Red blood cell as a universal optoacoustic sensor for non-invasive
temperature monitoring
Elena V. Petrova, Alexander A. Oraevsky, and Sergey A. Ermilov
TomoWave Laboratories, Inc., 6550 Mapleridge St., Suite 124, Houston, TX 77081-4629, USA
Supplementary Material
Experimental setup
The experimental setup (Fig. S1) was designed to study optoacoustic response of solutions as a
function of temperature. It utilizes a 128-channel real-time (10 frames per second, 1536
samples/channel, 40 MHz sampling rate) two-dimensional laser optoacoustic imaging system
(LOIS, TomoWave Laboratories, Houston, TX) with a linear ultrasound probe. Titanium-Sapphire
output of the laser unit (SpectraWave, TomoWave Laboratories, Houston, TX) was tuned to
805 nm near the isosbestic point of hemoglobin and produced 6 ns, 28 mJ per pulse laser radiation
with pulse repetition rate of 10 Hz. Two optical fiber bundles with rectangular output apertures of
1.5×50 mm2 each delivered light to the samples with a laser fluence about 3 mJ/cm2. The light bars
were attached on both sides of the ultrasonic array forming a backward optoacoustic illumination
mode. Fiberoptic illuminators were adjusted to maximize laser fluence in the imaging plane of the
probe at the level of sample tubes. Size of the probe and the established illumination pattern
allowed reconstruction of optoacoustic images with field of view up to 5555 mm2. The probe and
fiberoptic outputs were hermetically sealed to enable operation in liquid environment. Thin layer
of golden paint was sprayed over the front end of the probe, which significantly reduced noise
generated by impact of direct and diffuse laser light.
Fig. S1. Schematics of the experimental setup. The phantom frame with multiple tube
samples oriented orthogonally to the imaging plane was placed into a tank with an
acoustically coupling liquid.
Processing of optoacoustic signals
To increase signal-to-noise ratio and remove low-frequency optoacoustic artifacts manifested in
the background, we performed digital post processing of optoacoustic signals with zero-phase
infinite impulse response bandpass filter (1-5 MHz sixth order Butterworth) using built-in filtfilt
function in Matlab (Mathworks, Natick, MA). The optoacoustic signals generated by 0.635 mm
tubes had the main lobe of their spectrum within the bandwidth of utilized probe (1.5-6 MHz at 6dB) for the entire range of studied temperatures. The detected waveforms preserved their original
N-shaped form, and it was not necessary to perform deconvolution of the probe’s impulse
response.
Studied samples
Porcine blood samples were obtained from a local slaughterhouse on the day of experiments. To
prevent coagulation, the samples were aliquoted into 4mL BD Vacutainer blood collection tubes
containing sodium heparin (NH) 75 USP (BD, Franklin Lakes, NJ) and additional 0.1 mL of 2000
USP sodium heparin (Alfa Aesar, Ward Hill, MA) solution in phosphate buffered saline (PBS) at
pH 4.7 (Sigma-Aldrich, St. Louis, MO). The same PBS was used to dilute samples of whole blood,
when necessary.
Hemoglobin (Hb) samples were prepared using lyophilized powder of Hb human (Sigma-Aldrich,
St. Louis, MO) diluted in PBS pH 4.7. At low concentrations we were able to reach complete
dissolution of hemoglobin powder. However, at concentrations exceeding 1 mM, hemoglobin was
dissolving poorly and we used filtration with a GP 0.22 m Millex filter to remove undiluted
clusters. The concentrations were verified by measuring optical absorption. The extinction
coefficient of an Hb-PBS solution was found to be  = 2.21  0.01 M-1cm-1 at =805 nm.
Cupric sulfate solutions were used in experiments with objective to compare temperatures of zero
optoacoustic response and maximum solution density (see the dedicated section below). The
samples were prepared using CuSO45H2O (purity  99%, Kai Tech Labs) diluted in distilled
water. Previously we showed that optical absorbance of cupric sulfate around 800 nm has
negligible increase with temperature as compared to the overall changes in optoacoustic response,
and in our studies could be considered constant.15
To measure temperature of zero optoacoustic response in PBS and water we prepared suspensions
of dried Higgins Eternal Black Ink (Sanford, Bellwood, IL). The colloid solutions had no visible
precipitant for at least 3 weeks. The water-ink and PBS-ink compositions had 805 nm optical
absorbances of 0.91 and 0.92 cm-1, respectively.
The test tubes were filled with blood, hemoglobin, and other samples using 1 mL Luer Slip Tip
syringe and single-use 23 gauge hypodermic needles, avoiding air bubbles. Measurements of
optical absorbance were done using spectrophotometer (Evolution 201, Thermo Scientific,
Waltham, MA).
Measurements of density as a function of temperature
Temperature function of cupric sulfate solution density was evaluated using measurements with
specific gravity hydrometer 1.000-1.070 (Fisherbrand Hydrometers, Fisher Scientific, Pittsburgh,
PA). During experiments, a 300 mL 33 cm tall cylinder with hydrometer was filled with cupric
sulfate solution and placed in the temperature controlled bath. The measurements were performed
in the temperature range of -6 to 23C with precision of 0.0001. Lower temperatures were not
accessible due to spontaneous crystallization of cupric sulfate.
Processing of ThOR data
The normalized ThOR data was fitted with a second order polynomial function consistent with
other publications.20,23,32 According to our experimental methodology, we expressed the function
in the following manner:
4∆𝑇𝑚𝑎𝑥
𝑇−𝑇0
̅̅̅̅
(𝑇 − 𝑇0 )(𝑇 − 𝑇1 ) +
𝑂𝐴 = − (𝑇 −𝑇
.
)3
𝑇 −𝑇
1
0
1
0
(S1)
̅̅̅̅ is the normalized optoacoustic intensity; T – temperature (C), T1 – fixed normalization
Where 𝑂𝐴
temperature, where ̅̅̅̅
𝑂𝐴 = 1. In biological applications, it is prudent to select T1 as a normal
physiological temperature, for humans T1 = 37C; T0 is the temperature of zero optoacoustic
response; Tmax is a maximum nonlinear temperature deviation in the temperature range [T0 T1].
If Tmax = 0, the function becomes linear, identical to the one described in our previous studies of
the aqueous cupric sulfate in the smaller temperature range.15 Fig. S2 helps to understand the
mathematical meaning of Tmax.
Fig. S2. Mathematical illustration of the maximum nonlinear temperature deviation
Tmax.
Temperature dependent behavior of the normalized optoacoustic response can be represented as a
sum of its linear and nonlinear components. The linear component connects the points (T0, 0) and
(T1, 1) with a straight line:
𝑇−𝑇
̅̅̅̅
𝑂𝐴𝐿 = 𝑇 −𝑇0 .
1
(S2)
0
The nonlinear component is represented by the parabolic portion:
4∆𝑇𝑚𝑎𝑥
̅̅̅̅
(𝑇 − 𝑇0 )(𝑇 − 𝑇1 ).
𝑂𝐴𝑁𝐿 = − (𝑇 −𝑇
)3
1
0
(S3)
̅̅̅̅𝑁𝐿 (𝑇) =
Nonlinear temperature deviation T = TT* could be calculated by assuming 𝑂𝐴
∗
̅̅̅̅𝐿 (𝑇 ):
𝑂𝐴
4∆𝑇
𝑚𝑎𝑥
(𝑇 − 𝑇0 )(𝑇 − 𝑇1 ).
∆𝑇(𝑇) = − (𝑇 −𝑇
)2
(S4)
With maximum Tmax at T = (T0 – T1)/2.
(S5)
1
0
The procedure to find the parameters T0 and Tmax for each sample was as following:
(1) T0 was estimated directly for each sample as a temperature where polarity of the normalized
optoacoustic intensity changed from positive to negative. Due to very small noise, we were able
to determine zero transition of the normalized optoacoustic intensity with accuracy limited by
individual temperature measurements.
(2) Not-normalized optoacoustic intensity data was fitted with a parabolic function (S1) with fixed
parameters T0 and T1, and unknown Tmax and the normalization scaling factor.
Temperature of zero optoacoustic response and temperature of maximum density in cupric sulfate
solutions
It is known that for water optoacoustic effect should change polarity at 3.98C, a temperature
where volumetric thermal expansion coefficient changes its sign from positive to negative.31 That
implies that normally generated local optoacoustic compression will become rarefaction. The
phenomenon happens because of water having maximum density at that particular temperature.
Therefore, we suggest that in other aqueous solutions, including hemoglobin solutions and
intracellular environment of erythrocytes, optoacoustic effect disappears and then changes polarity
due to the same reason. However, we expect the temperature of maximum density will depend on
the composition and concentration of the solution. For example, such temperature shift was
observed in solutions of sodium chloride.44 In these experiments, we used a cupric sulfate model
to elucidate physical meaning of the parameter T0 in temperature dependent optoacoustic response.
We measured normalized optoacoustic intensity and density of aqueous cupric sulfate solutions as
a function of temperature. The cupric sulfate was preferred over hemoglobin, since it produces
larger variation of T0 for the set of achievable concentrations.15 To eliminate possible effects of
the acoustic coupling medium we performed experiments using distilled water and sodium
chloride (23wt%). Fig. S3(a) shows normalized optoacoustic intensity for two concentrations of
cupric sulfate and calculated normalized Grüneisen parameter of water as a control. The Grüneisen
parameter of water was calculated with 1C intervals using temperature dependences of speed of
sound, specific heat capacity, and thermal expansion coefficient.15 Fig. S3(b) shows T0 directly
measured as a temperature at zero optoacoustic intensity and its linear regression as a function of
concentration. Data matches our previous results obtained by extrapolation of the fitted data.15 The
measurements were not affected by using different surrounding media, implying that the entire
optoacoustic stress generation happens inside the tubes with sample solutions.
Fig. S3. Temperature of zero optoacoustic response and temperature of maximum
density in cupric sulfate solutions. (a) The temperature dependence of normalized
optoacoustic image intensity for aqueous solutions of CuSO4*5H2O and calculated
Grüneisen parameter of water. Dash-dot line indicates zero optoacoustic response. (b)
Concentration dependence of the measured temperature T0, where optoacoustic
response is equal to zero. Data was obtained from the samples placed in three different
surrounding media: distilled water and aqueous solution of NaCl (23wt%). (c)
Temperature dependence of specific gravity measured for aqueous solution of cupric
sulfate (240 mM) with a corresponding second-order polynomial fit. The relationship
for water is presented for reference.31 Arrows mark points of maximum density for the
salt and distilled water. (d) Temperature of the maximum density (TSGmax) as a function
of cupric sulfate concentration.
Fig. S3(c) shows two temperature dependent curves of density. The lower one – known
relationship for water.31 The top one – measured relationship for 240 mM cupric sulfate. Arrows
indicate maxima of the fitted parabolic functions. Consistent with the Despretz’s law37, maximum
density for cupric sulfate is shifted towards more negative temperatures. Fig. S3(d) summarizes
measured temperatures of the maximum density for different concentrations of cupric sulfate.
When fitted with a linear regression model, the resultant equation effectively replicates the one
obtained for T0 measured via normalized optoacoustic imaging.
The equivalence of two relationships allows us to conclude that T0 represents the temperature of
maximum density of a sample solution, which is manifested by the absence of thermal expansion,
and therefore – optoacoustic response. Note, that the data fits in the Fig. S3(b) and S3(d) intercept
the ordinate axis at about 4C, which corresponds to the temperature of maximum density of the
pure solvent – distilled water.
Temperatures of zero optoacoustic response in water and PBS
The linear fit line in Fig. 3(b) intercepts the ordinate at about 3C, which is slightly different from
3.98C expected from pure water. To prove that it represents properties of the used solvent
(phosphate buffered saline), we measured T0 in PBS with small amount of dried carbon ink
suspension providing optical absorption to otherwise clear solution. As a control we had the same
concentration of carbon microparticles suspended in distilled water. Since the carbon suspension
does not create chemical bonds with solvent, we expected that the found T0 would characterize
properties of the studied solvent. Fig. S4 shows two normalized ThOR profiles.
Fig. S4. Zoomed-in linear fragments of ThOR normalized at 12C reveal different T0
for distilled water and phosphate buffered saline at pH 7.4.
In the small temperature range (2-14C) linear fit could be applied. The estimated T0 in aqueous
solution was equal to 4.0  0.2C (N = 3), consistent with that of pure water, and in PBS it was 2.9
 0.3C (N = 3).