A New Imaging Technique Combining Diffusive Photon Density Waves

A New Imaging Technique Combining Diffusive Photon Density Waves and Focussed Ultrasound by Charles A. DiMarzio Richard J. Gaudette Center for Electromagnetics Research Northeastern University Boston, Massachusetts 02115 and Thomas J. Gaudette Massachusetts General Hospital NMR Center Building 149, 13th Street Charlestown, MA 02129 ABSTRACT Acousto photonic imaging (API), combines the technique of diffusive photon density wave (DPDW) imaging with ultrasound modulation of light in a new mode of medical imaging which promises improved resolution, accuracy, and penetration. Analytical results reported previously showed that a focussed ultrasound beam at one frequency, mixing with a diffusive wave at another, produces signals at the sum and difference frequencies, and that these signals originate near the ultrasound focus. In heterogeneous tissue, reconstruction from DPDW images is difficult because the problem is under determined and ill posed, because practical considerations constrain probe locations, and because probe placement and orientation are susceptible to motion. API provides additional data in several ways: First scanning the ultrasound focus throughout the sample volume and measuring the mixing signals images three-dimensional structures with contrasting optical or ultrasound properties. Secondly, the ultrasound focus acts as a "virtual" DPDW source which can be located deep inside the tissue without invasive probe placement. Surface detectors and deep virtual sources provide the equivalent of transillumination imaging. Diffusive imaging using transillumination and reflection together offers significant improvements in resolution and accuracy over that using either alone. Finally, sampling a few locations with the ultrasound focus, perhaps aided by ultrasound imagery, may to correct for probe motion. In summary, API combines DPDW and ultrasound imaging, retaining the best features of both. Part of the SPIE Conference on Optical Tomography and Spectroscopy of Tissue Ill 376 San Jose, California January 1999 SPIE Vol. 3597 0277-786X/99/$1o.oO

INTRODUCTION The interaction of light and focussed ultrasound [Wang et. al. (3); Marks et. al.] and of light and diffusive photon density waves [DiMarzio and Gaudette] have been demonstrated previously. This interaction has been used to produce images [Wang et. al.] by scanning the focus of the ultrasound beam across an object in a uniform background. This approach requires a significant amount of time to collect data from each position of the focus with small signals which may require temporal integration, but provides images with high resolution. In diffusive wave imaging, the usual approach is to turn on multiple modulated laser sources, one at a time, and make simultaneous measurements with multiple receivers. A three dimensional map of the optical properties (scattering and absorption coefficients) is produced using inverse scattering techniques. The success of these techniques depends in part on the location of sources and receivers. In this paper, we use the ultrasound modulation of the diffusive wave to produce a virtual source of a diffusive wave at a new frequency. The virtue of this technique is that it is possible to place these virtual sources at any point which is accessible to both the original diffusive wave and the ultrasound. We need to consider whether such virtual sources will improve our ability to solve the inverse problem, and we need to better understand the mechanism of interaction between the ultrasound and the diffusive wave in order to explore possibilities for maximizing the signal strength. This paper is directed toward these two issues. VIRTUAL SOURCES One of the problems encountered in medical applications of diffusive wave imaging is that potential probe locations are limited by the goal of making the measurement non invasively. In some cases, for example, only reflective geometry, in which all source and receiver probes are on the same side of the volume of interest, can be used. However, comparison to imaging using thermal waves [Miller et. a].] suggests that better reconstructions are possible with both reflective and transmissive geometries than with either alone. Intuitively, this can be understood by applying geometric optics to diffusive waves. Consider a diffusive wave from a source near the surface, received by a detector also near the surface. The received signal will be most strongly determined by the diffusive properties of the medium along a path parallel to the surface at shallow depths. For quantum limited detection, the noise will be proportional to the square root of this signal. The signal scattered from a deep anomaly, particularly in.view of the high loss associated with diffusive waves, will be small compared to the direct signal, and probably even small compared to the noise. Furthermore, paths for all transmitter and receiver pairs are quite similar, making the inversion problem ill posed. Transmissive geometries are better at sampling the deep anomaly, but may not do well at providing information about shallow anomalies. Numerical simulations have been performed with the model in Figure 1. A spherical object with an absorption coefficient 0.14/cm above that of the background is placed inside the otherwise uniform volume, and receivers are placed in an array on the surface. Sources 377

0-1 N3-4 -5.. I 11It. VSlIm,1, S 65 43 -. S 21 *11. 6 V axis 0 Xaxis Figure 1 The numerical model has virtual sources below the anomaly. 3785-05 are also placed on the surface, and virtual sources are placed deep inside the medium, in this case, at a depth of 5 centimeters. Figure 2 shows the results of using only the surface sources. This figure is a plot in the x z plane for y = 4 cm. The original object is shown on the left and the truncated singular value reconstruction on the right. The reconstruction is both too shallow and too weak in amplitude, by more than a factor of 4. Both of these errors are characteristic of a large number of inversion algorithms used with this model [Gaudette et. a].]. Figure 3 shows the same reconstruction on the left, and a reconstruction using the virtual sources on the right. Now. both the amplitude and the depth are nearly correct. One factor which must be considered is that with the virtual sources we are using twice as much data, so some improvement in performance might be expected because 378

0 1-2 -3-4 -s = =.*--4 FTt: -- - **l--*. - 0123456 0.14 0 0.12 1 10.1 0.08-2 0.06-3 0.04-4 0.02-5 : P0.05 0.04 0.03 0.02 0.01 0 Figure 2 In version with surface sources alone tends to underestimate both the depth and amplitude of the anomaly. 3785-07 O.15 -.11-1 -2 1 0.2 _ -3-3 4 0.054 _5.aa,a. u.aa*a aaa... 0 6 0 6 : 0.15 0.1 0.05 Figure 3 Virtual sources improve depth and amplitude estimation. 3785-09 379

of averaging over different noise samples. To test this idea, we performed the same reconstruction moving the virtual sources to the surface, so that they provided redundant sampling of noise but did not reduce the under determined nature of the problem. Figure 4 shows the original reconstruction on the left and the one with these virtual sources at the surface on the right. It is evident that the two results are similar. Thus it is the location of the virtual sources deep in the medium, rather than their number, which provides the improvement seen in Figure 3. -1 I Ii:._+.±.T ' - -.- -.05 ' 0 6 ).15 0 0.15 o - LLI I '-- 4 0 24 6 0.1 0.os 0 Figure 4 Extra surface sources do not improve depth and amplitude estimation. 3785-10 MECHANISM OF INTERACTION In large tissue samples, the diffusive waves themselves may be very weak for long paths between source and receiver. The acoustically modulated signals will be even weaker. It is important to understand the mechanisms of interaction in order to describe the virtual sources sufficiently to allow them to be used to produce valid reconstructions, and to examine geometries, frequencies, and other parameters which could increase their strength. There has been considerable debate as to the mechanisms, and four have been proposed. These four proposed mechanisms are: photon phonon interaction which modulates the index of refraction, as in an acousto optical modulator (the Raman-Nath effect), the Doppler 380

shift, speckle modulation, and modulation-of-particle-density effects on the bulk optical properties /2s and,ua. The Raman-Nath effect describes the interaction of light with ultrasound waves in a transparent medium to generate a moving diffraction grating which creates sidebands at multiples of the acoustic frequency exiting at small angles with respect to the incident direction. In the present case, the effect would occur between scattering events. The Doppler and speckle effects involve changes in the interference pattern of light scattered from randomly positioned particles. As particles move a fraction of a wavelength of the light, the resulting interference (speckle) pattern changes. An alternative description is that the light is Doppler shifted by the moving particles, and all the contributions add to produce the changing speckle pattern. In the modulation-of-density model, light propagation is described by diffusive waves, and the diffusivity and decay rate are modified by changes in the density of particles in the medium. The major issue is to determine whether index variations (Raman Nath) or particle motion (the other three) is responsible for the interaction. We have performed an experiment which indicates that the predominant source of interaction is particle motion. The experiment is based on the fact that particle motion in the ultrasound wave is caused by viscous forces acting on the particle. Specifically, the acceleration of a particle of density Pparticle, and radius r, in a wave in which the water velocity is Vwater, S dvparticie _ ar2 (Vwater Vparticie) + Fot her dt irr (Pwater Pparticle) g where Fother accounts for forces in addition to those of the ultrasound wave. Rather than attempt to measure size and mass of the particles, we use their fall velocity as a parameter in our analysis. If the external force is gravity, acting down with a magnitude mg, the steady state solution dv/dt = 0 is o!r Vfall (Pwater -- pparticie) g. Next, neglecting external forces including gravity, and assuming a sinusoidal velocity of the ultrasonic wave, V =.Vet, we obtain Integrating to obtain position,._ Vparticie = Vwater 1 + ivfallwg Xparticie = Xwater. 1 + ivfallwy Thus the strength of the acousto photonic signal will decrease with increasing frequency, and with increasing fall velocity. We tested this idea by sweeping the frequency of a wide band NDT transducer, centered nominally at 6 MHz, over frequencies from 3 to 9 MHz., 381

using a suspension of Titanium(IV) Oxide particles in water. These particles had a wide distribution of sizes, but settled out significantly in a tank 20 cm deep in a time scale of hours. To avoid measuring frequency variations of the transducer and other equipment, we calibrated the measurement by comparing it to a suspension of Intralipid 20% in water, diluted to provide about the same apparent scattering coefficient as determined by eye. The Intralipid has the same density as water, and will remain in suspension indefinitely, and so may be assumed to be a true tracer of the water velocity. The experimental configuration is shown in Figure 5.The light was generated by a Melles Griot laser package, using a 690nm Sharp laser. The 30-mW laser was operated at an output power of 15mW, and is coupled into a 1-mm-diameter plastic fiber. The ultrasound transducer is driven by a tunable RF source, amplitude modulated at 400 Hz. The RF eri is amplified by a 30 db amplifier from a level at the generator of -17 dbm. R}FTh Focusing Ultrasound Transducer I 400 fa Hz / APD and Amplifier Package Ref input Lock-In Amplifier Sig int Veil Out Spectrum Analyzer in Filter Mode Figure 5 An experiment to measure the acousto photonic interaction uses a spectrum analyzer as a fixed filter and detector estimation. 3785-23 382

The detection subsystem began with another plastic fiber of 1mm diameter similar to the one used to deliver the light into the tank. The fiber was connected to a Hamamatsu avalanche photon diode, APD, detector and power supply package. The signals were detected on a spectrum analyzer acting as a tuned filter. The video output of the spectrum analyzer was connected to a lock in amplifier, with the reference coming from the 400 Hz amplitude modulation. The lock in amplifer signal for the Titanium(IV) Oxide, divided by that for the Intralipid, is plotted in Figure 6, along with plots of the equation above for various fall velocities. The signals showed considerable variability, probably because of small motions of the source and receiver and the short wavelength (about 200 micrometers) of the ultrasound. Nevertheless, the results are unambiguous; The acousto photonic effect decreases with frequency, indicating that motion of the particles is responsible for most of the signal. We have shown that SUMMARY virtual sources generated by the interaction of light and focussed ultrasound can be useful adjuncts to diffusive wave imaging, and the signal from these virtual sources arises from the motion of the particles, the signals are large enough to be useful. Further work is under way to map the virtual sources, to quantify the amplitudes, and to develop a more accurate forward model and eventually a reconstruction algorithm. 383

0.8 0.6 0.4 0.2 10 100 1 2 10 10 Figure 6 Acousto photonic signals from large particles decrease with frequency, indicating that they arise from particle motion. 3785-24 Acknowledgements The authors wish to thank the students who collected data, Clifton Whilby and Eva N. Ng, colleagues Dana Brooks, Eric L. Miller, and Misha Kilmer, all of Northeastern University, and David A. Boas of the NMR Center at Massachusetts General Hospital. Funding for this project was provided by Northeastern University's Presidential Appropriation Fund, by NSF grants EEC9612524, EEC9812924, and ECS9413298. 384