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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 1 — Jan. 4, 2012
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Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration

R. Sriram Chandran, Debasish Roy, Rajan Kanhirodan, Ram Mohan Vasu, and C. Usha Devi  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 22837-22850 (2011)
http://dx.doi.org/10.1364/OE.19.022837


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Abstract

We demonstrate a method to recover the Young’s modulus (E) of a tissue-mimicking phantom from measurements of ultrasound modulated optical tomography (UMOT). The object is insonified by a dual-beam, confocal ultrasound transducer (US) oscillating at frequencies f0 and f0 + Δf and the variation of modulation depth (M) in the autocorrelation of light traversed through the focal region of the US transducer against Δf is measured. From the dominant peaks observed in the above variation, the natural frequencies of the insonified region associated with the vibration along the US transducer axis are deduced. A consequence of the above resonance is that the speckle fluctuation at the resonance frequency has a higher signal-to-noise to ratio (SNR). From these natural frequencies and the associated eigenspectrum of the oscillating object, Young’s modulus (E) of the material in the focal region is recovered. The working of this method is confirmed by recovering E in the case of three tissue-mimicking phantoms of different elastic modulus values.

© 2011 OSA

1. Introduction

Ultrasound-modulated optical tomography (UMOT) is a non-invasive optical imaging modality with the potential of providing spectral variation in absorption and scattering coefficients (μa and μs respectively) in soft-tissue organs for medical diagnostic imaging [1

1. C. Kim and L. V. Wang, “Multi-optical-wavelength ultrasound-modulated optical tomography: a phantom study,” Opt. Lett. 32, 2285–2287 (2007). [CrossRef] [PubMed]

, 2

2. L. V. Wang, “Ultrasound-mediated biophotonic imaging: A review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123–138 (2004). [PubMed]

]. Focused ultrasound (US) beam helps provide a frequency shift to the photons passing through the insonified region-of-interest (ROI) in the body; and these photons can be used to image the optical property of the ROI. Since in a highly scattering object like tissue, the ultrasound beam can be focused more tightly than light beam, UMOT provides parameter reconstruction with an increased spatial resolution [3

3. S. Leveque, A. C. Boccara, M. Lebec, and H. S. Jalmes, “Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing,” Opt. Lett. 24, 181–183 (1999). [CrossRef]

] than is possible with the usual stand alone near-infrared optical imaging modality, the diffuse optical tomography (DOT) [4

4. A P Gibson, J C Hebden, and S R Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005). [CrossRef] [PubMed]

].

Functional parameter estimation requires quantitative information on the optical properties, especially μa. However, to extract such information accurate mathematical models describing the interaction of US wave with tissue, and the propagation of light through the insonified ROI are required. In the past, considerable effort has been expended to arrive at and numerically study such interaction models [5

5. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E 66, 026603 (2002). [CrossRef]

8

8. W. Leutz and G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995). [CrossRef]

]. However, to the best of our knowledge, there have only been a few attempts at quantitative recovery of optical parameters from UMOT data [9

9. C. Kim, R. J. Zemp, and L. V. Wang, “Intense acoustic bursts as a signal-enhancement mechanism in ultrasound-modulated optical tomography,” Opt. Lett. 31, 2423–2425 (2006). [CrossRef] [PubMed]

12

12. E. Bossy, A. Funke, K. Daoudi, A. Boccara, M. Tanter, and M. Fink, “Transient optoelastography in optically diffusive media,” Appl. Phys. Lett. 90174111 (2007). [CrossRef]

].

The above models are used to derive explicit expressions linking M to μa,μs, n and < a2 > (in the ROI) opening up the possibility of recovery of these parameters from the set of measurements {M} over many ‘views’. A partial differential equation (PDE) describing the propagation of the amplitude correlation of light (G) through a turbid medium insonified by an US beam is derived in [7

7. S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006). [CrossRef] [PubMed]

], which can also be employed for the estimation of these object properties from the boundary measurements of G. Alternatively, the above non-linear parameter estimation problem can be recast as a linear source recovery problem of reconstructing the ultrasound-induced sources of perturbation in G (which are a(r) and Δn(r)) from the boundary measurements of this perturbation (Gδ).

The aim of the present work is to demonstrate quantitative recovery of elastic property of a tissue-like object from variation of M.vs.frequency of US forcing, in particular the frequency at which M has a dominant peak. To facilitate measurement of M at different US forcing frequencies we employ (as detailed further in Section 2) a confocal two-region transducer, one region resonating at a frequency (f) and the other at (f + Δf). The mixing of US pressure amplitudes produces a forcing at the beat frequency Δf [15

15. M. Fatemi, A. Manduca, and J. Greenleaf, “Imaging Elastic Properties of Biological Tissues by Low-Frequency Harmonic Vibration,” Proc. IEEE 91, 1503–1517 (2003). [CrossRef]

]. By varying the drive frequency of the transducer the forcing frequency can be varied. The essential strategy of the method here is to match (or tune) the forcing frequency at the ROI to the dominant natural frequency of the vibrating ROI (VROI), and the matching of the frequencies is helped by the fact that the peak in M vs frequency curve is indicative of resonance in the VROI. This natural frequency is a function of the Young’s modulus (E) of the material of the ROI, presently assumed to be linear elastic (Hookean) homogeneous and isotropic, which opens the way for a quantitative assessment of E from a measured resonant frequency. We note here that the natural modes of vibration depend not only on elastic properties of the VROI, but also on its shape/geometry and the boundary conditions. Therefore, as further elaborated in Section 3, for the recovery of E one needs to correctly obtain the shape of the VROI followed by an assignment of the correct local boundary conditions.

A summary of the work presented in the rest of the paper is as follows. Section 2 contains computation of the pressure and force in the focal volume of a two-region PZT transducer, and its experimental verification by measuring this pressure distribution. The solution of the momentum balance equation with the forcing from the US transducer for arriving at the dynamic response of the ROI is described in Section 3. Prior to this, we arrive at the shape of the ROI which undergoes non-trivial vibration. Transport of light through the insonified region and computation of the intensity autocorrelation of light and its modulation are the subjects discussed in Section 4. Section 5 provides details of the experimental set-up for measuring M for various Δf ’s. Apart from this, in this section we also describe a method to arrive at the unknown E from the measured dominant natural frequency using the method of bisection. Section 6 gives our concluding remarks.

2. Perturbation from ultrasound: modelling and verification

2.1. Ultrasound-induced force distribution in the focal volume

The confocal composite US transducer we use is driven by an input voltage just large enough to cause a modulation in the focal region and whose effect in the intervening region can be conveniently neglected. Focusing is normally done either using a concave transducer on which PZT is deposited or a plane one in conjunction with a US focusing element or an array with provision for controlled sequential firing for generating a spherical wave. In the present work the two regions of the confocal US transducer are driven by voltages oscillating at frequencies 1 MHz and 1 MHz + Δf where Δf can be varied from as low as 10 Hz to 1 kHz. The composite transducer helps us send MHz waves which have reasonable depth of penetration in the object and thus apply a sinusoidal force at the ROI oscillating at Δf Hz, the beat frequency.

Beating takes place at the ROI because the force is proportional to the acoustic intensity which is the square of the acoustic pressure amplitude. We use p1(f) and p2(f + Δf) to denote the sinusoidal pressure amplitudes at the ROI from the two regions in the transducer.
p1(f)=p10cos(2πft+ϕ1)
(1)
p2(f+Δf)=p20cos(2π(f+Δf)t+ϕ2)
(2)
The average intensity, I(X), of the combined US beam is given by I(X)=1sd<ξ˜(X)>dt where ξ(X) = < ξ̃(X) > is the time average of the energy deposited at X in the ROI, and s the cross-sectional area we are considering in the intersection volume of the two pressure waves. This energy ξ(X) can be shown to be equal to [14

14. E. Konofagou, J. Thierman, and K. Hynynen, “A focused ultrasound method for simultaneous diagnostic and therapeutic applicationsa simulation study,” Phys. Med. Biol. 46, 2967–2984 (2001). [CrossRef] [PubMed]

]
ξ(X)=P0+P1cos(2πΔft+ϕ2ϕ1)
(3)
where P0 and P1 are constants dependent on p102 and p202 and the integration time constant T. The radiation force experienced by the ROI in an area around X is given by F(X)=2αI(X)c where α is the sound absorption coefficient and c the velocity of sound in the object. This force can be shown to be equal to [14

14. E. Konofagou, J. Thierman, and K. Hynynen, “A focused ultrasound method for simultaneous diagnostic and therapeutic applicationsa simulation study,” Phys. Med. Biol. 46, 2967–2984 (2001). [CrossRef] [PubMed]

]
F(X)=F0sin(2πΔft)
(4)
where F0=4αP0Tcs

The pressure amplitude, p1 or p2, at the focal region can be computed by propagating the pressure at the transducer surface. The pressure at the transducer surface can be calculated from the electrical parameters of the transducer, such as the equivalent resistance, capacitance and inductance (R, C and L respectively) of the PZT. The acoustic pressure p0 on the transducer surface is given by [16

16. J. Huang, J.A. Nissen, and Erik Bodegom, “Diffraction of light by a focused ultrasonic wave,” J. Appl. Phys. 71(1), 70–75 (1992). [CrossRef]

]
p02=2ρcAkeff2V2R
(5)
where ρ is the material density and c the acoustic wave velocity, A the surface area of the transducer, V the applied voltage and keff2 the conversion coupling coefficient (electrical to acoustic and specified by the manufacturers to be 0.62 in our case) of the transducer.

2.2. Ultrasound-induced pressure distribution in the focal volume

In order to transport the pressure distribution p0 on the surface of the transducer to its focal volume, where the pressure can be very large, one needs a model that accounts for material nonlinearity apart from absorption and diffraction in the medium. Here we make use of such a model known as the Westervelt equation [13

13. T. Kamakura, T. Ishiwata, and K. Matsuda, “Model equation for strongly focused finite-amplitude sound beams,” J. Acoust. Soc. Am. 107, 3035–3046 (2000). [CrossRef] [PubMed]

].
2p1c22pt2+δc43pt2+βρc42p2t2=0
(6)
The first two terms of the above equation represent diffraction and linear propagation and the third term thermoviscous losses. The nonlinear effects are governed by the fourth term with a constant β which depends on the average transducer pressure and the density of the medium. The acoustic absorption α=δω22c3 where δ is the sound diffusivity.

The Westervelt equation is solved in [13

13. T. Kamakura, T. Ishiwata, and K. Matsuda, “Model equation for strongly focused finite-amplitude sound beams,” J. Acoust. Soc. Am. 107, 3035–3046 (2000). [CrossRef] [PubMed]

] using a series expansion in spheroidal coordinates and we have adopted the same technique here. Here the values of α and β used are α = 1.5 dBcm−1 and β = 6.2 to match the values quoted for breast tissue in [17

17. F. A. Duck, “Nonlinear acoustics in diagnostic ultrasound,” Ultrasound Med. Biol. 28(1), 1–18 (2002). [CrossRef] [PubMed]

]. We have computed the focal region pressure distribution for (i) transducer operating with just one element and (ii) the composite transducer with both the regions energized. We did this computation for US waves going into water as well as the (poly) Vinyl Alcohol (PVA) phantom used in the experiments. The axial (i.e., along the axis of the transducer) and lateral cross sections of the pressure distributions computed are shown in Figs. 1 and 2. Figure 3 shows the mesh and contour plots of the computed pressure in the xz plane which contains the transducer axis taken to be along the z-direction.

Fig. 1 Computed pressure distribution along the US transducer axis (i.e., (0,0,z)) in the ROI. Here d is the focal length of the US transducer. The origin is assumed to be at the centre of the ROI.
Fig. 2 Computed pressure distribution normal to the US transducer axis computed along (x,0,0). This distribution is observed to have radial symmetry. Here a is the aperture radius of the US transducer. The origin is assumed to be at the centre of the ROI.
Fig. 3 Mesh and contour plots of the pressure distribution in the (x,0,z) plane. Here d is the focal length and a is the aperture radius of the US transducer. The origin is assumed to be at the centre of the ROI.

2.3. Experimental verification of the shape of the focal volume

The US transducer, immersed in water is powered by two signal generators working at 1 MHz and 1.01 MHz and the force in the common focal volume in water is measured by scanning the region with a PVDF (Polyvinylidene fluoride) transducer. For a schematic diagram of the set-up and other details, see Section 5. The acceptance area of the transducer is ∼ 7mm2 which is masked to a smaller area of ∼ 0.38mm2. The transducer is mounted on an x-y-z stage and the voltages generated are measured at a number of points in the focal region (at many x-y cross-sections). Assuming that the measured voltages are proportional to the force experienced by points in the ROI, cross-sectional plots of the force experienced by the ROI are generated. The measured voltage distributions, giving axial and radial cross-sections, are shown in Figs. 4 and 5 respectively. Their variations are similar to (and compare well with) the computed pressure variation shown in Figs. 1 and 2. Figure 6 is the contour plot of the experimentally measured voltage in the xz plane.

Fig. 4 Experimentally measured voltage distribution along the US transducer axis (i.e., (0,0,z)) which is an experimental measure of the computed pressure shown in Fig. 1. d is the focal length of the US transducer. The origin is assumed to be at the centre of the ROI.
Fig. 5 Experimentally measured voltage distribution normal to the US transducer axis along both (x,0,0) and (0,y,0) which corresponds to the computed pressure distribution shown in Fig. 2. Here a is the aperture radius of the US transducer. The origin is assumed to be at the centre of the ROI.
Fig. 6 Contour plot of the experimentally measured voltage (normalized) in the xz plane. Here d is the focal length and a is the aperture radius of the US transducer. The origin is assumed to be at the centre of the ROI.

3. Response of the periodically excited focal volume via solution of the momentum-balance equation

We have employed ANSYS® (a commercially available finite element programme) to carry out the eigenanalysis of the vibrating ROI, obtaining as a result the subset of its natural frequencies corresponding to the dominant vibration (due to shear deformation along the transducer axis). Towards this, the initially selected Ω (the closed boundary of Ω) obtained experimentally in Section 2.3 is refined during the eigenanalysis. Theoretically verified/corrected Ω is obtained by solving the momentum-balance equation over one full cycle of forcing, followed by identifying the boundary nodes (of the VROI) that separate the vibrating region from its non-vibrating complement. (A good initial guess of Ω can also be had from the force distribution in the ROI. The boundary nodes may approximately be considered as those where F(X) drops to (1100)th of its maximum value). From the experimental measurement of pressure in the VROI, we notice that of the two confocal regions of the transducer, one (the outer one with f = 1 MHz) gives rise to pressure distributions slightly different with an asymmetry compared to the other one (Figs. 2 & 5). This is owing to a defect in the spherical mould on which PZT is coated.

The photons, on interaction with the US focal volume, pick-up a phase modulation owing to the oscillations of the scattering centres. As shown in [19

19. S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770–2772 (2004). [CrossRef] [PubMed]

] the detected g2(τ) contains an oscillation of the same frequency as that of the scattering centres. The oscillations of the VROI under US forcing are characterized by a set of eigenvalues (natural frequencies) and eigenvectors (mode shapes) which contain both compression and (dilatational) shear modes. The US vibration at the low beat frequency, however excites mainly shear modes in the VROI (along with the dilatational modes excited by the high frequency wave at 2f). The eigenanalysis helps us identify these shear modes corresponding decidedly to the lower end of the eigenspectrum. The shear waves attenuate rather quickly in the surrounding region of the ROI as shown in [12

12. E. Bossy, A. Funke, K. Daoudi, A. Boccara, M. Tanter, and M. Fink, “Transient optoelastography in optically diffusive media,” Appl. Phys. Lett. 90174111 (2007). [CrossRef]

], but are present in Ω. The shear wave attenuation is frequency dependent being higher as the frequency increases. However, as verified through ANSYS-based numerical assessment of the shear deformed region, the attenuation even at these low frequencies is fast enough for the shear displacement to be close to zero beyond the near-hyperboloidal VROI.

4. Propagation of light through a turbid medium insonified by the US beam

Light propagating through a turbid medium picks up a phase fluctuation even in the absence of the US forcing owing to the Brownian motion of the scattering centres induced by thermal excitation. This fluctuation manifests itself as a decay in the measured intensity autocorrelation (g2(τ)). To such an object a focused US beam brings in an extra forcing, deterministic and localised. Extensive work has gone into the modelling of the effect of US forcing on the object. As pointed out in Section 1, scattering centres in the insonified region undergo periodic oscillations. The region itself, owing to the compression and rarefaction induced by the pressure wave,presents to the light beam a refractive index modulation Δn. This modulation, owing to the near-incompressibility of the tissue material, should occur with very low amplitudes with very high frequencies. A typical optical path length inili (here {ni} and {li} are refractive index and path length corresponding to the ith scattering event) gets perturbed to i(ni+Δni)(li+ui) (here ui is the amplitude of oscillation of the ith scattering centre in the direction of li) which means that the US-induced path length fluctuation, to a first-order approximation, is Σ(niui + liΔni), giving the US-induced phase perturbation as Δϕ = Δϕu + Δϕn = k0Σniui + k0ΣliΔni where Δϕu and Δϕn are the perturbations owing to oscillation and Δn respectively.

Expressions are available for Δϕu and Δϕn when the medium has either scattering isotropy or anisotropy, which contain optical, acoustic and elastic properties of the medium as parameters [5

5. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E 66, 026603 (2002). [CrossRef]

]. These are used in the equation for the US-introduced contribution towards the temporal autocorrelation function (G1(τ)) of the electric field of light. In the weak scattering limit, assuming that there is no correlation between light arriving through different paths, photons travelling along the same path of length, s, have amplitude correlation given by G1,s(τ)=<Es(t)Es*(t+τ)>. G1,s(τ) is given by [5

5. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E 66, 026603 (2002). [CrossRef]

]
G1,s(τ)=exp[F(τ)/2]
(10)
where
F(τ)=<[j=1NΔϕu,j(t,τ)]2>,neglectingΔϕn
(11)
Here (N – 1) is the number of scattering events along the path of length s. To arrive at the overall amplitude autocorrelation G(τ), G1,s(τ) is ensemble averaged over all photon paths s: i.e., G(τ)=0p(s)G1,s(τ)ds.

Here p(s) is the probability density function for s. The normalized amplitude autocorrelation g1(τ) is G(τ)G(0) from which g2(τ) is estimated as 1 + β|g1(τ)|2 where β is a constant dependent on the optics used in the data gathering.

In [5

5. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E 66, 026603 (2002). [CrossRef]

], analytical expressions are derived for G1(τ); further p(s) evaluated through sending photons, using Monte Carlo (MC) simulations or by solving the diffusion equation for light propagation, is used to compute G(τ) and g1(τ). The effect of periodic phase fluctuation on G(τ) is the appearance of a modulation of the same frequency as that of the US-induced acoustic vibration frequency, Δf, from which we derive our measurement which is the modulation depth Mf) obtained as the modulus of the Fourier transform of g2(τ) evaluated at Δf. The MC simulation carries the advantage that in transporting photons one can compute both p(s) as well as Δϕu and their time averages. Δϕu is in fact the perturbation in the accumulated phase ϕ originating from the oscillations of scattering centres confined only to the insonified ROI.

Simulations proceed in the following lines: for a given (guessed) E of the phantom material, and the force at the focal region (evaluated using the pressure distribution in the focal region obtained from the Westervelt equation, in Eqs.(1)(4) [13

13. T. Kamakura, T. Ishiwata, and K. Matsuda, “Model equation for strongly focused finite-amplitude sound beams,” J. Acoust. Soc. Am. 107, 3035–3046 (2000). [CrossRef] [PubMed]

]), first the amplitude of vibration of scattering centres in the ROI is computed. Then 1 million photons are launched and tracked for those arriving at the detector. From the phase and weight of the photons G(τ) is calculated, from which g1(τ), g2(τ) and M are evaluated [19

19. S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770–2772 (2004). [CrossRef] [PubMed]

, 20

20. C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt. 10, 044020 1–10 (2005).

]. The above are repeated for Δf varying from 40Hz to 130Hz. A typical M vs Δf plot is shown in Fig. 7 for which E= 11 kPa. It is observed from these simulations that M goes through a prominent peak (for a particular Δf, say Δfr) and this Δfr depends on E of the material. This indicates that the vibration of the ROI induced by the (US) forcing at the beat frequency Δf goes through a resonant peak at Δfr, which results in a peak in phase modulation of photons traversed through the ROI, observed as a peak in the modulation depth in g2(τ). This evidence of a resonant peak and the inferring of the frequency from the M vs Δf plot are also verified through experiments. As is shown in Section 5 this resonant frequency can be used to recover E of the VROI.

Fig. 7 The variation of the experimental modulation depth (Me) with Δf which closely follows its simulated counterpart (Mc). The modulation depth was not measured at Δf = 50 and 60 Hz.

5. Experiments

5.1. Fabrication and characterization of the tissue-mimicking phantom

The details of the fabrication and characterization of the PVA phantom are given in [20

20. C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt. 10, 044020 1–10 (2005).

] and we only give a brief account here. PVA aqueous solutions with concentration of 20% by weight are prepared by heating PVA and demineralized water over a temperature bath at 90 to 93°C for 2 hours with continuous stirring. This solution is allowed to undergo repeated freeze-thaw cycles of freezing at −20°C for 12 hours, followed by thawing at room temperature for 12 hours [21

21. A. Kharine, S. Manohar, R. Seeton, R. G. M. Kolkman, R. A. Bolt, W. Steenbergen, and F. F. M. de Mul, “Poly Vinyl Alcohol gels for use as tissue phantoms in photoacoustic mammography,” Phys. Med. Biol. 48, 357–370 (2003). [CrossRef] [PubMed]

]. E and μs in the PVA slab can be tailored by varying the number of freeze-thaw cycles. As mentioned in reference [20

20. C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt. 10, 044020 1–10 (2005).

] E can be varied from 11 to 97kPa and correspondingly μs vary from 1.4 to 4.5 mm−1. For further increasing μs we mix polystyrene beads of diameter 0.1 μm whilst forming the PVA slab. The scattering coefficient of the resulting phantom is determined using an indirect method based on the reverse Monte Carlo procedure [20

20. C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt. 10, 044020 1–10 (2005).

] and E is measured and verified using a dynamic mechanical analyzer (DMA). The E for the three samples used are found to be 11 kPa, 45 kPa and 58kPa. We mixed 0.3ml of polystyrene bead solution in 100ml of stock solution and increased the μs to 8.14 mm−1.

5.2. Measurement of modulation depth

The experimental set-up is shown in Fig. 8. Light from a He-Ne laser (HRR170, Thorlabs, power 17 mW) illuminates the object insonified by the US transducer, which is a two element confocal one with a common focal length of 50mm (manufactured by Roop Telsonic Ultrasonix Ltd, Mumbai, India).The driver for the transducer is an ulra-stable dual-channel function generator (Tektronix Model AFG3022B). The output from function generator is amplified by a power amplifier (Tomco, Model No:BT00100-AlphaD-CW). A continuously variable neutral density filter from Thorlabs (NDC-100C- 4M) is used to control the intensity of light entering the object. The light gains access to the object through a hole in the transducer. The photons exiting the object are picked up by a photon-counting photo-multiplier tube (PC-PMT, Hamamatsu H7360-03) and current generated after signal conditioning is given to a correlator (DAC, Flex 021d, from www.correlator.com,Bridgewater NJ 08807) which can give a minimum delay time of up to 12.5 ns. The correlator output is given to the computer for further processing. The US transducer and the object are immersed in a water bath for acoustic impedance matching. The laser light is aligned to be along the US transducer axis. The composite US transducer with two elements oscillating at 1 MHz and (1 + Δf) MHz is driven by an ultra-stable dual-channel function generator with suitable power amplification. To achieve a frequency scan of the ROI starting at a Δf as low as tens of Hz we drive one of them slightly away from resonance. A slight drop in output because of this deviation is neglected. We note that the ability to generate a stable low frequency acoustic wave critically depends on the frequency stability of the driving function generator. Our ability to select a frequency to match the desired computed resonant modes (see Section 3) is hampered because of the limitation of possible frequencies that can be selected in the function generator. The photons are picked up by a single-mode fibre and delivered to the PC-PMT. For maximizing the signal-to-noise ratio the fibre is aligned carefully to capture a single speckle from the boundary photon fluctuation.

Fig. 8 The Experimental Setup: Light from laser L, illuminates the insonified volume through a hole in the ultrasound transducer (UST). The exiting light is detected by the detector (PC-PMT) and is given to the correlator DAC and then to a computer C. The UST is driven by ultra- stable dual-channel function generator (DCFG) after power amplification

In the experiment the objects which are slabs made of PVA of dimensions 6cm×6cm×20cm, designed to have a μs equal to that of healthy breast tissue (8 mm−1) and μa kept at a nominal low value of 0.00025 mm−1 and E = 11 kPa, 45 kPa and 58 kPa are used. Light is gathered over 1200 s and the intensity autocorrelation g2(τ) is measured. For a single g2(τ), 2000 samples are collected and averaged. g2(τ) gathered for slabs with E = 11 kPa to 58 kPa are analyzed to arrive at Me (experimentally measured modulation depth) which is measured from the area around the peak at Δf in the Fourier spectrum of g2(τ).

The variation of M vs Δf is shown in Fig. 7 for a typical slab with E = 11 kPa. The computed M (Mc) is also shown in the same figure. Mc is seen to closely follow Me at the peak, an evidence of the resonance in vibration of the VROI, observed at ∼ 70 Hz.

Figures 911 show variation of Me with Δf for objects with E = 11, 45 and 58 kPa respectively. For comparison, the locations of the resonant modes of the VROI as computed using ANSYS® (in Section 3) are also shown. These figures prove that the peak resonant modes can be measured using the peak observed in the Me.

Fig. 9 Variation of the modulation depth (Me) with Δf compared with the similar variation of the computed resonant amplitude (obtained through ANSYS®) for the 11 kPa phantom. Both Me and the computed amplitudes are normalized using their maximum value observed at Δfr which is 70 Hz for this phantom
Fig. 10 Same as those given in Fig. 9 repeated for 45 kPa phantom
Fig. 11 Same as those given in Fig. 9 repeated for 58 kPa phantom

We make the following observations in regard to the results of Fig. 7 and Figs. 911. In Fig. 7 there is agreement between Me and Mc only around the resonant frequency. A possible reason for the deviation at other frequencies is the error accrued in the computation of the acoustic radiation force consequent to the uncertainty in the values used to account for coupling loss between transducer and object, losses at the interface between water and phantom and also the variable acoustic absorption in the object. An incorrect magnitude of the forcing used does not however shift the resonant frequency but only its strength. Also, the other errors we may have incurred may have a broad spectrum and therefore hardly contribute to the negligibly small bandwidth around the resonant frequency wherein most of the structural energy is concentrated.

In Figs. 911. the location of the computed resonant modes are not the same as where Me is found experimentally. This mismatch is owing to the spread of the resonant modes as dictated by the mechanical properties and shape of the vibrating ROI (as computed by ANSYS) and the fact that the set of Me was evaluated at frequencies possible to be selected in the function generator around 1.01 MHz. Limitations on the stability of the function generator used precludes generation of more experimental sample points in these frequency ranges.

Since our recovery of E is from the measured resonant frequency data-model mismatch elsewhere has not affected the accuracy of the recovered E. However in an algorithm that tries to reconcile a ‘data-model misfit’, the difference between computed and experimental ‘measurements’ owing to the incorrect input of certain quantities to the algorithm, say the force in the insonified area, can pose serious problems. One possible way to overcome this difficulty is to consider force also as a parameter to be identified in the inversion algorithm.

6. Conclusions

We have demonstrated, experimentally and with theoretical backing, quantitative recovery of Young’s modulus from UMOT data, which is the modulation depth introduced in the light intensity autocorrelation by the US induced dynamics. The method depends on measurement of a frequency and therefore is unaffected by phase and amplitude variations in the light source. In other words we have a measurement which is unaffected by the fluctuations in detected intensity. Since the detection of modulation depth in UMOT is a challenging task owing to speckle noise, the enhanced SNR afforded in measurement of M because of resonance will make the usual UMOT based recovery of optical absorption coefficient more accurate, which can be cited as an added benefit resulting from the present work. The fact that the variation of Δf provides different sets of modulation depth measurements, can be further utilized to do tomographic inversion for μa, n and E for the ROI, which is left for investigation in the future.

References and links

1.

C. Kim and L. V. Wang, “Multi-optical-wavelength ultrasound-modulated optical tomography: a phantom study,” Opt. Lett. 32, 2285–2287 (2007). [CrossRef] [PubMed]

2.

L. V. Wang, “Ultrasound-mediated biophotonic imaging: A review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123–138 (2004). [PubMed]

3.

S. Leveque, A. C. Boccara, M. Lebec, and H. S. Jalmes, “Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing,” Opt. Lett. 24, 181–183 (1999). [CrossRef]

4.

A P Gibson, J C Hebden, and S R Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005). [CrossRef] [PubMed]

5.

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E 66, 026603 (2002). [CrossRef]

6.

M. Kempe, M. Larionov, D. Zaslarsky, and A. Z. Genack, “Acoustooptic tomography with multiple scattered light,” J. Opt. Soc. Am. A 14, 1151–1158 (1997). [CrossRef]

7.

S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006). [CrossRef] [PubMed]

8.

W. Leutz and G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995). [CrossRef]

9.

C. Kim, R. J. Zemp, and L. V. Wang, “Intense acoustic bursts as a signal-enhancement mechanism in ultrasound-modulated optical tomography,” Opt. Lett. 31, 2423–2425 (2006). [CrossRef] [PubMed]

10.

R. J. Zemp, C. Kim, and L.V. Wang, “Ultrasound-modulated optical tomography with intense acoustic bursts,” Appl. Opt. 46, 1615–1623 (2007). [CrossRef] [PubMed]

11.

X. Xu, H. Zhang, P. Hemmer, D. Qing, C. Kim, and L. V. Wang, “Photorefractive detection of tissue optical and mechanical properties by ultrasound modulated optical tomography” Opt. Lett. 32, 656–658 (2007). [CrossRef] [PubMed]

12.

E. Bossy, A. Funke, K. Daoudi, A. Boccara, M. Tanter, and M. Fink, “Transient optoelastography in optically diffusive media,” Appl. Phys. Lett. 90174111 (2007). [CrossRef]

13.

T. Kamakura, T. Ishiwata, and K. Matsuda, “Model equation for strongly focused finite-amplitude sound beams,” J. Acoust. Soc. Am. 107, 3035–3046 (2000). [CrossRef] [PubMed]

14.

E. Konofagou, J. Thierman, and K. Hynynen, “A focused ultrasound method for simultaneous diagnostic and therapeutic applicationsa simulation study,” Phys. Med. Biol. 46, 2967–2984 (2001). [CrossRef] [PubMed]

15.

M. Fatemi, A. Manduca, and J. Greenleaf, “Imaging Elastic Properties of Biological Tissues by Low-Frequency Harmonic Vibration,” Proc. IEEE 91, 1503–1517 (2003). [CrossRef]

16.

J. Huang, J.A. Nissen, and Erik Bodegom, “Diffraction of light by a focused ultrasonic wave,” J. Appl. Phys. 71(1), 70–75 (1992). [CrossRef]

17.

F. A. Duck, “Nonlinear acoustics in diagnostic ultrasound,” Ultrasound Med. Biol. 28(1), 1–18 (2002). [CrossRef] [PubMed]

18.

J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity (Dover Publications, Inc., New York, 1993)

19.

S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770–2772 (2004). [CrossRef] [PubMed]

20.

C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt. 10, 044020 1–10 (2005).

21.

A. Kharine, S. Manohar, R. Seeton, R. G. M. Kolkman, R. A. Bolt, W. Steenbergen, and F. F. M. de Mul, “Poly Vinyl Alcohol gels for use as tissue phantoms in photoacoustic mammography,” Phys. Med. Biol. 48, 357–370 (2003). [CrossRef] [PubMed]

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(110.6150) Imaging systems : Speckle imaging
(110.7170) Imaging systems : Ultrasound
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3880) Medical optics and biotechnology : Medical and biological imaging

ToC Category:
Medical Optics and Biotechnology

Virtual Issues
Vol. 7, Iss. 1 Virtual Journal for Biomedical Optics

Citation
R. Sriram Chandran, Debasish Roy, Rajan Kanhirodan, Ram Mohan Vasu, and C. Usha Devi, "Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration," Opt. Express 19, 22837-22850 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-23-22837


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References

  1. C. Kim and L. V. Wang, “Multi-optical-wavelength ultrasound-modulated optical tomography: a phantom study,” Opt. Lett.32, 2285–2287 (2007). [CrossRef] [PubMed]
  2. L. V. Wang, “Ultrasound-mediated biophotonic imaging: A review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers19, 123–138 (2004). [PubMed]
  3. S. Leveque, A. C. Boccara, M. Lebec, and H. S. Jalmes, “Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing,” Opt. Lett.24, 181–183 (1999). [CrossRef]
  4. A P Gibson, J C Hebden, and S R Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50, R1–R43 (2005). [CrossRef] [PubMed]
  5. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for aniostropically scattering media,” Phys. Rev. E66, 026603 (2002). [CrossRef]
  6. M. Kempe, M. Larionov, D. Zaslarsky, and A. Z. Genack, “Acoustooptic tomography with multiple scattered light,” J. Opt. Soc. Am. A14, 1151–1158 (1997). [CrossRef]
  7. S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett.96, 163902 (2006). [CrossRef] [PubMed]
  8. W. Leutz and G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B204, 14–19 (1995). [CrossRef]
  9. C. Kim, R. J. Zemp, and L. V. Wang, “Intense acoustic bursts as a signal-enhancement mechanism in ultrasound-modulated optical tomography,” Opt. Lett.31, 2423–2425 (2006). [CrossRef] [PubMed]
  10. R. J. Zemp, C. Kim, and L.V. Wang, “Ultrasound-modulated optical tomography with intense acoustic bursts,” Appl. Opt.46, 1615–1623 (2007). [CrossRef] [PubMed]
  11. X. Xu, H. Zhang, P. Hemmer, D. Qing, C. Kim, and L. V. Wang, “Photorefractive detection of tissue optical and mechanical properties by ultrasound modulated optical tomography” Opt. Lett.32, 656–658 (2007). [CrossRef] [PubMed]
  12. E. Bossy, A. Funke, K. Daoudi, A. Boccara, M. Tanter, and M. Fink, “Transient optoelastography in optically diffusive media,” Appl. Phys. Lett.90174111 (2007). [CrossRef]
  13. T. Kamakura, T. Ishiwata, and K. Matsuda, “Model equation for strongly focused finite-amplitude sound beams,” J. Acoust. Soc. Am.107, 3035–3046 (2000). [CrossRef] [PubMed]
  14. E. Konofagou, J. Thierman, and K. Hynynen, “A focused ultrasound method for simultaneous diagnostic and therapeutic applicationsa simulation study,” Phys. Med. Biol.46, 2967–2984 (2001). [CrossRef] [PubMed]
  15. M. Fatemi, A. Manduca, and J. Greenleaf, “Imaging Elastic Properties of Biological Tissues by Low-Frequency Harmonic Vibration,” Proc. IEEE91, 1503–1517 (2003). [CrossRef]
  16. J. Huang, J.A. Nissen, and Erik Bodegom, “Diffraction of light by a focused ultrasonic wave,” J. Appl. Phys.71(1), 70–75 (1992). [CrossRef]
  17. F. A. Duck, “Nonlinear acoustics in diagnostic ultrasound,” Ultrasound Med. Biol.28(1), 1–18 (2002). [CrossRef] [PubMed]
  18. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity (Dover Publications, Inc., New York, 1993)
  19. S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett.29, 2770–2772 (2004). [CrossRef] [PubMed]
  20. C. Usha Devi, R. M. Vasu, and A. K. Sood, “Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography,” J. Biomed. Opt.10, 044020 1–10 (2005).
  21. A. Kharine, S. Manohar, R. Seeton, R. G. M. Kolkman, R. A. Bolt, W. Steenbergen, and F. F. M. de Mul, “Poly Vinyl Alcohol gels for use as tissue phantoms in photoacoustic mammography,” Phys. Med. Biol.48, 357–370 (2003). [CrossRef] [PubMed]

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