2.1.

Au NP Properties

The importance of metallic nanostructures originates in their ability to absorb and scatter the incident light in both the visible and infrared regions. The interaction of an electromagnetic field $E(r,t)=[E_0(t){\mathrm{e}}^{i(kz-\omega t)}]$ of a laser with gold nanoparticles causes the dielectric polarization, $\mu$, of surface charges as a result of which charges oscillates like simple dipole moment nanoparticles where $\omega$ is the angular frequency of light traveling in the $z$-direction and $k$ is the wave number. The oscillating dipole radiates electromagnetic waves with a large enhancement of the local electric field at the NP surface and polarization proportional to the incident field. This electric field leads to strong absorption and scattering at the SPR frequency by the particle which consequently damps the oscillations, causing the displacement to become out of phase, $\phi$, with the varying field and requiring an input of energy to sustain the oscillation.

The SPR absorption in Au NPs is followed by energy relaxation through nonradiative decay channels. This results in an increase in kinetic energy, leading to overheating of the local environment around the light-absorbing species. The complex refractive index is defined as

According to the principle of causality, the real and imaginary parts of the complex refractive index are connected through Kramers–Kronig relations. The real part, $n_b(\omega )$, is the refractive index of blood and the imaginary part, $k_e(\omega )=\lambda {\mu }_a/4\pi$, is the extinction coefficient, $\lambda$ is the laser wavelength, and ${\mu }_a$ is the absorption coefficient. $\tilde{n}(\omega )$ of the metal (gold) nanoparticle is related to the frequency dependent NP complex dielectric permittivity ${\epsilon }_g={\epsilon }_r+i{\epsilon }_i$ through ${\epsilon }_{\mathrm{g}}={\tilde{n}}^2={(n_r+i{k}_e)}^2$ where $n_r=k\lambda /2\pi$ is the real part of the refractive index indicating the phase velocity. Substituting ($n_r+i{k}_e$) in the plane wave expression, it gives

The real part, ${\epsilon }_r=(n_g^2-k_e^2)$, determines the degree to which the metal polarizes in response to an applied external electric field and determines the SPR spectral peak position. The imaginary part, $i{\epsilon }_i=2n_g{k}_e$, quantifies the relative phase shift, $\mathrm{\Delta }\phi =\mathrm{\Delta }[2\pi (n_{r+}i{k}_e)/\lambda ]$ $2R_g$ of the induced polarization with respect to the external field, i.e., it determines the bandwidth and includes losses such as ohmic heat loss.

The extinction coefficient is maximum when ${\epsilon }_g+2{\epsilon }_m=0$, where ${\epsilon }_g$ represents the Au particle giving rise to the SPR band.⁴⁴ According to Mie theory, the absorption cross section, ${\sigma }_{abs}$, of a particle embedded in a medium, ${\epsilon }_m\approx -{\epsilon }_g/2$, is given by¹⁵

Using ${\epsilon }_r=(n_g^2-k_e^2)\approx -7.6$ and ${\epsilon }_i=2n_g{k}_e\approx 1.56$ yields ${\epsilon }_g\approx -6$ and ${\epsilon }_m={\epsilon }_g/2\approx -3$. Substituting these values in Eq. (3) yields ${\sigma }_{\mathrm{abs}}\approx 1.35\times {10}^{-15}{\mathrm{m}}^2$, which is comparable with the values obtained by Jain et al.⁴⁵ and Pustovalov et al.²⁴ Furthermore, using $\lambda =810\mathrm{nm}$ and $\mathrm{Rg}=50\mathrm{nm}$, Eq. (6) yields, ${\eta }_{\mathrm{abs}}\approx 17\times {10}^{-2}$.

2.2.

Optical and PA Interaction with (B-Au NP) Medium

A schematic diagram representing the interaction and propagation of a laser beam and US with a blood-gold (B-Au) NP ensemble is illustrated in Fig. 1, where the direction of the laser beam is perpendicular to the surface of the medium and the US incidence is oblique. It is seen that RBCs can be oriented in random directions with a different number density causing a different amount of backscattering, while agglomeration (e.g., in static mode) can change the spatial configuration of the cells which can also affect optical and US backscattering.

Fig. 1

Schematic diagram of laser interaction with a (B-Au NPs) tube. The inset shows an example of a PA signal generated by a local B-Au NP volume when crossed by the laser beam. $R_g$: radius of Au-NP, $R_e$: radius of irradiated blood element, $h$: height of the container, and US: ultrasound.

When light passes through a suspension of an absorbing medium such as blood, photons that do not encounter RBCs are not absorbed. This is called the “absorption flattening effect.”⁴⁶ As a consequence, the transmitted light intensity is higher than it would be if all hemoglobin were uniformly dispersed in the solution. When a beam of light interacts with a blood volume element, the first event taking place between the RBC and the surrounding medium (plasma) is Fresnel reflection, $F$, defined by

Here $n(\overrightarrow{u})$ indicates the number of RBCs per unit volume with orientation $\overrightarrow{u}$ and ${\sigma }_{\mathrm{c}}(\overrightarrow{u},\overrightarrow{X})$ corresponds to the cross-sectional area of an RBC with an orientation $\overrightarrow{u}$ when exposed to light in the $\overrightarrow{X}$ direction. The value of ${\sigma }_c(\overrightarrow{u},\overrightarrow{X})$ mainly depends on the shape of the cells interacting with light, i.e., the shape or structure factor $S(\overrightarrow{q})$ which quantifies the effect of the spatial random organization of the scatterers on the backscattering coefficient where the scattering vector, $\overrightarrow{q}=-\overrightarrow{k}$. Here, $|\overrightarrow{k}|=k=2\pi f/c_a$ is the acoustic wavenumber, $f$ is the acoustic frequency and $c_a\approx 1570{\mathrm{ms}}^{-1}$ is the speed of sound in blood.⁴⁸ The ability of a tissue to generate acoustic echoes is often quantified by the frequency-dependent backscattering coefficient, $\beta \prime$, which for a heterogeneous material such as blood composed of weakly scattering particles is given as⁴⁹

The PAR technique involves light that is intensity modulated at high frequencies which, when propagating through a scattering medium, exhibits amplitude and phase variations. However, if the distance between NPs is larger than their size, the NPs act as discrete thermal point sources and the temperature should be a sum over all the sources provided there is no clustering. Then the heat source becomes⁵⁰

The spectral component $Q_s(z,{\omega }_m)$ at any value of ${\omega }_m$ is given by

3.1.

Preparation

A 25 mL 100-nm diameter gold nanoparticle source with a concentration of $3.8\times {10}^9\text{particles}/\mathrm{mL}$ stabilized as a suspension in a citrate buffer was purchased from Sigma–Aldrich. Sheep whole blood was kept in a refrigerator before each experiment. Prior to each test, the blood was anticoagulated with ethylene diamine tetraacetic acid (EDTA). Initially, 30 mL of blood were mixed with 3 mL of EDTA (i.e., 10:1) giving a total blood source volume of 33 mL. For a sample labeled S2 (10% ratio of $0.05:0.5\mathrm{mL}$ of NPs: blood) was used and for a sample labeled S3 (20%) the amount of NPs was doubled. The number of NPs and the corresponding concentration for S2 using 0.05 mL of Au were calculated as $196\times {10}^6$ and $345\times {10}^6{\mathrm{mL}}^{-1}$, respectively. Similarly, for S3 using 0.55 mL of B-Au, the values of $380\times {10}^6$ and $633\times {10}^6{\mathrm{mL}}^{-1}$ were obtained. A total of four samples were prepared using the aforementioned labeling: S1(blood only), S2 [$\text{blood}+10\%(3.8\mu \mathrm{g}/\mathrm{mL})$ Au NPs], S3[blood $+20\%$ ($7.6\mu \mathrm{g}/\mathrm{mL}$) Au NPs], S4(Au NPs only). All samples were safely mounted next to each other with a 5-mm separation inside a saline solution container 50 mm below the water surface and were irradiated with laser light in the transverse and longitudinal directions. In the former (latter) case, the direction of scanning was perpendicular (parallel) to the sample surface.

3.2.

Experimental Setup

As shown in Fig. 2, the intensity modulated output of a CW 800-nm diode laser (Jenoptik AG, Germany) with a chirp duration, ${\tau }_c$, of 1 ms was used as an excitation source for PA generation at a 1.6-W peak power.

Fig. 2

The experimental setup.

The laser driver was controlled by a software function generator to sweep the laser power modulation frequency range between 0.3 and 2.6 MHz. A collimator was used to produce a collimated laser beam with a 2 to 3 mm spot size on the sample. A focused ultrasonic transducer (V382, Olympus NDT Inc., Panametrics) with a FWHM bandwidth of 65% at 3.95 MHz, 12.5 mm diameter, a focal length of 25 mm, and an estimated lateral resolution of 0.87 mm was used for transmitting the US signal. The sensitivity of this transducer was measured to be $31.8\mu \mathrm{V}/\mathrm{Pa}$ using a calibrated hydrophone. The back scattered pressure waves were detected by a focused transducer (V305, Olympus NDT Inc., Panametrics) with a FWHM bandwidth of 64.4% at 2.25 MHz, 18.8 mm diameter, a focal length of 25 mm, and a beam width of approximately 0.9 mm. The distance between the samples and the transducer immersed in water was kept at about 25 mm. The setup was designed for a backscattering mode operation and the angle between the laser beam and the center axis of each transducer was about 27 deg. A 3-mm diameter silicone rubber tube was used to simulate a blood vessel in a physiological saline container. The tube was linearly scanned with a 0.5-mm step. The scanned distance was shorter than the tube length. In the NIR ($\ge 700\mathrm{nm}$) region, blood has an absorption coefficient ${\mu }_a=7{\mathrm{cm}}^{-1}$ corresponding to an optical penetration depth of about 1.4 mm. Depending on the type of silicone rubber, the acoustic impedance, $Z$, ranges between $(1.1\mathrm{to}1.5)\times {10}^6{\mathrm{kgm}}^{-2}{\mathrm{s}}^{-1}$. Blood has an acoustic impedance of about $1.60\times {10}^6{\mathrm{kgm}}^{-2}{\mathrm{s}}^{-1}$. Therefore, the amplitude reflection at the tube wall-blood interface varies between 0.1 and 3.4%. Data acquisition and signal processing were performed using Lab View software. Linear frequency modulation and matched filtering were used to generate A-scans with the PAR system. The similarity between two waveforms as a function of delay time is defined by the cross-correlation function where time delay is equivalent to a phase shift in the frequency domain. In our experiments, over 80 detected signals of 16 trains of 1-ms long chirps (i.e., one package consisting of four 1-ms chirps which was repeated four times: $4\mathrm{ms}\times 4\mathrm{ms}$) with a 1-s delay between them were averaged by software processing the collected data at each point, thereby giving a total of 1280 chirps. The chirp bandwidth was adjusted to simultaneously maximize the PAR and US SNRs.

3.3.

Results

The results are based on the backscattered signals using a volume fraction, $V_f$, in calculations related to S1 and S2

Table 1

Acoustic characteristics of blood, Au and B-Au NPs [for S2 (10%) and S3 (20%)].

An example of a PA pulsed signal (A-line) is shown in the inset of Fig. 1, where the time represents the depth location of NPs. This is an important example because the imaging contrast depends on physical processes such as the scattering mechanism which is also a size-dependent factor, the particle distribution density, orientation, and the shape factor of RBCs as described by Eq. (8). One such situation is the mismatch between the hemoglobin solution inside the cell and the surrounding plasma. Figure 3 indicates the US and PA cross correlations for 10% Au NPs (a) and 20% (b), respectively, generated by a 3.95-MHz transducer. The PA signals are very similar. The oscillations are mainly due to reflections of ultrasonic waves from the walls of the silicone rubber tube and transducer. The cross-correlation peak position on the PA delay time axis is related to the depth of the signal source (e.g., RBC or NPs).

Fig. 3

Normalized cross-correlation amplitude of US and photoacoustic (PA) for (a) S2 (10%) and (b) S3 (20%).

Figure 4(a) shows the envelope for the US cross correlation where the amplitudes decrease in the order $\mathrm{S}4(\mathrm{Au}\mathrm{only})>\mathrm{S}3(20\%)>\mathrm{S}2(10\%)>\mathrm{S}1(\text{blood only})$. The area under the curve of each envelope represents the total output energy of the matched filter at constant input energy. The profile amplitude provides a better SNR than the in-phase correlation alone. The noise level is similar in both the in-phase and envelope signals. However, the peak amplitude increases in the envelope signal due to the vectorial summation of the in-phase and quadrature signals. In general, envelope detection is a standard US practice to detect objects or layers and generate an image.

Fig. 4

Cross-correlation amplitude envelope for S1, S2, S3, and S4 for (a) US and (b) PA.

Although the US cross correlation produces a better SNR, its absorption is insensitive to material composition, but the degree of reflection depends on the acoustic impedance of the medium. Since S4 contains Au NPs only, it exhibits the highest reflection, in other words, by decreasing the NPs concentration in S3, S2, and S1, blood plays a more effective role in producing the frictional forces which consequently reduce the amplitude of acoustic reflection. On the contrary, the PA correlation amplitudes, Fig. 4(b), decrease in the order $\mathrm{S}2>\mathrm{S}3>\mathrm{S}1>\mathrm{S}4$. Despite its lower SNR, the PAR response is superior to US due to its specificity, as the results are based on the NP material optical absorption, concentration and also on the blood absorption coefficient. The fact that RBCs are very deformable and their shapes vary in response to thermal and mechanical stresses⁵¹ which may damage their membrane may be a reason for $\mathrm{S}2>\mathrm{S}3$.

Acoustic attenuation in whole blood can be attributed to a number of different mechanisms: (1) at the cellular level due to the cell membrane separating different intracellular and extracellular fluids; and at the molecular level within the (2) intracellular and (3) extracellular fluids. Molecular level absorption mechanisms include viscosity, thermal relaxation time and structural processes. The longer the relaxation time of a medium, the higher the absorption of US is. Another factor to be considered in US interaction with RBC cells is the attenuation linearity where the scattering component is mainly due to a mismatched acoustic impedance between the encapsulated proteins by RBC membrane and the surrounding fluid. However, according to Zinin⁵², for suspended erythrocytes the contribution of scattering to attenuation in the frequency range of 0.2 to 10 MHz may be neglected. By far the most dominant contribution of US absorption by biological tissues is due to relaxation processes among potential, chemical and structural forms of energy. There are frequency ranges over which some energy can transform to another state during ultrasonic compression, but with insufficient time for the process to completely reverse itself during rarefaction. Therefore, there will be a net energy transfer and hence absorption. As a result, quantitative US techniques are based on the frequency analysis of backscattered signals by biological tissues.

Power spectral density (PSD) is the frequency response of a random or periodic signal $x(t)$ indicating the average power distribution as a function of frequency

Figure 5(a) shows the corresponding US-PSD for S1 with a peak maximum at about 500 kHz followed by decreasing amplitudes due to higher attenuation in the B-Au NP medium. However, when 10% Au NPs were added (S2), Fig. 5(b), the amplitude increased significantly between 300 and 800 kHz. In addition, an increased distribution between 1.4 and 3.0 MHz was observed, indicating that a possible effect of Au NP agglomeration is the result of modification in the spatial configuration of the cells, producing increased US backscattering. At 20%, Fig. 5(c), the power spectrum amplitude decreased by almost 37% compared with Fig. 5(b) in the same frequency range, leading to a lower SNR and indicating a nonlinear behavior possibly due to additional structural and thermal relaxation processes at the cellular level. Again, there is an increased frequency distribution between 1.5 and 2.5 MHz. This will be discussed in detail in Sec. 4. The US response exhibits more peaks with relatively higher side lobes which may be due to its stronger interaction with the medium followed by more pronounced reflections from the tube walls and the blood. Secondary features like oscillations at higher frequencies are likely due to reflections of signals from particles closer to the surface of the tube. This is because the diffusion length depends on the modulation frequency as ${\omega }^{-1/2}$, and a higher frequency corresponds to probing the sample closer to the surface. Figures 5(b) and 5(c) clearly show the peaks in the 1.5 to 2.5 MHz range which are not observed in Fig. 5(a) corresponding to blood without Au NPs. Also, high-frequency oscillations can be partly attributed to agglomeration of Au NPs causing these high frequency US oscillations.

Fig. 5

Variation of power spectral density of US with frequency for (a) S1 (blood only), (b) S2 (10%), and (c) S3 (20%).

Figure 6 shows the corresponding PAR-PSD results for S1(a), S2(b), and S3(c), respectively. Inspection of the spectra of two signals [Figs. 6(b) and 6(c)], shows that the PA signal is dominated by low-frequency components with the amplitudes in the order $\mathrm{S}2>\mathrm{S}3>\mathrm{S}1$. In the low-frequency range, the PA response is affected only by the mixture of blood and NPs, so it does not reflect the signature of each individual component. The possible reasons to explain $\mathrm{S}3<\mathrm{S}1$ are primarily due to the lower optical absorption saturation of S3 than S1, and second, because of thermal-induced damage which will be discussed in Sec. 4. The higher resolution of the US cross-correlation signals is mainly due to the thermoelastic energy conversion effect of the PA phenomenon which affects the spectrum like a low-pass filter, thereby limiting spatial resolution.

Fig. 6

Variation of power spectral density of PA with frequency for (a) S1 (blood only), (b) S2 (10%), and (c) S3 (20%).

Furthermore, the PAR-PSD exhibits a nonlinear behavior consistent with the US results which can be related to the thermal effects of Au NPs on the RBC biomechanical properties and structure.⁵³ The main feature in the case of PAR, unlike US, is that there is little frequency content above the main peak frequency and the information is completely concentrated within the 300 to 800 kHz range, particularly for S2, which exhibits the strongest power spectrum. Physically, this implies that light does not penetrate as much as US, as expected, and thus does not interact with the Au NPs which are situated deeper than the optical penetration depth in the blood sample. A two-dimensional image (scan direction versus depth) was produced by plotting all one-dimensional (1-D) depth images (time traces) next to each other. Figure 7 illustrates the images obtained by scanning along the length of each tube using US (a) and PAR (b). Clearly, the best images correspond to S2 for PAR and S4 for US, which is consistent with Figs. 4(a) and 4(b) and is further discussed in Sec. 4. This confirms the well-known fact that the US reflection amplitude, ${[(Z_2-{\mathrm{Z}}_1)/(Z_1+Z_2)]}^2$, increases with the concentration of Au NP whereas in the PAR case, it is the absorption coefficient of the medium which is the determining parameter. Transversely scanned (cross-sectional) PAR images of S2 and S3 artificial blood vessel tubes are illustrated in Fig. 8. They, too, are indicative of the higher intensity distribution produced by 10% than that with 20% Au NPs.

Fig. 7

Two-dimensional (2-D) longitudinal image of the blood vessel simulating tube: (a) ultrasonic imaging and (b) photoacoustic imaging.

Fig. 8

2-D transverse images along a cross-section of the blood vessel.

4.1.

Heat Generation and Transfer by Au NPs

Initially, the absorption of pulsed or modulated laser energy by NPs produces a heating effect which is quickly equilibrated within the NP ensemble. Subsequently, the heat is transferred from the NPs to the surrounding medium or matrix (blood) via nonradiative relaxation within a few ps. In the absence of phase transformations, heat transfer in a system with NP thermal sources is described by the heat conduction equation

The total amount of heat produced is $Q_T=Q_b+Q_g$, where $Q_b$ and $Q_g$ represent the components produced by blood and gold NPs, respectively. In our case, the approximation $2\pi R_g/\lambda (\approx 0.4)<1$ holds, so it is assumed that each NP is quasitransparent to the incident light and $Q_g$ is constant across each nanoparticle. For a single Au NP exposed to a laser beam, the generated power is $P=I_0{\sigma }_{\mathrm{abs}}(\mathrm{W})$ where ${\sigma }_{\mathrm{abs}}$ is defined by Eq. (4) and $Q_g=P/V_g(\mathrm{W}{\mathrm{cm}}^{-3})$ where $V_g$ is the volume of the NP. The heat source is derived from the heat power density $h_{\rho }(r)={\int }_v{h}_{\rho }(r){\mathrm{d}}^{3}r$, where the integral is over the NP volume $V_g$. To calculate $Q_g(r,t)$, we assume the size of an Au NP is smaller than the laser wavelength so that electrons inside the NPs respond collectively to the applied electric field of the laser radiation, $E(r,t)=[3{\epsilon }_b/2{\epsilon }_g+{\epsilon }_g]E_0$, where ${\epsilon }_b$ is the blood permittivity. It is found that¹⁵

The maximum temperature change of blood volume element, $∆T_{\max /e}$, is

Normally, in soft matter physics, the Brownian motion of colloidal dispersions (as in this case) results in a Lorentzian distribution. Therefore, assuming, $\mathrm{\Psi }(r^{\prime })=d^3{r}^{\prime }{N}_D(r^{\prime })$ where $\mathrm{\Psi }(r^{\prime })$ is the probability of finding an NP at a distance $r\prime$ in a volume $d^3{r}^{\prime }$, and $N_D(r^{\prime })$ is the density distribution of NPs, a function which decays according to the spatially damped radial function⁵⁶

4.2.

PA Generation and its Transfer by B-Au NP

While PA signal generation is mainly based on the illuminated material optical absorption properties, the subsequent US propagation within the medium is directly conditioned by the properties of the surrounding medium such as the acoustic matching impedance, the absorption coefficient which is affected by the viscosity and the relaxation time of the medium, the scattering coefficient which depends on the particle number density, and the size and level of the spatial distribution of the scatterers. The transducer properties and the signal processing instrumentation can also affect the sensitively of the PA signal. The interaction of a laser pulse with a relatively weakly absorbing heterogeneous medium, such as blood containing a suspension of strongly absorbing nanoparticles, generates a PA signal enhancement effect. While the absorbers are the NPs, the signal propagates in the surrounding fluid and heat transfer defines the signal generation process. Therefore, the produced acoustic signal is proportional to the amount of energy deposited into the NPs and the thermoelastic properties of the surrounding environment. Absorption of optical chirp energy by the medium results in the generation of similar-frequency-modulated acoustic waves propagating within the medium. Quantitative PAI in the presence of nanoparticles is a function of the PA response signal (maximum signal voltage, $V_{\text{max}}$). The amplitude is given as a function of independent responses from single particles, the wavelength-dependent optical ${\sigma }_{\mathrm{abs}}$, the number of nanoparticles ($N_{\mathrm{NP}}$), and the deposited energy (${\sigma }_{\mathrm{abs}}F$). The PA signal is given as⁵⁷

Here, ${\mu }_{ab}={\epsilon }_{\mathrm{Hb}}(\lambda )[\mathrm{Hb}]+{\epsilon }_{{\mathrm{HbO}}_2}(\lambda )[{\mathrm{HbO}}_2]$, Hb, and ${\mathrm{HbO}}_2$ are the relative hemoglobin and oxyhemoglobin concentrations. ${\epsilon }_{\mathrm{Hb}}$ and ${\epsilon }_{\mathrm{HbO}}$ are the corresponding molar extinction coefficients.⁵⁹ If, however, $V_0$ is negligible, then $V_{\text{max}}$ is due to NPs only. Equation (20) holds as long as the NP absorption cross-section and environment are constant, and particle-to-particle thermal and electromagnetic coupling can be neglected. The propagating spherical pressure field detected by a transducer at a distance, $r_d$ has a spatial profile⁴¹

Table 2

Calculated thermo-acoustic properties of B-Au N Ps for S2 (10%) and S3 (20%). The subscript c indicates the value of a parameter based on the combined volume fraction.

Figure (9) shows the $X_T(f)$ values for a 0.3 to 2.6-MHz chirp using $X_T\approx {(2D_c/{\omega }_m)}^{1/2}$, where $D_c$ is the combined, or volume fraction, value of thermal diffusivity of the B-Au NP medium. One key result is that almost 75% of the total thermal-wave penetrates the medium within 0.3 to 1 MHz and correspondingly 19% between 1 and 2 MHz and 6% between 2 and 3 M Hz. Figure 10 indicates that not only does $X_T$ increase with chirp duration, but after 8 ms, the curves show a sublinear increase. Two biophysical reasons can be invoked for interpreting this finding. First, the depth of diffusive laser-induced heating occurs within a given time and possible implications regarding the breakdown of blood tissue integrity within that depth must be considered. Next, the laser-tissue interaction process may be nonlinear. Therefore, identifying that process might be crucial in further understanding its bioclinical consequences.

Fig. 9

Variation of diffusion length with modulation frequency for S2 (10%) and S3 (20%).

Fig. 10

Variation of diffusion length with chirp duration for S2 (10%) and S3 (20%).

Figure 11 shows further analysis of thermal diffusion length distribution for different frequency ranges during a given chirp duration, i.e., a thermal diffusion length breakdown in terms of frequency. It is interesting to note that not only does the thermal diffusion length increase with chirp duration as expected from photothermal-wave behavior, but the energy content of thermal diffusion for a given chirp duration also takes place at lower frequencies as expected from the low-pass filtering nature of PA signals.⁴²

Fig. 11

Distribution of thermal length as a function of chirp duration for Au NPs’ concentration: (a) S2 (10%) and (b) S3 (20%).

It can be seen from Eq. (16) that the amount of heat generated is directly proportional to modulation angular frequency and Eq. (18) states that the larger the number of NPs and the higher the laser fluence, the higher the temperature in each volume element of a blood-vessel simulating tube during irradiation. Consequently, for contrast-enhanced PAI of a given blood containing tissue volume, not only the laser parameters, but also the NP concentration should be carefully optimized. Furthermore, according to Eq. (19), it is expected that temperature changes for each volume element with the density distribution function of NPs. This is then followed by a corresponding PA signal voltage generation according to Eq. (20). This PA pressure increase is described by Eq. (22). Therefore, it appears that both the temperature increase due to a higher number of NPs and their density variation within each volume element and on the entire volume can increase the PA signal and the imaging SNR. It is well known that any modification of cellular plasma membrane or even the cytoplasm contents including proteins will affect the absorption and scattering behavior of RBC. Therefore, it is expected that a better image contrast should be obtained with S2 compared with S3, as observed in Figs. 8 and 4(b). In fact, it has been suggested ⁵³ that the change of the optothermal properties of blood due to the decrease of osmolarity changes the shape of the erythrocytes due to higher optical absorption. Based on this fact and on the fact that the cross-sectional area of an RBC, ${\sigma }_c(\overrightarrow{u},\overrightarrow{X})$, depends on the shape of the cells interacting with light and the shape factor ($S(\overrightarrow{q})$), see Eq. (9), the lower PA amplitude of S3 than S2, Fig. 4(b), can be better understood: i.e., higher rates of optical absorption and heat transfer to the surrounding medium may have a direct impact on the structural integrity and the optical properties of RBCs. The basis of this fact goes back to 1865 when Scultz⁶³ reported for the first time the morphological changes induced by heating cells when microspherocytosis and fragmentation were observed. Since then much research has confirmed this thermo-biological effect. One related issue of interest is the deformation of RBCs irradiated with laser power and the consequences of laser irradiation in biomedical applications.^64,65 Thus, the number of Au NPs which can be used to enhance the PA signal is a decisive factor and must be optimized. In our case, this is clearly shown by the higher Au NP concentration (S3) which generated a lower PA signal due to probably irreversible cellular thermal damage. The heating efficiency of Au NPs is defined as²⁴

Fig. 12

Change of Au NPs’ thermal efficiency with chirp duration for S2 (10%) and S3 (20%).

The maximum efficiency of heat transformation into acoustic pressure is given by²⁴