Time Reversing Waves For Biomedical Applications

Abstract

Time reversal is a concept that always fascinated the majority of scientists. In fact, this fundamental symmetry of physics, the time reversal invariance, can be exploited in the domain of wave physics, in acoustics and more recently in electromagnetism, leading to a huge variety of experiments and instruments both for fundamental physics and applications. Today, these applications go from medical imaging and therapy to telecommunications, underwater acoustics, seismology or non-destructive testing. The evolution of electronic components enables today the building of time reversal mirrors that make a wave live back all the steps of its past life. These systems exploit the fact that in a majority of cases the propagation of acoustics waves (sonic or ultrasonic) and electromagnetic waves is a reversible process. Whatever the distortions (diffraction, multiple-scattering, reverberation) suffered in a complex environment by a wave emerging from a point source, there always exists, at least theoretically, a dual wave able to travel in the opposite direction all the complex travel paths and finally converges back to the initial source location, exactly as if the movie of the wave propagation had been played backwards in time. The main interest of a Time Reversal Mirror (TRM) is to experimentally create this dual wave, thanks to an array of reversible transducers (able to work both in transmit and receive modes) driven using A/D and D/A converters and electronic memories. The TRM is thus able to focus the wave energy through very complex media. In Ultrasonics, a TRM consists in a 2D surface covered with piezoelectric transducers that successively play the role of hydrophones and loudspeakers. The ultrasonic wave is emerging from a given source in the medium and recorded by each of the microphones in electronic memories. Then, in a second step (the time reversal step), all memories are read in the reverse direction. More precisely, the chronology of the signals received by each hydrophone is reversed. The signals recorded at later times, are read first. All hydrophones switch synchronously in a transmit mode (loudspeaker) and re-emit the “time reversed” signals coming from the electronic memories. Thus, new initial conditions for the wave propagation are created, and thanks to reversibility, the diffracted wave has no other solution than living back step by step its past life in a reversed way. Of course, this kind of mirror is totally different than a classical mirror. A time reversal mirror builds the real image of the source at its location whereas as a classical mirror builds a virtual image of the source. The great robustness of the time reversal focusing ability has been verified in many scenarios ranging from ultrasonic propagation (millimetric wavelength) in the human body over several centimeters, to ultrasonic propagation (metric wavelength) in the sea over several tens of kilometers and finally since recently the propagation of centimetric electromagnetic waves over several hundreds of meters [3, 9].