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Towards single molecule detection
using photoacoustic microscopy
Amy M. Winkler, Konstantin Maslov, Lihong V. Wang
Amy M. Winkler, Konstantin Maslov, Lihong V. Wang, "Towards single
molecule detection using photoacoustic microscopy," Proc. SPIE 8581,
Photons Plus Ultrasound: Imaging and Sensing 2013, 85811A (4 March
2013); doi: 10.1117/12.2004265
Event: SPIE BiOS, 2013, San Francisco, California, United States
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Towards single molecule detection using photoacoustic microscopy
Amy M. Winkler
a
, Konstantin Maslov
a
, Lihong V. Wang
*a
a
Department of Biomedical Engineering, Washingt
on University in St. Louis, Whitaker Hall, One
Brookings Dr., St. Louis, MO USA 63130
ABSTRACT
Recently, a number of optical imaging modalities have ach
ieved single molecule sens
itivity, including photothermal
imaging, stimulated emission microscopy, ground state depletion microscopy, and transmission microscopy. These
optical techniques are based on optical absorption contrast, extending single-molecule detection to non-fluorescent
chromophores. Photoacoustics is a hybrid technique that utilizes optical excitation and ultrasonic detection, allowing it to
scale both the optical and acoustic regimes with 100% sensitivity to optical absorption. However, the sensitivity of
photoacoustics is limited by thermal noise, inherent in the medium itself in the form of acoustic black body radiation. In
this paper, we investigate the molecular sensitivity of photoacoustics in the context of the thermal noise limit. We show
that single molecule sensitivity is achievable theoretically
at room temperature for molecules with sufficiently fast
relaxation times. Hurdles to achieve single molecule sensitivity in practice include development of detection schemes
that work at short working distance, <100 microns, high frequency, >100 MHz, and low loss, <10 dB.
Keywords:
photoacoustic, microscopy, single molecule, thermal noise, acoustic black body radiation
1.
INTRODUCTION
Photoacoustic tomography has been drawing the attention of the biomedical imaging community in the last decade [1].
A cross-over between optical imaging and ultrasound imaging, photoacoustics harnesses both the exquisite molecular
contrast of optical absorption and the low scattering of ultrasound. Clinically, photoacoustic tomography is being used
to add optical contrast to ultrasound imaging of breast canc
er, due to its ability to image with acoustic resolution at
depths beyond the optical diffusion limit, down to 2 cm demonstrated
in vivo
[2] and 8 cm in tissue phantoms [3], while
retaining specific molecular sensitivity from optical absorption. Photoacoustics has also proven to be a highly scalable
technique, achieving subcellular resolution within a millimeter
depth of tissue [1, 4, 5]. Since the photoacoustic effect
involves the transduction of light energy into sound ener
gy, photoacoustic images are largely background free and
present 100% sensitivity to optical absorption [6]. The high imaging contrast of photoacoustics has enabled
quantification of a number of vascular metrics, including total hemoglobin concentration (C
Hb
), blood oxygen saturation
(sO
2
), flow speed or volumetric flow rate, ca
pillary density, metabolic rate of oxygen (MRO
2
), and pulse wave velocity
(PWV) [7, 8]. Furthermore, nonlinear effects have enabled ultrasharp spectroscopy [9] and even sub-diffraction imaging
with spatial resolution <100 nm [10], making photoacoustic imaging the only optical imaging technique to break through
both the optical diffusion and optical diffraction limits. At the
sub-diffraction scale, however, the achievable resolution is
limited by sensitivity as the number of molecules within a resolvable voxel becomes very small; for example, a 10 nm
cube contains only 3 hemoglobin molecules at the corpuscular concentration, i.e. the concentration within a red blood
cell.
Recently, a number of absorption-sensitiv
e optical techniques have achieved si
ngle molecule sensitivity at room
temperature, including photothermal [11], stimulated emission [12], ground state depletion [13], and transmission
microscopy [14]. In this paper, we discuss the challenges in achieving a similar sensitivity using photoacoustic
microscopy and estimate the sensitivity with optimum illumination and state-of-the-art acoustic detectors to be between
10s and 1000s of molecules, depending on the molecule.
*
e-mail: lhwang@biomed.wustl.edu
Photons Plus Ultrasound: Imaging and Sensing 2013, edited by Alexander A. Oraevsky, Lihong V. Wang,
Proc. of SPIE Vol. 8581, 85811A · © 2013 SPIE · CCC code: 1605-7422/13/$18 · doi: 10.1117/12.2004265
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Photocoustics is sensitive to the rapid deposition of heat due to optical absorption. In order to maximize our signal, we
must consider how rapidly a single molecule can generate heat. Molecules have a finite relaxation time which ultimately
limits the amount of heat deposited, or equivalently the number of photons absorbed, in a given time interval. The rate of
heat deposition,
ܪ
ሺ
ݐ
ሻ
, follows the formula for absorption saturation, described in laser theory [15].
ܪ
ሺ
ݐ
ሻ
ܫߪߟ=
ሺ
ݐ
ሻ
ቀ1+
ூ
ሺ
௧
ሻ
ூ
ೞೌ
ቁൗ
(1)
where
ߟ
is the fraction of absorbed energy released as heat,
ߪ
is the absorption cross-section,
ܫ
ሺ
ݐ
ሻ
is the optical intensity,
ܫ
௦௧
is the saturation intensity, and
ܾ
is a factor of 1 or 2 depending on the elect
ronic energy states of
the molecule. In the
Fourier domain, absorption saturation induces harmonics for
ܫ
ሺ
ݐ
ሻ
ܫ=
൫1+cos
ሺ
݂ߨ2
ݐ
ሻ
൯
, and the harmonic amplitudes,
ܪ
, are given by:
ܪ
=
ଶ
൬
ఎఙூ
బ
൫
ଵାୡ୭ୱ
ሺ
ଶగ
௧
ሻ
൯
ଵାூ
బ
൫
ଵାୡ୭ୱ
ሺ
ଶగ
௧
ሻ
൯
ூ
sat
⁄
൰cos
ሺ
݂ߨ2݊
ݐ
ሻ
dt=
ଶఎఙூ
sat
ඥ
ଵାଶூ
బ
ூ
sat
⁄
൬
ඥ
ଵାଶூ
బ
ூ
sat
⁄
ି
ሺ
ଵାூ
బ
ூ
sat
⁄ሻ
ூ
బ
ூ
sat
⁄
൰
భ
మ
ൗ
ି
ଵ
ଶ
ൗ
,
≥1݊
.
(2)
This explicit solution was found in [16]. For
ܪ
ଵ
, the peak occurs at
ܫ
≈2.4ܾ
ିଵ
ܫ
sat
and the peak value is about
ܪ
ଵ ୮ୣୟ୩
≈
ܾߪߟ0.34∙
ିଵ
ܫ
sat
.
Consider the Fourier domain solution in the
linear case for a cubic source of dimension,
ܽ
, using the Born approximation
[17]:
ሺ
݂
ሻ
=
ఉ
ଶ
షమഏ/ೡ
ೞ
௭
ܪ݂
෩
ሺ
݂
ሻ
sinc
ሺ
ݒ2/݂ܽߨ2
௦
ሻ
(3)
where
ߚ
is the thermal expansion coefficient,
ݒ
௦
is the speed of sound,
ܥ
is the specific heat at constant pressure,
ݖ
is the
distance from the center of
the spherical absorber to th
e point of measurement, and
ܪ
෩
ሺ
݂
ሻ
is the Fourier transform of
ܪ
ሺ
ݐ
ሻ
.
A single molecule is small compared to the wavelength of so
und and is therefore approximat
ely an acoustic point source.
By allowing
గ
௩
ೞ
→0
, we arrive at the equation fo
r an acoustic point source:
ሺ
݂
ሻ
=
ఉ
ଶ
షమഏ/ೡ
ೞ
௭
ܪ݂
෩
ሺ
݂
ሻ
. (4)
To account for ultrasonic absorption in the medium, which becomes significant for large
݂
, Eq. 4 can be modified to
include the exponential attenuation term:
ሺ
݂
ሻ
=
ఉ
ଶ
షమഏ/ೡ
ೞ
௭
ܪ݂
෩
ሺ
݂
ሻ
݁
ିఈ
ം
௭
. (5)
The optimum acoustic frequency can be de
termined analytically by setting the derivative with respect to frequency equal
to zero:
݂
peak
=
ଵ
ሺ
ఊఈ௭
ሻ
భ/ം
. (6)
In aqueous medium, the attenuation is
ߙ
water
=25∙10
ିଵହ
Hz
-2
m
-1
and
ߛ
water
=2
. The optimum frequency for a giving
imaging depth,
ݖ
, is shown in Figure
1
.
2.
THEORY
2.1.
Photoacoustic Signal
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The optimum regime for single molecule de
tection is clearly at shallow depth an
d at high frequency. This regime also
facilitates tight optical focusing, meaning that optical intensities above the saturation intensity can be achieved for many
molecules. For example, the saturation intensity of oxygenated hemoglobin in the Q-band of the absorption spectrum is
100 MW/cm
2
[18]. In the case of a Gaussian beam profile, a peak intensity of 500 MW/cm
2
can be achieved with 2 W
incident power with beam waist 0.5
μ
m, achievable with commercially available
continuous wave lasers and objective
lenses.
Substituting
ܪ
ଵ ୮ୣୟ୩
ܾߪߟ≈0.34∙
ିଵ
ܫ
sat
and
݂
peak
=
ሺ
ݖߙߛ
ሻ
ିଵ/ఊ
into the equation for pressure amplitude, we arrive at an
expression for the optimized
pressure amplitude at the fundamental frequency,
|
ଵ
|
, given by:
|
ଵ
|
=0.17∙൬
ఉ
షభ/ം
ሺ
ఊఈ
ሻ
భ/ം
൰
ሺ
ܾߪߟ
ିଵ
ܫ
ୱୟ୲
ሻ
ݖ൫
ି
ሺ
ଵାଵ/ఊ
ሻ
൯
. (7)
Here, the expression for
|
ଵ
|
is grouped such that the first term in parentheses contains parameters related to the medium,
the second term to the absorber, and the last term to the detector.
2.2.
Acoustic Black Body Radiation
Thermal noise exists in the medium and can be detected by a transducer in the form of acoustic black body radiation
[19]. The form of thermal noise is derived using the equal pa
rtition principle of statistical mechanics, which states that
each degree of freedom contributes a noise energy equal to
ࢀ
, where
is the Boltzmann constant and
ࢀ
is
temperature. Analogous to the derivation of black body radiation in optics, the power spectrum of thermal noise can be
calculated by computing the number of degrees of freedom in a unit volume of temperature
ࢀ
and differentiating with
respect to frequency,
ࢌ
. The power spectrum of thermal noise radi
ation per unit area per unit solid angle,
ࢁ
, is given by
[19]:
ܷ
ሺ
݂
ሻ
݇=
݂∙ܶ
ଶ
ݒ/
௦
ଶ
(8)
where
ݒ
௦
is the speed of sound. Here we assume that black
body radiation condition is satisfied, i.e. that acoustic
absorption in the media is sufficiently high, which is va
lid for a semi-infinite medium. This energy is radiated
omnidirectionally; however, an acoustic
detector only receives a fraction of
this energy based on its etendue,
ߝ
. The
etendue is defined in terms of the area of the detector,
ܣ
, which we assume is uniform and not apodized, and the
normalized directivity of the transducer,
ܦ
ሺ
ߚ,ߙ
ሻ
.
ܣ=ߝ
∫∫
|
ܦ
ሺ
ߚ,ߙ
ሻ|
ଶ
ߚ݀ߙ݀
(9)
The theory of angular spectrum relates
ܦ
ሺ
ߚ,ߙ
ሻ
to the amplitude transmittance of the transducer,
ݐ
ሺ
ݕ,ݔ
ሻ
[20]:
Figure 1: (color online) Pressure amplitude vs.
frequency for various depth regimes in water.
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ܦ
ሺ
ߚ,ߙ
ሻ
=
∫∫
ݐ
ሺ
ݕ,ݔ
ሻ
exp
ߣ/ߨ2݆൫
ሺ
ݕߚ+ݔߙ
ሻ
ݕ݀ݔ݀൯
∫∫
|
ݐ
ሺ
ݕ,ݔ
ሻ|
ଶ
ݕ݀ݔ݀
ൗ
(10)
where
ሺ
ߚ,ߙ
ሻ
are direction cosines,
ሺ
ݕ,ݔ
ሻ
is position on the transducer, and
ߣ
is the acoustic wavelength. For an
unapodized transducer,
=ܣ
∫∫
|
ݐ
ሺ
ݕ,ݔ
ሻ|
ଶ
ݕ݀ݔ݀
. (11)
Applying Parceval’s theorem and substituting
ܣ
for
∫∫
|
ݐ
ሺ
ݕ,ݔ
ሻ|
ଶ
ݕ݀ݔ݀
yields:
∫∫
|
ܦ
ሺ
ߚ,ߙ
ሻ|
ଶ
ߣ= ߚ݀ߙ݀
ଶ
. (12)
So
ߝ
of a diffraction-limited transducer is equal to
ߣ
ଶ
and the power spectrum of th
ermal noise received by the
transducer,
ܵ
, is given by:
ܵ
ሺ
݂
ሻ
ܷ=
ሺ
݂
ሻ
ߣ∙
ଶ
݇=
ܶ
. (13)
In order to be detectable even with an ideal detector, the
power spectrum of the photoacoustic signal must be larger than
݇
ܶ
. Cooling the medium to actually counterproductive in the case of photoacoustics since the thermal expansion
coefficient,
ߚ
, decreases with temperature. The power of the op
timized photoacoustic signal at the fundamental
frequency within a bandwidth
݂݀
,
ܵ
௦
, is given by:
ܵ
௦
ሺ
݂=݂
ሻ
=݂݀
|
ଵ
|
ଶ
ܣ
ሺ
ܼ2
ሻ
⁄
=0.014∙൭
ఉ
మ
ష
మ
ം
ೌ
మ
ሺ
ఊఈ
ሻ
మ
ം
൱
ሺ
ܾߪߟ
ିଵ
ܫ
ୱୟ୲
ሻ
ଶ
ݖ൬
ିଶ
ቀ
ଵା
భ
ം
ቁ
൰ܣ
(14)
where
ܼ
is the characteristic acoustic impedance of the medium.
Here, again, we group terms into parameters related to the medium, absorber, and detector. The detector parameters can
be written in terms of the numerical aperture,
ܣܰ
ଶ
/ܣ≈
ሺ
ݖߨ
ଶ
ሻ
. In water,
ߚ
୵ୟ୲ୣ୰
=4x10
ିସ
1/K,
ߛ
water
=2
,
ܼ
୵ୟ୲ୣ୰
=
1.5
MRayls/m
2
,
ܥ
୵ୟ୲ୣ୰
=4000
J/kg/K, and
ߙ
water
=25∙10
ିଵହ
Hz
-2
m
-1
, so the acoustic power of an absorber in water
is given by:
ܵ
௦ ୵ୟ୲ୣ୰
ሺ
݂=݂
ሻ
=݂݀
ሺ
687 m/W
ሻ
∙
ሺ
ܾߪߟ
ିଵ
ܫ
ୱୟ୲
ሻ
ଶ
ሺ
ܣܰߨ
ଶ
ݖ/
ሻ
. (15)
Figure 2 shows the acoustic powers and pressures generated from a single molecule of methylene blue (MB), oxygenated
hemoglobin (HbO
2
), and deoxygenated hemoglobin (HbR) as a function of working distance. At a bandwidth of 1 Hz, a
single Hb molecule generates sufficient power to overcome acoustic thermal noise in the medium at a working distance
of 1 mm. The optimum frequency at a 1 mm working distance is about 150 MHz, which presents a problem from a
detection standpoint since most transducers that operate at this frequency are optimized from broadband detection and
therefore exhibit more than 20 dB insertion loss. This lo
ss directly reduces our molecular sensitivity and pushes the
minimum detectable di
stance to around 10
μ
m, which is significantly more difficult to achieve.
The Q-band absorption properties of thes
e three molecules is shown in Table
1
[18, 21]. Note that the optimized optical
intensity only depends on the absorption lifetime,
߬
, and b. The acoustic power is calculated for a
ܣܰ
of 0.5.
Table 1: Properties of methylene blue (MB), oxygenated hemoglobin (HbO
2
), and deoxygenated hemoglobin (HbR) at
532 nm.
Molecule
Lifetime,
߬
(picoseconds)
b
ܾߪ
ିଵ
ܫ
ୱୟ
୲
ܾ=
ିଵ
߬/ߥ∙ℎ
(nanowatts)
MB 380 1 1.0
HbO
2
22 1 17
HbR 2 1 190
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loo
102
104
10
-
10-"
lo-30-
102
101
I/_
Fi
g
as
a
de
o
fre
q
ho
r
m
e
To test the t
h
a 6 mm wor
k
terms of nu
m
measured th
e
hemoglobin
w
intensity. Af
t
(NEM) by c
a
which was 3
%
using our m
o
We estimate
d
intensity in
a
b
lue and 60
0
our transduc
e
hemoglobin
m
value to wit
h
We derived
a
ultrasonic tr
a
oxygenated
h
low loss (<1
0
Pressure amplitude (Pa)
a
)
g
ure 2: (color
o
a
function of
w
o
xygenated he
m
q
uency for an
N
r
izontal black
l
e
dium in a 1 H
z
h
eory, we built
k
ing distance i
n
m
ber of molec
u
e
signal-to-noi
s
w
ithin a mono
l
t
er verifying li
n
a
lculating the
n
%
of the satur
a
o
del.
d
an NEM of 1
a
10% duty cy
c
oxygenated h
e
er
. According
t
m
olecules at a
h
in an order of
a
nd verified th
e
a
nsducer, we d
e
h
emoglobin m
o
0
dB insertion
M
o
nline) a) The
o
w
orking distan
c
m
oglobin (Hb
R
N
A of 0.5 as
a
l
ine at around
1
z
bandwidth.
3
.
a continuous
w
n
wate
r
and lo
s
u
les by about 1
0
s
e ratio for 0.1
%
l
ayer of red bl
o
n
earity with r
e
n
umber of mol
e
a
tion intensity
f
86,000 methy
l
c
le of modulat
e
e
moglobin mo
t
o our model,
w
working dista
n
magnitude.
e
sensitivity o
f
e
monstrate a s
e
o
lecules. In o
r
loss), shallow
z
(
mm
)
M
B
HbO
2
H
b
o
ptimum press
c
e for methyle
n
R
). b) The opti
m
a
function of w
o
1
0
-21
watts ind
i
.
MATERI
A
w
ave photoac
o
s
ses of around
0
X. The band
w
%
, 0.01%, an
d
o
od cells with
spect to intens
e
cules in the v
o
f
or both mole
c
4.
l
ene blue and
8
e
d continuous
w
lecules under
o
w
e should hav
e
n
ce of 6 m
m
w
5.
C
O
f
photoacousti
c
e
nsitivity of t
h
r
der to reach si
n
working dista
n
b
R
ure amplitude
n
e blue (MB),
m
um acoustic
o
rking distanc
e
i
cates the acou
A
LS AND M
o
ustic microsc
o
20 dB. The tr
a
w
idth was limi
t
d
0.001% meth
y
an average thi
c
ity, we extrap
o
o
xel and divid
i
c
ules. We then
RESULTS
8
6,000 oxygen
a
w
ave illumina
t
o
ptimum illu
m
e
an NEM of 4
w
ith 20 dB tran
O
NCLUSIO
N
c
microscopy t
o
h
ousands of m
e
n
gle molecule
n
ce (<1 mm),
a
Acoustic Power (watts)
b)
in Pascals at t
h
oxygenated h
e
power in watt
s
e for MB, Hb
O
stic noise due
t
M
ETHODS
o
py system. W
e
a
nsducer losse
s
t
ed using a loc
k
y
lene blue in
a
c
kness of 2
μ
m
o
lated the nois
e
i
ng by the SN
R
extrapolated t
o
ated hemoglo
b
t
ion. We extra
p
m
ination condit
i
4
000 methylen
e
sducer losses,
N
o
number of
m
e
thylene blue
m
sensitivity, p
h
a
nd high frequ
e
z
MB
HbO
2
H
b
h
e fundament
a
e
moglobin (H
b
s
at the funda
m
O
2
, and HbR.
T
t
o thermal noi
s
e utilized a 50
s
should reduc
e
k
-in-amplifier
a
12.7
μ
m thic
k
m
as a function
e
equivalent n
u
R
at the highes
o
the NEM at
t
b
in molecules
a
p
olated an NE
M
i
ons at the 6-
m
e
blue and 200
which agrees
w
m
olecules. Usi
n
m
olecules and
h
h
otoacoustic d
e
e
ncy (>100 M
H
z
(
mm
)
2
b
R
k
a
l frequency
b
O
2
), and
m
ental
T
he
s
e in the
MHz transdu
c
e
our sensitivit
y
to 1.25 Hz.
W
k
mold and ox
y
of incident op
u
mber of mole
t optical inten
s
t
he optimum i
n
a
t 3% the satu
r
M
of 1500 me
t
m
m working di
s
oxygenated
w
ith our meas
u
n
g a readily av
a
h
undreds of
e
tectors that w
o
H
z).
k
B
T 1Hz
c
er with
y
in
W
e
y
genated
tical
cules
s
ity,
n
tensity
r
ation
t
hylene
s
tance of
u
red
a
ilable
o
rk with
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REFERENCES
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