PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 54 (2009) 3129–3139
Audio frequency in vivo optical coherence elastography
Steven G Adie1, Brendan F Kennedy, Julian J Armstrong,
Sergey A Alexandrov and David D Sampson
Optical+Biomedical Engineering Laboratory (OBEL), School of Electrical, Electronic &
Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley,
Western Australia 6009, Australia
Received 1 December 2008, in final form 3 April 2009
Published 6 May 2009
Online at stacks.iop.org/PMB/54/3129
We present a new approach to optical coherence elastography (OCE), which
probes the local elastic properties of tissue by using optical coherence
tomography to measure the effect of an applied stimulus in the audio frequency
range. We describe the approach, based on analysis of the Bessel frequency
spectrum of the interferometric signal detected from scatterers undergoing
periodic motion in response to an applied stimulus. We present quantitative
results of sub-micron excitation at 820 Hz in a layered phantom and the first
such measurements in human skin in vivo.
(Some figures in this article are in colour only in the electronic version)
For centuries physicians have used palpation, i.e. sensing stiffness through touch, as an
indicator of abnormal or diseased tissue (Greenleaf et al 2003, Fatemi et al 2003). For
example, cancer is often detected via the increased hardness or stiffness of a tumour compared
to the surrounding tissue (Fatemi et al 2003, Gao et al 1996). Young’s modulus (the ratio
of stress to strain) of breast tumours may vary from that of the surrounding tissue by up to a
factor of 90, and may vary by up to four orders of magnitude in soft tissues (Greenleaf et al
2003, Sarvazyan et al 1998). The ability to move beyond the subjectivity and low resolution
of palpation to the quantitative and non-invasive imaging of the elastic properties of tissue
should provide an important advance in diagnostic capability.
The term elastography refers to the measurement and imaging of the elastic properties
of tissue. Elastography has been performed with magnetic resonance imaging (MRI), with
ultrasound imaging and with optical methods (Greenleaf et al 2003, Fatemi et al 2003, Parker
1Present address: Biophotonics Imaging Laboratory, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, 405 North Mathews Avenue, Urbana, IL 61801, USA.
0031-9155/09/103129+11$30.00 © 2009 Institute of Physics and Engineering in MedicinePrinted in the UK3129
3130 S G Adie et al
et al 1996, Gao et al 1996). The elastic properties of the medium so determined are subject
to the spatial resolution and noise limitations of the respective parent modalities, as well as
to other practical limitations such as gross tissue motion artefact and the acoustic propagation
loss (Parker et al 2005). Optical coherence tomography (OCT) has superior spatial resolution
to the aforementioned modalities up to its penetration depth, typically a few millimetres; thus,
The majority of OCE schemes reported to date have been based on speckle-tracking
techniques and have employed predominantly quasi-static mechanical loading of tissue to
quantitatively assess local tissue motion (Ko et al 2006, Rogowska et al 2004, Chan et al
2004, Schmitt 1998). One study has utilized non-contact acoustic excitation (20 kHz) with
the objective of enhancing OCT contrast (Edney and Walsh 2001) but did not demonstrate
quantitative elastography. More recently, techniques have been developed based on phase-
sensitive spectral-domain OCT (Liang et al 2008, Wang et al 2006). However, in these
techniques, the excitation frequency has been limited to 20 Hz or less.
In this paper, we present a new approach to OCE suitable for quantitative measurement
of tissue elastic properties in the hundred hertz to kilohertz frequency range. This frequency
range, which has been the target range for elastography based on other imaging modalities,
1998, Parker et al 1990, Potts et al 1983). Section 2 describes the theory behind our approach.
and human skin tissue in vivo. Section 5 reports the main conclusions and implications of the
Consider an interferometric signal generated by the combination of a reference light beam
and light backscattered from scatterers undergoing harmonic displacement along the optical
(z) axis in response to an external excitation, all light having been derived from the same
low-coherence source. At frequencies of up to several kHz (with the corresponding sound
wavelength ? ∼ 1 m), scatterers in a medium of typical thickness ∼1 mm can be expected
to move in phase with each other. The dynamic interferometric signal amplitude of interest
depends not only on the scatterer’s vibration amplitude but also on the quasi-static phase of
the interferometer, which, in turn, is governed by the precise differential axial position of the
scatterer relative to the reference path in the interferometer. This undesired dependence of the
dynamic displacement on the quasi-static displacement is generally known as interferometric
signal fading (Udd 1991). It can be overcome by various means, including by polarization-
in the orthogonal polarization channels, denoted by the subscripts 1 and 2, can be described
i1(z,t) = 2ρ
i2(z,t) = 2ρ
IRIScos[φDC+ φSsin(2π?t)] (1)
where ? is the frequency of the harmonic excitation, ISand IRare the sample and reference
optical intensities, respectively, φDCis the quasi-static interferometric phase (modulo 2π)
governed by the mean axial position of the scatterer, φs =
λd(z,?), where λ is the
Audio frequency in vivo optical coherence elastography3131
Figure 1. (a) Amplitude of Bessel functions J1–J4versus vibration amplitude; (b) J3/J1and J4/J2
versus vibration amplitude. The dashed line denotes the asymptote.
mean optical wavelength in the medium, d is the local, generally frequency-dependent, axial
displacement amplitude, and ρ is the detector responsivity. It is readily seen from (1) and
(2) that the value of φDCalters the detected signal and therefore the apparent dynamic signal
amplitude. Equations (1) and (2) may be expanded as a series of Bessel functions (Udd 1991,
Sasaki and Okazaki 1986), resulting in the following:
where Jnis the nth-order Bessel function of the first kind. Choosing for example φDC= π/2 in
(3) and (4), it is clear that the even harmonics of the signal fade in channel 1 and the converse
is true in channel 2. Thus, to account for the effect of signal fading, the quadrature channels
may be combined incoherently, i.e. by calculating the sum of the envelopes squared followed
by a square root operation. Having accounted for signal fading, the amplitude of the even
harmonics is proportional to J2n, and that of the odd harmonics to J2n+1.
The objective of the OCE scheme presented here is to determine from an interferometric
measurement of φSthe amplitude of the dynamic axial displacement, i.e. the vibration
amplitude of the scatterer. This has been achieved through the piecewise mapping of the
measured ratios of Bessel harmonic terms to vibration amplitude based on (3) and (4).
Figure 1 displays the dependence of these terms as a function of vibration amplitude.
In our approach, the (full-fringed) interferometric signal is recorded in two dimensions
(an OCT B-scan), and the quadrature signals are filtered and incoherently combined at ?,
i1(z,t) = 2ρ
J0(φS) + 2
J2n+1(φS)sin(2π(2n + 1)?t)
i2(z,t) = 2ρIRIS
J0(φS) + 2
J2n+1(φS)sin(2π(2n + 1)?t)
3132 S G Adie et al
Figure 2. Schematic of the OCT system employing balanced optical quadrature detection. The
insets show the phantom and in vivo experimental geometries. BBS: broadband source, PC:
polarization controller, FD-ODL: frequency-domain optical delay line, VOA: variable optical
attenuator and PBS: (fibre-based) polarizing beamsplitter.
2?, 3? and 4?. The theoretical values of the ratio J3/J1are used to map the experimentally
measured value of the ratio to vibration amplitude, as shown in figure 1(b). By also computing
the ratio J4/J2, the unambiguous range of operation can be extended beyond the asymptotic
point at approximately λ/3 by using it to identify on which side of the asymptotic value lies
the measured value of the ratio J3/J1. At a mean wavelength of λ = 1.3 μm, this permits the
measurement of vibration amplitudes of up to about 0.65 μm, corresponding to the second
zero of J3. Note that the measured vibration amplitude is the product of the physical vibration
amplitude and the refractive index of the scattering medium, which we term ‘optical vibration
amplitude’ for clarity.
3. Experimental method and data analysis
A schematic of the experimental fibre-based, time-domain OCT system utilizing balanced
optical quadrature detection is presented in figure 2. The broadband superluminescent source
emitted light at a mean wavelength of 1334 nm with a near-Gaussian spectrum and 3 dB
bandwidth of 42 nm, launching 7.75 mW of polarized light into the OCT system. After
passing through a circulator, the light was split by a 50/50 coupler into the sample and
reference arms. The reference arm comprised a frequency-domain optical delay line utilizing
a blazed grating with 400 lines mm−1and a blaze angle of 13.9◦. In the sample arm, a triplet
lens (f = 30 mm) was used to focus the beam through a glass window that provided a rigid
platform upon which the samples were placed and provided a lateral resolution of 15.3 μm.
The sensitivity of the system, using a glass–air interface at normal incidence as a calibrated
reflector, was measured to be 113 dB. Dynamic compression was applied to the sample,
as indicated in figure 2 (inset), with a piezoelectric rod actuator operated at a frequency of
820 Hz. The stiffness of the actuator was 4 N μm−1.
After recombination, the light was split into orthogonal polarization channels by
fibre-based polarization beam splitters with >27 dB extinction ratio.
photodetectors, providing a common-mode rejection ratio of 25 dB, were used to detect
the polarization channels.
of the sample arm window while adjusting the polarization controllers and the variable optical
Audio frequency in vivo optical coherence elastography3133
attenuator. Signalsinexactquadrature(zeromean, equalamplitudesand90◦phasedifference)
produced a circular pattern on an oscilloscope operated in the XY mode.
the sample was vibrated or not. Without applied vibration, conventional OCT images were
et al 2003). With applied vibration, the FD-ODL was operated on-pivot and the carrier
frequency was, in effect, generated by the vibration of sample scatterers. On-pivot operation
has the advantage of reducing the impact of the phase noise (e.g. arising from the jitter of the
galvanometer) and maximizing the vibration sensitivity of the system, which we measured to
be 50 nm. Phase noise introduced by jitter of the galvanometer would directly contribute to
the vibration harmonics and, therefore, could not be removed by filtering. As the vibration
amplitude is determined through measurement of the ratio between vibration harmonics, the
minimum detectable vibration would increase.
spectra do not overlap each other, which in turn restricts the OCT electrical signal bandwidth
to a fraction of the vibration frequency. We define a = ?/?f as the ratio of the vibration
frequency to the electrical bandwidth ?f and required a ? 4 to ensure adequate separation
(anddetection)oftheharmonicspectra. TheA-scanvelocity, ν, canberelatedto?f(Sampson
and Hillman 2004) and, therefore, the velocity must satisfy
Higher vibration frequencies, therefore, permit higher acquisition rates. In this study, a
conservative A-scan frequency of 0.26 Hz was used, leading to an electrical signal bandwidth
of 130 Hz, which resulted in a ≈ 6.
To test the approach, we constructed a three-layer phantom comprising a readily
compressible layer (translucent silicone sealant) sandwiched between two stiffer, less
compliant layers (translucent polypropylene plastic) of near-identical elastic properties. All
three layers were approximately 0.3 mm thick and ∼20 mm square. The piezoelectric rod
actuator (∼2 mm diameter rod) was coupled to the phantom via a glass layer (∼10 mm square
piece cut froma microscope slide) to facilitateapplication of uniform pressureto the phantom.
The glass and actuator were aligned to the centre of the phantom, and the rod was collinear
with the optical beam, as shown in the inset of figure 2. For the in vivo measurements, the
actuator wascoupled directlytothehuman skin, withouttheuseof anintermediate glasslayer.
OCE images were recorded for a range of piezoelectric actuator drive voltages.
Both OCT (no vibration) and OCE measurements were made on the phantom and on
human skin. All images to be presented in the next section were generated from single
B-scans. The OCE images contain fewer A-scans and were acquired over a smaller field-of-
view than the OCT images in order to limit the total acquisition time and, therefore, minimize
both sample motion artefact and boundary effects between OCT and OCE images. Naturally,
these effects were more prominent in the in vivo measurements.
The interferometric signal in each channel was 12-bit digitized at a rate of
0.6 MSamples s−1with a 12-bit analogue-to-digital converter.
signals was carried out in post-processing. Intensity images were calculated for four separate
harmonic frequencies by applying bandpass filters centred at ?, 2?, 3? and 4? (producing,
in total, eight images from the two channels). The signals forming these images were then
separately demodulated utilizing the Hilbert transform, to extract the vibration harmonics,
and the resulting orthogonal envelopes at each frequency in each channel were incoherently
combined to account for signal fading. The resulting four images were used to produce an
image of the local vibration amplitude using the ratio J3/J1, as previously described.
Analysis of the recorded
3134S G Adie et al
Figure 3. OCT and OCE images and derived plots for the three-layer phantom: (a) OCT image
(no applied vibration), dimensions: 1.6 by 1.1 mm; (b) average A-scan derived from (a); (c) OCE
imageforactuatordrivevoltageof1.0Vp-p, dimensions: 1.6by0.4mm, and(d)averagevibration
amplitude for indicated actuator drive voltages (black superimposed lines are linear fits). For all
parts of the figure, the optical beam was incident from the left and vibration was applied from the
When the signal-to-noise ratio (SNR) of the harmonic signals corresponding to J3or J1
is low, it was found that calculation of the vibration amplitude from their ratio is prone to
error. Notably, in the case of zero vibration amplitude, the ratio J3/J1is simply determined
by the spectral noise floor of the system. To determine the validity of the computed vibration
amplitude, two conditions based on the SNR of the detected harmonics were applied. The
measured signal was considered valid when the SNRs of both J1and J3were at least 15 dB, or
if the SNR of J1was at least 30 dB. The SNR of each harmonic was calculated relative to the
noise floor of the spectrum in its vicinity, in order to account for any spectral dependence. The
spectral noise floor was calculated as the average of the bandpass filtered signals centred at
Jm−3?f and Jm+3?f, where m = 1 or 3 and ?f is the signal bandwidth of the fundamental
to be 30 dB below the signal for skin measurements.
4. Results and discussion
The OCT and OCE images of the three-layer phantom are presented in figure 3. Figure 3(a)
shows the OCT image (64 A-scans over a lateral range of 1.1 mm) and the average A-scan
is shown in figure 3(b). Figure 3(c) shows the OCE image (16 A-scans over the central
0.4 mm part of the OCT lateral range). OCE images were recorded for a range of piezoelectric
actuator drive voltages between 0.6 and 2.2 V peak-to-peak. Both the depth dimension and
vibration amplitude are products of their respective physical dimension and refractive index,
as described in section 2.
The OCT image and average A-scan clearly show the three layers of the phantom. In
the first layer, a higher optical signal is evident than that in the third layer, even though both
Audio frequency in vivo optical coherence elastography3135
Figure 4. Gradient of linear fits to the traces in figure 3(d).
layers are made from identical material, because of the extinction upon propagation through
the turbid medium.
the first and third layers and show an approximately linear variation with depth in the silicone
(middle) layer. This behaviour is expected since the silicone is much more compressible than
the plastic. In contrast to the OCT signal, the average vibration amplitude is greatest in the
third layer, as expected, since it is proximal to the applied pressure and distal to the sample
arm window. The finite vibration amplitude of the first layer and its increase with actuator
drive voltage indicates that the sample arm glass window is not perfectly rigid.
The actual vibration amplitude in a given layer of the phantom is related to the strain,
defined as ?L/L0, where L0is the thickness of the layer. The gradient of the vibration
amplitude is equal to the total strain in the layer less the strain due to the pressure when the
actuator is at rest. Therefore, in effect, we measure the amplitude of the dynamic differential
strain in each layer. Constant vibration amplitude is observed in the first and third layers
indicating bulk motion of the layer, for which the dynamic differential strain is approximately
zero. In contrast, a linear variation in the strain is observed within the silicone layer (see linear
fits in figure 3(d)), indicating that it is relatively more compressible than the plastic layers
and, therefore, has a lower dynamic Young’s modulus (at 820 Hz). The Young’s modulus E is
where the stress is defined as the force, F, applied to an object over the cross-sectional
Figure 4 plots the gradient of the optical vibration amplitude versus optical pathlength
by the actuator has the expected linear dependence on drive voltage, this linear relationship
indicates that the compression of the silicone layer is elastic, i.e. in the linear region of the
material’s stress–strain curve. The gradient of the optical vibration amplitude versus optical
pathlength against actuator drive voltage in the second plastic layer is also plotted in figure 4.
A linear fit of the gradient in both layers is presented. The ratio of the dynamic differential
strain between the silicone and plastic layers (average of the dynamic differential strain in the
two plastic layers) is calculated to determine their relative elastic properties. Using (6), it is
3136S G Adie et al
Figure 5. OCT and OCE images and derived data for human skin in vivo: (a) OCT image (without
applied vibration), dimensions: 1.6 by 0.8 mm; (b) average A-scan; (c) vibration amplitude image
at an actuator drive voltage of 2.4 V p-p, dimensions: 1.6 by 0.4 mm, and (d) average vibration
amplitude for various actuator drive voltages (black superimposed lines are linear fits). For all
parts of the figure, the optical beam was incident from the left and the excitation was applied from
calculated that the dynamic (820 Hz) Young’s modulus of the plastic, based on these five data
points, is 30 ± 12 times greater than that of the silicone, assuming equal stress in each layer.
It should be noted that the first plastic layer also responds approximately linearly (not plotted
here), due to residual bulk motion of the sample, indicating that it is not rigidly coupled to the
Figure 5 presents results of in vivo measurements of human skin obtained by compressing
the ‘webbing’ between the thumb and index finger between the actuator rod and the sample-
arm window. The OCT image in figure 5(a) consists of 32 A-scans taken over a lateral scan
range of 0.8 mm. The lateral spacing is relatively large compared to the lateral resolution in
order to obtain both reasonable field of view and acquisition time given the low A-scan rate.
The vibration amplitude measurement in figure 5(c) consisted of eight A-scans centred at the
same lateral position, but over a 0.4 mm range.
A relatively uniform signal is in evidence from the skin’s surface to a depth of 0.2 mm,
corresponds to a layer with low vibration amplitude in figure 5(d). This layer is attributed to
the stratum corneum and is expected to display negligible vibration amplitude due to its tight
coupling to the rigid glass window and its low compressibility.
Below the expected extent of the stratum corneum, z = 0.2 mm, the OCT image does
not show any clear boundary between skin layers until a depth of approximately 0.85 mm. In
contrast, all the vibration amplitude traces in figure 5(d) show a distinct difference in slope
at about 0.65 mm. This change in slope indicates the presence of two layers of different
compressibility, with the deeper layer (with greater slope) being relatively more compressible.
These layers are attributed to the epidermis and dermis, respectively, which are known to have
distinct elastic properties (Agache and Humbert 2004).
Audio frequency in vivo optical coherence elastography3137
Figure 6. Gradient of linear fits to traces in figure 5(d).
The discontinuity evident in the vibration amplitude versus pathlength curves of
figures 3(d) (1.8 V p-p and 2.2 V p-p traces) and 5(d) is an artefact occurring at the intersection
of the two calibration regions in the J3/J1curve plotted in figure 1(b) (when the vibration
amplitude is approximately λ/3).
The slopes of the vibration amplitude versus pathlength within the epidermis and dermis
were estimated by performing linear fits to each region, as shown in figure 5(d). Figure 6
plots the gradients of these linear fits versus actuator drive voltage. A highly linear response
is observed for the epidermis indicating that the response is elastic. In the same manner as for
the epidermis, the resulting linear relationship suggests that the response of the dermis is also
elastic. From the measurements in figure 6, it is calculated that the epidermis has a Young’s
modulus 3.7 ± 0.2 times greater than the dermis, assuming equal stress in the epidermis and
Accordingly, our experimental geometry was designed so that, in each case, the actuator
applied even pressure to the sample coaxially with the optical beam. Further work is required
to establish the feasibility of accurately detecting vibration amplitude in the presence of lateral
scatterer motion, such as when shear waves are excited.
The in vivo application of dynamic OCE is limited by two factors: acquisition speed
and the need for coaxial optical beam and vibration excitation, with the light source and
excitation source incident from the same direction. In our acquisition scheme, point-by-point
acquisition with TD-OCT is limited by the requirement for adequate frequency separation
between the OCT signal spectra at each of the vibration harmonics, each of which broadens
as the acquisition rate increases. At the present A-scan rate of 0.26 Hz, the measurements
are more susceptible than desirable to sample motion artefacts. Acquisition time can be
improved by an excitation frequency in the kHz regime and beyond, for example, through
the use of ultrasonic transducers (Fatemi and Greenleaf 1998). Potentially, both issues could
be addressed by use of an ultrasonic transducer array such that a focussed ultrasound beam
excites the sample in the 1–10 kHz range. Alternatively, the use of phase-sensitive spectral-
domain OCT (Wang et al 2006, 2007) could be used with a high-speed A-scan rate and slow
lateral scan to observe a given lateral location over several oscillation cycles. However, to
date, this method has not been utilized for in vivo measurements or measurements at vibration
frequencies beyond about 20 Hz.
3138S G Adie et al
Quantitative measurements of tissue elastic moduli require the local stress field to be
including tissues. Such moduli are also dependent on tissue viscosity at low frequencies, and
excitation at above 100 Hz may prove an advantage in this regard, avoiding this potential
ambiguity. A combination of careful calibration and modelling, and comparison with gold
standards, will be required to accurately measure absolute elastic properties. This will be the
focus of future work.
In conclusion, we have presented a new dynamic OCE method suited to differential strain
measurement based on sub-micron displacements at frequencies in the 100 Hz to 10 kHz
regime. Using the method, it was possible to distinguish the differences in elasticity at
820 Hz between the layers in a three-layer phantom. The first reported quantitative in vivo
OCE measurements of human skin presented here demonstrated varying elastic responses
between layers. The minimum detectable vibration amplitude was measured to be 50 nm, and
the maximum measured vibration amplitude was 0.65 μm.
of samples by scanning the excitation frequency over the audio range, which has the potential
to detect weak resonances. Such measurements of tissue response, at single or multiple
excitation frequencies, could potentially aid in the diagnosis of a range of medical conditions,
including tumours and arterial plaques.
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