  The fast scintillation decay time and the high scintillation yield of liquid
xenon makes it an appropriate material for nuclear medicine. Moreover, being a
continuous medium with a uniform response, liquid xenon allows one to avoid
most of the geometrical distortions of conventional detectors based on
scintillating crystals. In this paper, we describe how these properties have
motivated the development of a novel concept for positron emission tomography
scanners with Time-Of-Flight measurement, which uses liquid xenon as a
scintillating material and silicon photomultipliers as sensors. Monte Carlo
studies have indicated that this technology would provide a very good intrinsic
time resolution, of around 70 ps. Moreover, being liquid xenon transparent to
UV and blue wavelengths, both scintillation and Cherenkov light can be
exploited. While the former can be used for energy measurements, the latter is
a prompt signal (of a few picoseconds), which provides a very precise time
measurement. Monte Carlo simulations point to a time resolution of 30-50 ps
obtained using Cherenkov light. A first prototype is being built to demonstrate
the high energy, spatial and time resolution of this concept, using a ring of
around 30 cm of internal diameter and a depth of 3 cm instrumented with
VUV--sensitive silicon photomultipliers.
