Photoacoustic measurement of the
Grüneisen parameter of tissue
Da-Kang Yao
Chi Zhang
Konstantin Maslov
Lihong V. Wang
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Photoacoustic measurement of the Grüneisen
parameter of tissue
Da-Kang Yao, Chi Zhang, Konstantin Maslov, and Lihong V. Wang
*
Washington University in St. Louis, Optical Imaging Laboratory, Department of Biomedical Engineering, St. Louis, Missouri 63130
Abstract.
The Grüneisen parameter, a constitutive parameter in photoacoustics, is usually measured from iso-
baric thermal expansion, which may not be valid for a biological medium due to its heterogeneity. Here, we
directly measured the Grüneisen parameter by applying photoacoustic spectroscopy. Laser pulses at wave-
lengths between 460 and 1800 nm were delivered to tissue samples, and photoacoustic signals were detected
by flat water-immersion ultrasonic transducers. Least-squares fitting photoacoustic spectra to molar optical
absorption spectra showed that the Grüneisen parameter was
0
.
81
0
.
05
(mean
SD) for porcine subcuta-
neous fat tissue and
0
.
69
0
.
02
for porcine lipid at room temperature (22°C). The Grüneisen parameter of a red
blood cell suspension was linearly related to hemoglobin concentration, and the parameter of bovine serum was
9% greater than that of water at room temperature.
©
2014 Society of Photo-Optical Instrumentation Engineers (SPIE)
[DOI:
10.1117/1
.JBO.19.1.017007
]
Keywords: Grüneisen parameter; photoacoustic; spectroscopy.
Paper 130780R received Oct. 29, 2013; revised manuscript received Dec. 23, 2013; accepted for publication Dec. 31, 2013; published
online Jan. 28, 2014.
1 Introduction
As a new biomedical imaging technique, photoacoustic tomog-
raphy (PAT) is able to noninvasively visualize relatively deep
structures in biological tissue.
1
–
3
In PAT, light pulses are deliv-
ered into biological tissue. Light absorbed by tissue is converted
to heat that generates an initial pressure rise, which produces
the acoustic waves used to construct a photoacoustic image.
The Grüneisen parameter
Γ
of tissue relates the initial pressure
p
0
to the light absorption by the following expression:
1
,
4
p
0
¼
Γ
μ
a
F
, where
μ
a
is the absorption coefficient of tissue,
and
F
is the local light fluence. Therefore, quantitative photo-
acoustic imaging of
μ
a
relies on accurate knowledge of the
Grüneisen parameter.
The Grüneisen parameter can be expressed as
Γ
¼
β
v
2
s
∕
C
p
¼
β
∕
ð
κρ
C
p
Þ
,
1
,
4
where
β
is the isobaric volume expan-
sion coefficient,
C
p
is the specific heat,
v
s
is the acoustic speed,
κ
is the isothermal compressibility, and
ρ
is the mass density.
Unfortunately, Grüneisen parameters measured from bulk iso-
baric thermal expansion may not be valid in photoacoustics
in heterogeneous biological media. In pulsed photoacoustics,
due to the short heating time, thermal expansion can occur in
the immediate vicinity of the optical absorbers, where the tis-
sue
’
s thermo-mechanical parameters are different from its aver-
age bulk parameters as measured by the conventional isobaric
thermal expansion method. In addition, Grüneisen parameters
were found to vary even within the same type of tissue.
5
For
example, the Grüneisen parameter of fat tissue is estimated to
be between 0.7 and 0.9,
5
and that of blood is estimated to be
between 0.152 and 0.226,
6
causing uncertainty in photoacoustic
imaging and errors in inverting for tissue composition from
the PAT measurements. So far only a few measurements of
the Grüneisen parameter of tissue have been conducted using
photoacoustic and photothermal methods.
6
–
8
Soroushian et al.
8
measured the Grüneisen parameter of liver tissue using an
interferometric method, in which thermal expansion due to
light absorption causes sample surface displacement. Once
the surface displacement was measured, the Grüneisen param-
eter was calculated based on Poisson
’
s ratio of the tissue, its
acoustic speed, the optical attenuation depth, and a complicated
geometrical correction factor, resulting in
>
38%
relative error.
8
Savateeva et al.
6
measured the Grüneisen parameter of blood
using a photoacoustic method, in which 2090-nm-wavelength
light heated water in blood to generate photoacoustic signals.
The signals were detected by an ultrasonic transducer with
calibrated absolute sensitivity. The absorption coefficient of
blood was determined by the temporal profile of the signal,
and the Grüneisen parameter was calculated from the signal
amplitude. However, the measured Grüneisen parameter
6
was
significantly lower than the minimal value of the theoretically
estimated one. In addition to biological materials, Laufer
et al.
9
observed linear relations between the Grüneisen param-
eters of copper and nickel chloride solutions and their
concentrations.
Photoacoustic pressure wave generation and detection is a
complicated process, making quantitative measurements pos-
sible only by calibrating the measuring system with homo-
geneous media that have well-known Grüneisen parameters.
However, the relationship between the Grüneisen parameter
and the signal detected by the ultrasonic transducer depends
on other optical and mechanical parameters of the medium.
To account for the potential influences, we apply photoacoustic
spectroscopy (PAS)
10
,
11
over a wide optical wavelength range.
We chose the wavelength range at the peak absorption of tissue
constituents, such as hemoglobin in blood and lipid in fat tissue,
to reduce measurement uncertainties due to optical scattering.
The difference between our method and the isobaric thermal
expansion method lies in the way molecules are heated.
Although the isobaric thermal expansion method heats up
*Address all correspondence to: Lihong V. Wang, E-mail:
lhwang@wustl.edu
0091-3286/2014/$25.00 © 2014 SPIE
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both the optical absorbers and the interstitial less absorbing
material, our method heats up only the optical absorbers.
2 Materials and Method
2.1
Photoacoustic Spectroscopy
To acquire photoacoustic spectra of tissue, we assembled a PAS
system, shown schematically in Fig.
1
. An optical parametric
oscillator (OPO) laser system (NT242-SH, Altos Photonics,
Bozeman, Montana) emits light pulses at a wavelength tunable
from 460 to 1800 nm. The laser pulse repetition rate was 1 kHz,
and the pulse duration was 5 ns. The laser beam passed through
a 1.2-mm-diameter aperture and a beam sampler (BSF10-B,
Thorlabs, Newton, New Jersey), and then irradiated a 1.4-
mm-thick tissue sample in the front part of a water-filled cylin-
drical chamber. The tissue sample was enclosed between two
2.5-
μ
m-thick ultrafilm membranes (01865-AB, SPI Supplies,
West Chester, Pennsylvania). The chamber, with a 20-mm-
inner-diameter, was fixed horizontally. A flat ultrasonic trans-
ducer was installed coaxially with the laser beam at the
rear of the chamber and positioned at roughly one acoustic
Rayleigh distance from the sample. When a 6-mm diameter,
2.25-MHz ultrasonic transducer (V323-SU, Olympus, Waltham,
Massachusetts) was used, its distance from the sample was
19 mm; when a 3-mm diameter, 20-MHz ultrasonic transducer
(V316-SM, Olympus) was used, the distance was 33 mm.
Each laser pulse reflected from the free sample surface
produced a bipolar photoacoustic signal whose amplitude is
proportional to the specific optical absorption (i.e., absorbed opti-
cal energy per laser pulse per unit volume in
J
∕
m
3
) and the
Grüneisen parameter of the tissue. After being detected by the
ultrasonic transducer, the photoacoustic signal was amplified
by two amplifiers of 56 dB combined gain (ZFL-500LN, Mini-
Circuits, Brooklyn, New York). Two photodiode detectors,
calibrated by a digital power meter (PM100D, Thorlabs, Newton,
New Jersey) with a thermal power sensor (S302C, Thorlabs),
were used separately to measure the pulse energy: one
(SM05PD2A, Thorlabs) for the 460- to 1050-nm wavelength
range and another (SM05PD4A, Thorlabs) for the 1050- to
1800-nm range. Both photoacoustic and photodiode signals
were collected by a computer through a 12-bit, 200-MHz
digitizer (NI PCI-5124, National Instruments, Austin, Texas).
Photoacoustic spectra were acquired by extracting peak-to-
peak amplitudes from the photoacoustic signals measured at
varied optical wavelength at room temperature (22°C).
2.2
Setup Calibration
The Grüneisen parameter of tissue was determined by fitting the
photoacoustic spectra, which were measured in a wavelength
range in which the absorption coefficient of the tissue is
much greater than its reduced scattering coefficient. Thus, the
effect of optical scattering was negligible. The initial photo-
acoustic signal
p
ð
t
Þ
generated in planar transmission geometry
nearly follows the energy deposition along the acoustic axis
within the boundaries of the sample:
7
p
ð
t
Þ¼
Γ
μ
a
F
exp
ð
μ
a
ct
Þ
;
(1)
where
Γ
is the Grüneisen parameter,
μ
a
is the absorption coef-
ficient of the tissue,
F
is the light fluence,
c
is the speed of
sound, and
t
is time of acoustic arrival at the ultrasonic trans-
ducer. Correspondingly, the peak-to-peak voltage amplitude (
A
)
of a photoacoustic signal normalized by
F
can be expressed as
Λ
ð
λ
Þ¼
A
∕
F
¼
α
Γ
μ
a
ð
λ
Þ
;
(2)
where
α
is a system calibration factor and
λ
is the optical wave-
length. The normalized amplitude,
Λ
, is plotted versus
λ
to yield
a photoacoustic spectrum. Although independent of
Γ
, the
parameter
α
is affected by the frequency response of the ultra-
sonic transducer and by many other factors, including light
penetration depth, transmittance through interfaces, acoustic
diffraction, and acoustic attenuation.
7
Estimates show that in
our system geometry, the greatest error can be caused by the
ultrasonic transducer, which works as a bandpass filter for
the acoustic pressure at the transducer surface. By convolving
Eq. (
1
) with the electrical impulse response of the transducer
—
experimentally measured and then approximated as the first
derivative of a Gaussian pulse
—
one can find that
α
depends
on the central frequency of the transducer
ω
0
, approximately
following:
α
∼
ω
2
0
∕
½
ω
2
0
þð
c
μ
a
Þ
2
.
Fig. 1
Schematic of the photoacoustic spectroscopy system.
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To reduce errors in the photoacoustic spectra, the normalized
amplitude was acquired by averaging 1000 photoacoustic sig-
nals at each wavelength. The acquired photoacoustic spectra
of the tissue were linear least-squares fitted to its molar absorp-
tion spectra with the Grüneisen parameter being the fitting
parameter.
To calibrate for the parameter
α
for the 2.25-MHz ultrasonic
transducer, we measured the photoacoustic spectrum of water
at 22°C from 1100 to 1400 nm, with a 10-nm wavelength
step size. A photoacoustic spectrum of water is shown in
Fig.
2(a)
. Knowing the absorption spectrum of water and the
Grüneisen parameter of water (0.12 at 22°C),
12
we set
α
as a
fitting parameter. The solid curve in Fig.
2(a)
is a fit to the
absorption spectrum of water.
13
After measuring three water
samples,
α
was calibrated to be a constant of
25.3
0.3 mV
·
cm
∕
μ
J
(
mean
standard error
). Corresponding to Fig.
2(a)
,
Fig.
2(b)
shows a plot of the normalized amplitude versus
the absorption coefficient, indicating that the normalized ampli-
tude is proportional to the absorption coefficient.
Similarly, we calibrated the PAS system with a 20-MHz
ultrasonic transducer. A wavelength range from 1200 to
1600 nm was scanned with a 10-nm wavelength step size. A
typical photoacoustic spectrum of water at 22°C is shown in
Fig.
2(c)
, in which the solid curve is a fit to the absorption spec-
trum of water.
13
We scanned five water samples, and found that
the constant
α
was
20.8
0.1 mV
·
cm
∕
μ
J
(
mean
SE
). A cor-
relation between the normalized amplitude and the absorption
coefficient is shown in Fig.
2(d)
, indicating the linearity of
the PAS system because
ω
2
0
≫
ð
c
μ
a
Þ
2
for a 20-MHz transducer.
3 Results
3.1
Grüneisen Parameter of Lipid
We used the PAS system with a 2.25-MHz ultrasonic transducer
to measure the Grüneisen parameter of porcine lipid. Lard, i.e.,
porcine lipid, was melted at 50°C. After being injected into the
front part of the chamber shown in Fig.
1
, the lipid sample was
cooled to room temperature (22°C). An acoustic impedance of
1.43 MPa
·
s
∕
m
14
was lower than that of water, causing a trans-
mission coefficient to water of 1.03. Photoacoustic spectra of
the lipid were measured at a wavelength range from 1680 to
1800 nm, with a 10-nm scan step size. In the wavelength
range, the value of the absorption coefficient of lipid is from
1.6 to
10.6 cm
−
1
,
15
and the reduced scattering coefficient is esti-
mated to be
1.4 cm
−
1
.
16
In our method, spectral fitting for the
Grüneisen parameter is mainly affected by the large-amplitude
data points with large
μ
a
, which overwhelms the scattering coef-
ficient. A typical photoacoustic spectrum measured from a sam-
ple is shown in Fig.
3(a)
, in which the solid curve shows a fit to
the absorption spectrum of 100% lipid, previously obtained by
Fig. 2
Photoacoustic spectra of water used for system calibration. (a) Typical photoacoustic spectrum
measured by a 2.25-MHz ultrasonic transducer, in which the normalized amplitude (mean
standard error) is plotted versus wavelength. Knowing the absorption coefficient of water and the
Grüneisen parameter of water at 22°C (0.12), we fitted Eq. (
1
) to the photoacoustic spectrum (solid
curve), yielding a value of
25
.
4
mV · cm
∕
μ
J for
α
. (b) Correlation of the normalized amplitude measured
by the 2.25-MHz transducer and the absorption coefficient, showing that the normalized amplitude is
proportional to the absorption coefficient. (c) Typical photoacoustic spectrum measured at 22°C by a
20-MHz ultrasound transducer. A fit to Eq. (
1
) yields a value of
21
.
0
mV · cm
∕
μ
J for
α
. (d) The normalized
amplitude measured by the 20-MHz transducer linearly related to the absorption coefficient.
Journal of Biomedical Optics
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Anderson et al.
15
with a relatively large spectral step size. Our
photoacoustic spectrum matches their absorption spectrum very
well at wavelengths from 1680 to 1800 nm, except at 1730 nm.
Anderson et al. found that 1720 nm was a peak wavelength,
but we found that the peak wavelength was 1730 nm, which is
consistent with a recent report.
17
Therefore, when we fitted the
photoacoustic spectrum, we excluded the 1730-nm wavelength.
After fitting five lipid samples, we found that the Grüneisen
parameter of porcine lipid at 22°C was
0.69
0.02
(
mean
standard deviation
).
With the five samples, we estimated the absorption coeffi-
cient of lipid at 1730 nm. The normalized amplitude is plotted
versus the absorption coefficient, as shown in Fig.
3(b)
, but the
amplitude at 1730 nm is excluded. We found that the absorp-
tion coefficient of lipid at 1730 nm was
11.7
0.3 cm
−
1
(
mean
SD
), instead of
8.7 cm
−
1
as reported by Anderson
et al.
3.2
Grüneisen Parameter of Subcutaneous Fat
Tissue
We used the PAS system with a 2.25-MHz ultrasonic transducer
to measure the Grüneisen parameter of fat tissue. Porcine sub-
cutaneous fat tissue with a 16-mm thickness from the loin was
cut into 1.4-mm-thick slices. After being attached to the ultra-
film in front of the ultrasonic transducer (Fig.
1
), the fat tissue
slice was scanned over the wavelength range from 1690 to
1800 nm, with a 10-nm scan step size, except 1730 nm.
Since the absorption coefficient of fat tissue in this wavelength
range is close to
10 cm
−
1
and the reduced scattering coefficient
is
2.4 cm
−
1
,
18
the effect of scattering was negligible. Figure
4
shows a typical photoacoustic spectrum of fat tissue at 22°C.
The composition of the fat tissue was measured thoroughly.
By weight, the porcine subcutaneous fat was composed of
81.6%
0.7%
(
mean
SE
) lipid,
14.1%
0.6%
water, and
2.0%
0.1%
collagen,
19
which is equivalent to a mean volume
fraction of 0.83 for lipid (
f
lipid
) and 0.13 for water (
f
water
)
since the lipid density is
0.91 g
∕
ml
.
20
We calculated the absorp-
tion coefficients of fat tissue (
μ
fat
a
) in terms of the absorption
coefficients of lipid (
μ
lipid
a
) and water (
μ
water
a
):
μ
fat
a
¼
μ
lipid
a
f
lipid
þ
μ
water
a
f
water
.
18
The calculated absorption spectrum fits the photo-
acoustic spectra of fat tissue well. The measurement from one
sample is shown in Fig.
4
. Using six samples, we found that
the Grüneisen parameter of the fat tissue at 22°C was
0.81
0.05
(
mean
SD
).
3.3
Grüneisen Parameter of Serum
We used the PAS system with a 20-MHz ultrasonic transducer to
measure the Grüneisen parameter of bovine serum. Ten milliliters
of defibrinated bovine blood (Quad Five, Ryegate, Montana)
was centrifuged at
700
×
g
for 20 min. The supernatant was
Fig. 3
Photoacoustic spectrum of porcine lipid (lard). (a) Typical plot
of the normalized amplitude (mean
SE) versus wavelength. The
solid curve is a fit to the lipid absorption spectrum reported previ-
ously,
15
except at the 1730-nm wavelength. (b) Plot of the normalized
amplitude (mean
standard deviation) versus the absorption coeffi-
cient, showing that the normalized amplitude of lard is proportional
to its absorption coefficient. The absorption coefficient of lipid at
1730 nm was calculated to be
11
.
7
0
.
3
cm
−
1
(mean
SD).
Fig. 4
Typical photoacoustic spectrum of porcine subcutaneous fat
tissue. The normalized amplitude (mean
SE) is plotted versus
wavelength. The solid curve is a fit to the absorption spectrum of
81.6% lipid and 14.1% water, yielding a Grüneisen parameter of 0.79.
Fig. 5
Typical photoacoustic spectrum of bovine serum. The normal-
ized amplitude (mean
SE) is plotted versus wavelength. The solid
curve is a fit to the absorption spectrum of 92% water, yielding the
Grüneisen parameter to be 0.13.
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collected to measure the photoacoustic spectrum of bovine
serum. We scanned the serum at 22°C at wavelengths from
1100 to 1550 nm, with a 10-nm step size. A typical photoacous-
tic spectrum of the bovine serum is shown in Fig.
5
. Using
Γ
as
a fitting parameter, we found that the serum photoacoustic
spectrum matched the absorption spectrum of water well, as
shown in Fig.
5
. We dried 7.83 g of serum in an isotemp
incubator (Fisher Scientific, Pittsburgh, Pennsylvania) at 65°C
overnight, and found 0.64 g remaining, indicating that 92%
of the serum was water. The 8% remainder consists of proteins,
whose absorption coefficient is negligible in the wavelength
range. By fitting the photoacoustic spectra of three serum
samples to the absorption spectrum of 92% water, we found
that the Grüneisen parameter of bovine serum at 22°C was
0.132
0.002
(
mean
SD
).
3.4
Grüneisen Parameter of Red Blood Cells
We used the PAS system with a 20-MHz ultrasonic transducer to
measure the Grüneisen parameter of bovine red blood cells, col-
lected from defibrinated bovine blood after centrifugation. The
cells were washed two times using phosphate buffered saline
(PBS; Sigma-Aldrich, St. Louis, Missouri) and then suspended
in PBS. We measured the hemoglobin concentration of the cell
suspension using a spectrophotometer (Varian Cary 50). After
a cell sample was mixed with Drabkin
’
s solution (Sigma-
Aldrich), the hemoglobin concentration was determined by
the absorbance of the mixture, which was measured by the
spectrophotometer at a 540-nm wavelength. We prepared
three cell suspensions, RBC1, RBC2, and RBC3, in which the
hemoglobin concentrations were 59.3, 39.6, and
15.9 mg
∕
ml
,
respectively. To oxygenate the red blood cells, we incubated
the cell suspensions with oxygen for 1 h. The oxygenated cell
suspensions at 22°C were scanned in the wavelength range from
460 to 560 nm, with a 5-nm scan step size. Within the wave-
length range, the mean value of the absorption coefficient of
oxygenated blood with
96.5-g
∕
l
hemoglobin concentration
has been reported to be
111 cm
−
1
and the corresponding
reduced scattering coefficient is
27 cm
−
1
21
, indicating that the
effect of scattering is negligible. Figure
6(a)
shows three typical
photoacoustic spectra of red blood cell suspensions at the differ-
ent hemoglobin concentrations, where the solid curve, long
dashed, and short dashed lines are fits to the absorption spectra
of 59.3, 39.6, and
15.9 mg
∕
ml
oxygenated hemoglobin, respec-
tively.
22
After measuring six RBC1 samples, six RBC2 samples,
and 10 RBC3 samples, we found that the Grüneisen parameters
were
0.129
0.006
(
mean
SD
) for the cell suspension with
15.9-mg
∕
ml
hemoglobin at 22°C,
0.138
0.004
for that
with
39.6 mg
∕
ml
, and
0.144
0.002
(
mean
SD
) for that
with
59.3 mg
∕
ml
, as shown in Fig.
6(b)
. A linear fit yields
the relation of the Grüneisen parameter of red blood cell suspen-
sion to its hemoglobin concentration
C
HbO
2
(
mg
∕
ml
):
Γ
¼
0.124
þ
0.000333
C
HbO
2
.
(3)
4 Discussion
Our measurement is based on the linearity of the normalized
photoacoustic signal amplitude to the product of the absorption
coefficient and the Grüneisen parameter. However, the linearity
can easily fail due to many experimental factors, such as optical
scattering,
23
finite ultrasonic transducer bandwidth,
24
and
optical absorption saturation,
25
leading to the mismatch of
a photoacoustic spectrum to its absorption spectrum. We exam-
ined the linearity by fitting the photoacoustic spectrum to the
absorption spectrum. In this study, the hemoglobin concentra-
tion was <
60 mg
∕
ml
, and we obtained a coefficient of determi-
nation
>
0.97
, as shown in Fig.
6
. We used the photoacoustic
spectrum with
R
2
>
0.97
to determine the Grüneisen parameter,
greatly reducing uncertainty in the measurement. As mentioned,
it is estimated that the Grüneisen parameter of fat tissue is in a
range from 0.7 to 0.9.
5
We found that the Grüneisen parameter
was 0.81 for subcutaneous fat tissue, consistent with the estima-
tion. For blood with
110-mg
∕
ml
hemoglobin, the Grüneisen
parameter is estimated to be between 0.152 and 0.226.
6
Consistent with that estimation, we estimate using Eq. (
2
)
that the Grüneisen parameter of the blood is 0.16.
In our method, the measurement uncertainties in the normal-
ized amplitude, the setup constant, and the absorption coeffi-
cient cause uncertainty in the measured Grüneisen parameter.
The standard error in the normalized amplitude can be reduced
to
3.6
×
10
−
5
by averaging. The system error in the calibration
can be estimated as follows. Water was used to calibrate our
PAS system, but the acoustic attenuation in fat tissue, about
0.63 dB
·
cm
−
1
·
MHz
−
1
,
26
is different from that of water.
Since we used a 2.25-MHz ultrasonic transducer to measure
1.4-mm-thick fat tissue samples, the acoustic attenuation in
the fat samples caused a 2% decrease in photoacoustic signal
amplitude. Another system error may result from the acoustic
impedance mismatch between the fat sample and water (acoustic
coupling medium). Since the acoustic impedance of fat is
Fig. 6
Photoacoustic spectra of bovine red blood cell suspension.
(a) Typical plots of the normalized amplitude (mean
SE) versus
wavelength. The hemoglobin concentrations of the red blood cell
suspensions (RBC1, RBC2, and RBC3) were 59.3, 39.6, and
15
.
9
mg
∕
ml. Each curve (solid, long dashed, and short dashed) is
a fit to the absorption spectrum of oxygenized hemoglobin. (b) Plot
of the Grüneisen parameter (mean
SD) of red blood cell suspension
versus hemoglobin concentration. The solid line indicates a linear fit.
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Yao et al.: Photoacoustic measurement of the Grüneisen parameter of tissue
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1.38 MPa
·
s
∕
m
,
27
the mismatch caused a 3% increase in photo-
acoustic signal amplitude, which is larger than the signal
decrease caused by acoustic attenuation and partially compen-
sates for it. Correspondingly, the largest error in the Grüneisen
parameter of fat tissue is caused by the inaccuracy in the absorp-
tion coefficient. Here, the absorption coefficient of the fat tissue
was calculated in terms of the absorption coefficients of lipid
and water and their volume fractions. Assuming that the uncer-
tainty in the absorption coefficient of the fat tissue comes from
the uncertainties in the volume fractions, in which standard
errors are 0.0074 for lipid and 0.0052 for water,
19
we estimate
that the standard error
σ
Γ
∕
Γ
of the Grüneisen parameter is 2.4%
for fat tissue.
Similarly, the uncertainty in the normalized amplitude and
acoustic attenuation is negligible in the red blood cell measure-
ment. The attenuation coefficient of the cell suspension with 5%
hematocrit is
0.5 dB
∕
cm
at 20 MHz,
28
and at the frequency the
attenuation coefficient of water is
0.9 dB
∕
cm
.
29
We estimate that
the difference in acoustic attenuation between the red blood cell
sample and water is 0.5%. Therefore, the accuracy in the
Grüneisen parameter of the red blood cell suspension is deter-
mined by the accuracy of the absorption coefficient of the cell
suspension. In this study, we fitted the photoacoustic spectrum
to published data of absorption coefficients measured by spectro-
photometry, which usually yields a <
0.5%
relative standard
deviation (
σ
μ
a
∕
μ
a
). From Eq. (
3
), we estimate that the relative
standard error
σ
Γ
∕
Γ
of the Grüneisen parameter is 2.2% for
the red blood cell suspension with
15.9-mg
∕
ml
hemoglobin.
Our results show that the Grüneisen parameter not only
varies between different types of tissues, but also changes
with different tissue compositions. We found that the Grüneisen
parameter of subcutaneous fat tissue at 22°C was 0.81. In the
human body, various adipose tissues are found within bone
marrow, the brain, breast, colon, and liver, with different
lipid percentages. It is very likely that these adipose tissues
have different Grüneisen parameters. Precise measurement of
the Grüneisen parameter of each adipose tissue will allow us
to reconstruct quantitative photoacoustic images of organs.
The Grüneisen parameter of blood linearly increases with the
hematocrit, and it might be necessary to take this fact into
account in photoacoustic imaging of the circulatory system.
The Grüneisen parameter of whole subcutaneous fat tissue,
0.81, is greater than that of its either major component, lipid
(0.69) and water (0.12). As water and lipid do not mix, they
are compartmentalized in fat tissue. Correspondingly, at the
optical wavelength at which light is absorbed by lipid, thermal
expansion occurs in lipid only. As water is significantly less
compressible than lipid, the surrounding water suppresses the
expansion of the enclosed lipid, reducing the effective com-
pressibility of the lipid.
30
Inversely proportional to the effective
compressibility, the measured Grüneisen parameter of fat
becomes greater than that of pure lipid. Further, the lower the
concentration of lipid is, the greater the Grüneisen parameter of
the lipid-water mixture becomes.
Similar to the case of lipid, the dependence of the Grüneisen
parameter of RBCs on concentration [Eq. (
3
)] can be partially
explained by the fact that the temperature rise is confined to
RBCs, which have smaller compressibility (
34.1
·
10
−
11
m
2
∕
N
than plasma (
44.3
·
10
−
11
m
2
∕
N
) by a factor of 1.3.
Correspondingly, the measured Grüneisen parameter must be
related to the Grüneisen parameter of RBCs by a factor of
½
1.3
·
ð
1
−
x
Þþ
x
−
1
,
30
where
x
is the volume concentration
of RBCs. Therefore, a higher concentration of RBCs leads to
a greater Grüneisen parameter.
5 Conclusions
We measured the Grüneisen parameter of tissue by applying
PAS. Using the photoacoustic spectrum, which linearly fits to
its corresponding absorption spectrum, we improved measure-
ment accuracy by precluding nonlinear uncertainties. We found
that at 22°C, the Grüneisen parameter was 0.80 for porcine sub-
cutaneous fat tissue and 0.69 for porcine lipid. The Grüneisen
parameter of red blood cell suspension was linearly related to
hemoglobin concentration, and the parameter of serum was
9% greater than that of water at 22°C. Our method relies on
accurate system calibration and a linear relationship between
the photoacoustic amplitude and optical absorption. The accu-
racy of our measurement can be further improved by precisely
modeling the systematic errors due to acoustic attenuation,
impedance mismatch, etc. This method can potentially be
applied to measure the Grüneisen parameters of many other
types of tissue, where the optical wavelength ranges should
be chosen carefully to ensure that absorption overwhelms
scattering.
Acknowledgments
We thank Prof. James Ballard for his close reading of the manu-
script. This work was sponsored in part by National Institutes of
Health grants DP1 EB016986 (NIH Director
’
s Pioneer Award),
R01 EB016963, R01 CA134539, U54 CA136398, R01
EB010049, R01 CA157277, and R01 CA159959. L.W. has
a financial interest in Microphotoacoustics, Inc. and Endra,
Inc., which, however, did not support this work. K.M. has a
financial interest in Microphotoacoustics, Inc., which, however,
did not support this work.
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