibility issues for clinical studies and are relevant to recent development of near-infrared fluorescent probes and molecular beacons for in vivo applications.     

Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis

We develope a method to optimize the resolution of diffuse optical tomographic instruments. Singular-value analysis of the tomographic weight matrix associated with specific data types, geometries, and optode arrangements is shown to provide a measure of image resolution. We achieve optimization of device configuration by monitoring the resolution measure described. We introduce this idea and demonstrate its utility by optimizing the spatial sampling interval and field-of-view parameters in the parallel-plane transmission geometry employed for diffuse optical breast imaging. We also compare resolution in transmission and remission geometries.     

Potentiometric behavior of electrodes based on overoxidized polypyrrole films

Electrodes based on oxidized polypyrrole films have potentiometric selectivity toward anions. When the films are overoxidized, however, electron-rich groups are introduced on to the polymer chains, reversing the selectivity of the electrodes from anionic to cationic. In this study, electrochemically overoxidized polypyrrole film electrodes were prepared, and the conditions for film formation that lead to near-Nernstian potentiometric response were investigated. It was found that the doping ion, overoxidation solution, and pH affect the response of these electrodes. Redox interference is significantly lower for the overoxidized polypyrrole films than for polypyrrole electrodes.     

Microfabrication of screen-printed nanoliter vials with embedded surface-modified electrodes

A self-contained ion-selective sensing system within a nanoliter-volume vial has been developed by integrating screen printing, laser ablation, and molecular imprinting techniques. Screen printing and laser ablation are used in tandem to fabricate nanoliter-volume vials with carbon and Ag/AgCl ring electrodes embedded in the sidewalls. Using multisweep cyclic voltammetry, the surface of the carbon electrode can be modified with a polypyrrole film. By polymerizing pyrrole in the presence of nitrate, pores complementary to the nitrate anion in size, shape, and charge distribution are formed in the resulting film. Electrochemical cells modified with this nitrate-imprinted polypyrrole film show a near-Nernstian response to nitrate, and excellent reproducibility. The integration of molecular recognition and electrochemical response in the nanoliter vials is demonstrated by the detection of as little as 0.36 ng nitrate in nanoliter-volume samples. The integration of tailored molecular recognition within nanoliter vials via established fabrication and imprinting protocols should result in a number of nanosensor devices with applications in BioMEMS and micro total analysis systems.     

Liposome-gold nanorod hybrids for high-resolution visualization deep in tissues

The design of liposome-nanoparticle hybrids offers a rich toolbox for the fabrication of multifunctional modalities. A self-assembled liposome-gold nanorod hybrid vesicular system that consists of lipid-bilayer-associated gold nanorods designed to allow deep tissue detection, therapy, and monitoring in living animals using multispectral optoacoustic tomography has been fabricated and characterized in vitro and in vivo.     

High-sensitivity compact ultrasonic detector based on a pi-phase-shifted fiber Bragg grating

A highly sensitive compact hydrophone, based on a pi-phase-shifted fiber Bragg grating, has been developed for the measurement of wideband ultrasonic fields. The grating exhibits a sharp resonance, whose centroid wavelength is pressure sensitive. The resonance is monitored by a continuous-wave (CW) laser to measure ultrasound-induced pressure variations within the grating. In contrast to standard fiber sensors, the high finesse of the resonance--which is the reason for the sensor's high sensitivity--is not associated with a long propagation length. Light localization around the phase shift reduces the effective size of the sensor below that of the grating and is scaled inversely with the resonance spectral width. In our system, an effective sensor length of 270 μm, pressure sensitivity of 440 Pa, and effective bandwidth of 10 MHz were achieved. This performance makes our design attractive for medical imaging applications, such as optoacoustic tomography, in which compact, sensitive, and wideband acoustic detectors are required.