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Photoacoustic remote sensing elastography

Yanchi Yuan, Xue Wen, Bo Yuan, Haishu Xin, Bingyan Fang, Sihua Yang, and Kedi Xiong

Open Access Open Access

Abstract

The mechanical properties of organisms are important indicators for clinical disputes and disease monitoring, yet most existing elastography techniques are based on contact measurements, which are limited in many application scenarios. Photoacoustic remote sensing elastography (PARSE) is the first, to the best of our knowledge, elastography modality based on acoustic pressure monitoring, where elastic contrast information is obtained by using an all-optical non-contact and non-coherent intensity monitoring method through the time-response properties of laser-induced photoacoustic pressure. To validate PARSE, sections of different elastic organs were measured and this modality was applied to differentiate between bronchial cartilage and soft tissue to confirm the validity of the elasticity evaluation. PARSE, through a mathematical derivation process, has a 9.5-times greater distinction detection capability than photoacoustic remote sensing (PARS) imaging in stained bronchial sections, expands the scope of conventional PARS imaging, and has potential to become an important complementary imaging modality.

© 2023 Optica Publishing Group

Biomechanical properties can convey substantial physiological and pathological information about tissue, participating in pathological development [1]. Mechanical elasticity or stiffness of soft biological tissues is dependent on the microscopic and macroscopic structural organization of their constituent molecules, whereas changes in the stromal density and molecular texture of biological tissues—which are closely associated with changes in physiological activities resulting from the development and progression of diseases—are correlated with pathophysiological states of tissues [2,3]. In the past several decades, ultrasound elastography [4] and magnetic resonance elastography [5] have been developed for the diagnosis of breast cancer and pancreatitis, estimating the mechanical properties of tissue by measuring the propagation speed of a shear wave or the deformation [6–8]. These modalities have been used in clinical applications, including breast cancer and pancreatitis diagnosis. However, their limited spatial resolution and contact-based excitation and detection are discouraged and even forbidden in some applications like burn situations.

In simple terms, the photoacoustic (PA) technique, involving ultrasonic waves based on thermoelastic expansion by short-pulse-width laser excitation, is a hybrid imaging mode that combines high resolution and imaging depth [9,10]. Photoacoustic elastography (PAE) is a new noninvasive method to detect tissue elasticity. Previous PAE works studied tissues’ mechanical properties by utilizing thermoelastic deformation [11], but this modality cannot provide quantitative elastic information. Another work introduced a compression-based method to analyze elastic properties by local strain measurement [12]. One of our previous works proposed a PAE technique to acquire viscoelastic information by exploring the time and phase characteristics of the PA response [13]. Although these techniques are promising methods for studying tissue elasticity information, their reliance on a conventional contact-based piezoelectric transducer restricts their application [14,15]. In addition, the limited bandwidth of piezoelectric transducers will distort the initial PA signal, which brings some challenges to subsequent image reconstruction [16]. Therefore, we presented all-optical non-contact phase-domain PAE (NPD-PAE) [17], a novel approach leveraging the temporal response characteristics of surface PA displacement using an optical interferometric detection method to calculate the bulk elastic modulus. However, these methods offer potential sensitivity to the scattered probe beam phase modulations associated with the motion of scatters, subsurface, surface oscillations, and unwanted vibrations [18].

Photoacoustic remote sensing (PARS) microscopy is an emerging non-contact [19–22], non-interferometric, all-optical PA modality with high detection sensitivity and high resolution. Especially in the field of tissue section imaging, PARS imaging enables rapid imaging of cell nuclei and fibers in non-stained sections [23]. However, sound pressure-detection-based PARS cannot indicate the physical principles of distinguishing different tissues [24].

In this Letter, we present photoacoustic remote sensing elastography (PARSE), a non-contact, non-interference method that uses the time response of an object’s refractive index modulated by an elasto-optic effect to obtain the elastic modulus. The elasticity of the object can be reflected by the response time of the PARS signal under laser excitation because of the nature of the elasto-optic effect.

Figure 1(a) shows the PARSE detection mechanism. PARSE is sensitive to initial pressure: the elasto-optical refractive index changes when the absorber has obvious refractive index contrast caused by PA initial pressure. This change modulates the backscattered light intensity of probe light, which can be described as

$$n(x,t) = {n_0}(x) + \delta n(x,t) = {n_0}(x)\left( {1 + \frac{{\eta {n_0}{{(x)}^2}p(x,t)}}{{2\rho v_a^2}}} \right),$$
where η is the elasto-optic coefficient, $p({x,t} )$ is the pressure field, ρ is mass density, and ${v_a}$ is the speed of sound in the medium. PA initial pressure ${p_0} = \Gamma \phi {\mu _a}$, where $\Gamma $ is the Grüneisen parameter, ${\mu _a}$ is the optical absorption coefficient, and ϕ is the incident fluence. PA pressure field is given as $P = {P_0}f(t )exp [{ - {{({x/R} )}^2}} ]$, where $f(t )$ is the pulse time function with square wave profile, R is the waist of the Gaussian beam, and x is the radial position. Modulation of reflectivity ΔR(t) can be described as
$$\begin{aligned} \Delta R(t) &= \left|{\frac{{{n_1} + \delta n(t) - {n_2}}}{{{n_1} + \delta n(t) + {n_2}}}} \right|- R\\ &= \delta n(t)\frac{{2Re \{ {n_1} - {n_2}\} }}{{|{{n_1} + {n_2}} |}} - \frac{{2Re \{ {n_1} + {n_2}\} }}{{|{{n_1} - {n_2}} |}}{\left|{\frac{{{n_1} - {n_2}}}{{{n_1} + {n_2}}}} \right|^2}, \end{aligned}$$
where $R = {\left|{\frac{{{n_1} - {n_2}}}{{{n_1} + {n_2}}}} \right|^2}$.

 figure: Fig. 1.

Fig. 1. Mechanism of PARSE. (a) PA pressure detection: all-optical generation and detection of PA pressure. (b) Material mechanical response: elasticity estimation from a material’s temporal response characteristics.

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Consider the equation of the PA effect:

$$p(x,t) ={-} \rho {C_L}\frac{{\partial u}}{{\partial t}}.$$
The relationship between the PA pressure and the thermoelastic displacement induced by the PA pressure can be obtained. The relationship between the obtained light intensity signal I(t) and the PA elastic displacement can be obtained by integrating Eqs. (1), (2), and (3):
$$u(t) = \int K \cdot I(t)dt,$$
where
$$K = \frac{{2Re \{ {n_1} - {n_2}\} }}{{{{|{{n_1} + {n_2}} |}^2}}}.$$
In linear, isotropic, and viscoelastic media, the displacement field u due to optical-absorption-induced thermoelastic expansion follows Navier’s equation [7,25]:
$$\begin{array}{l} \rho \frac{{{\partial ^2}u}}{{\partial {t^2}}} - \left( {E + \eta \frac{\partial }{{\partial t}}} \right){\nabla ^2}u\\ = {\mu _\alpha }{\mu _{att}}\Gamma {P_0}f(t) \times exp \left( { - {\mu_{att}}z - \frac{{{x^2}}}{{{R^2}}}} \right). \end{array}$$
Here, ${\mu _{att}}$ is the optical attenuation coefficient and t and z are the time and axial coordinates, respectively.

When it comes to a point excitation source at the absorber, displacement at the laser focal spot (z = 0, x = 0) can be described with Fourier and Hankel transforms as

$$u(t) = \frac{{\sqrt \pi {\mu _\alpha }{\mu _{att}}\Gamma {P_0}f(t)}}{{2\sqrt {\rho E} }}\frac{{\left( {\frac{{\sqrt {E/\rho } }}{R}} \right)t}}{{\left( {\frac{{\sqrt {E/\rho } }}{R}} \right){t^2} + \frac{{2\eta }}{{\rho {R^2}}}t + 1}}.$$
Here, τ is the pulse width of the excitation laser. Equation (5) shows temporal response characteristics of displacement that are highly related to the mechanical parameters. In response to laser excitation, the pressure field makes thermoelastic displacement expand around the absorber. The thermoelastic displacement initially increases, and then reaches its maximum at
$${t_{\max }} = \frac{R}{{\sqrt {E/\rho } }}.$$
The thermoelastic displacement, called rise time ${t_{\textrm{max}}}$, is inversely proportional to the bulk modulus E. Hence, elasticity can be calculated as $E = M\cdot\rho {R^2}/t_{\textrm{max}}^2$, where M is a constant parameter decided by the system and equilibrium temperature. By combining Eqs. (6) and (7), it can be concluded that the elastic displacement of the system reaches a maximum when the signal integration reaches a maximum. As shown in Fig. 1(b), a material with greater elasticity can more quickly respond (black envelope curve) to external stimuli; a softer material (gray envelope curve) typically exhibits a longer rise time.

The experimental system of PARSE is shown in Fig. 2(a). Briefly, the system includes two main subsystems: excitation system and interrogation system, based on the principle of PARS. The excitation system contains a pulsed laser (model DTL-319QT, Laser-export) operating at 532 nm with 9 ns pulse width being used. The laser beams are focused by a lens and coupled in an SMF (HI1060) by a fiber port (PAF-X-15-PC-A, Thorlabs), Then the laser beams are collimated by fixed focus fiber collimation (FC-240, Thorlabs). The collimating light passes vertically through a dichromatic mirror (DMLP1000, Thorlabs) and objective (PAL-5-NIR, OptoSigma) to the sample surface.

 figure: Fig. 2.

Fig. 2. Schematic of the PARSE system. (a) PARSE system: DAQ, data acquisition; BPD, balance photodetector; FP1–3, fiber ports; C1, C2, collimators; DM1, DM2, dichroic mirrors; L1, L2, focusing lenses; OL, objective lens. (b) Lateral resolution of the PARSE system. Scale bar: 200 μm.

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A 1310 nm continuous super-luminescent diode (SLD) source with 15 nm FWHM linewidth (IPSDM1302C, INPHENIX) was used for detection. The beam was split by using a 90:10 spectroscope (TW1300R2A1, Thorlabs). The 10% fraction of the light passed through an in-line variable attenuator (VOA50-APC, Thorlabs) and then was connected to the reference port of a balanced photodiode (PDB420C-AC, Thorlabs). The 90% fraction of the light passed through a circulator (CIR1310-APC, Thorlabs) to interrogate the sample with a spot that was cofocused with the excitation beam and returned the reflected light to the other port of the 75-MHz-bandwidth balanced photodiode (PDB420C, Thorlabs). The excitation and detection beams were combined using a dichroic mirror and then scanned across the sample via a 2D motorized system. System resolution is obtained by imaging a carbon fiber with a diameter of 7 μm, selecting the signal in the blue line section and assuming a Gaussian beam for the focused laser, giving the lateral FWHM of 10.36 μm.

To validate the proposed method, three organ slices of three different degrees of stiffness (heart, kidney, and liver) were prepared to conduct elasticity measurements. The components of these slices are single. To provide absorption contrast for PARS imaging, hematoxylin and eosin staining was performed on all three sections, which were still able to embody biomechanical properties [26]. The reason for the bright and dark stripes in the PARS image is that the backscattered light modulation exceeds the detection threshold of the balanced photodetector, leading to saturation, which also proves that the PARSE signal is independent of the PARS signal. Figures 3(a) and 3(b) show the PARSE images and PARS images, respectively.

 figure: Fig. 3.

Fig. 3. Images of mouse heart, kidney, and liver hematoxylin- and eosin-stained sections. (a) PARSE images of three organ slices; (b) PARS images of three organ slices; (c) PARS signal profiles in three organ slices; (d) zoomed-in temporal displacement profiles; (e) rise time in slices (n = 60 for each phantom). Scale bar: 300 μm.

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Three slices have similar signal amplitude in PARS images, while PARSE images can provide different details about tissue properties: heart tissue is the most elastic, kidney tissue is the next most elastic, and liver tissue is the least elastic. The results of the experiment are consistent with known medical findings [27]. Figure 3(c) shows the temporal PARS signal profiles of the three kinds of organ slices, which provide PA initial pressures. The thermoelastic displacement is integrated over the time domain of PA pressures. To capture the initial rapid expansion, the temporal sampling is high enough (200 Msamples/s). Equation (7) shows that a sample with greater elasticity has a faster response to an external stimulus. In the displacement profile in Fig. 3(d), a significant decrease in the rise time can be observed with increasing tissue elasticity, which conforms well to the theoretical prediction. Figure 3(e) shows the rise times of the three organ tissue signals from 60 samples each. The data show that the average rise time of the signals of the three organs is 72 ns, 91 ns, and 102 ns, respectively. PARSE can clearly distinguish the difference between the three signals in the time domain, which reflects PARSE’s detection sensitivity.

To verify the image differentiation capability of more complex tissues, porcine bronchial sections were imaged. Figure 4(a) shows a PARS image of a porcine bronchus, where the periosteal and cartilage divisions cannot be distinguished, but the periosteal and cartilage divisions (red lines) can be seen in the PARSE image in Fig. 4(b). Figure 4(c) shows a microscopic image of the section. To quantify the image differentiation capability, we define the distinction detection factor:

$${Q_e} = \frac{{{\Delta _{a.u}}}}{S},$$
where ${\Delta _{a.u}}$ is the difference in signal amplitude between the two substances in any mode and S is the larger amplitude of the two types of substances. In Fig. 4(d), we randomly selected 200 signals each from the periosteum and cartilage in the white box in Figs. 4(a) and 4(b) to calculate the results. Values of ${Q_{e(PARS)}}$ of 0.055 and ${Q_{e(PARSE)}}$ of 0.525 were obtained, the comparison showing that ${Q_e}$ was increased by 9.5 times. Furthermore, the variance of the PARS signal amplitude is much larger than the variance of the PARSE signal amplitude. This demonstrates the very significant improvement in the elastic resolution of PARSE compared with PARS and can be used to resolve components that PARS cannot.

 figure: Fig. 4.

Fig. 4. Images of porcine bronchial hematoxylin- and eosin-stained sections. (a) PARS image of porcine bronchial section; (b) PARSE image of porcine bronchial section; (c) microscopic image of a hematoxylin- and eosin-stained section of a porcine bronchus; (d) signal amplitude of PARS and PARSE (n = 200 for each phantom). Scale bar: 300 μm.

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Notably, in this work, the theoretical model for elasticity estimation is simplified to an ideal absorption point under unsurface excitation, and the elasticity information obtained is that of the material surrounding the absorption point, such that the effect of the object geometry on the temporal profile of the PARSE signal is negligible. In future studies, this effect can be further reduced by a larger numerical aperture of the microscope objective. At the same time, three-dimensional elastic distribution information could be obtained by adding a three-dimensional scanning system to realize three-dimensional elastography. Furthermore, the exact values of the elastic parameters always depend on the parameters of the measurement system: the size of the laser spot, the bandwidth of the PA detector, etc. In summary, in this work, we present a completely non-contact time-domain PARSE method for comparing elasticity information through a non-coherent approach and validate the performance of PARSE in animal tissue sections. We believe that this technique will be widely used and may have a wide impact in fields such as medical imaging and the mechanics of materials.

Funding

STI2030-Major Projects (2022ZD0212200); Science and Technology Program of Guangzhou (2019050001, 202206010094); Natural Science Foundation of Guangdong Province (2022A1515010548, 2022A1515011247); National Natural Science Foundation of China (61822505, 62005084).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (4)
Fig. 1.
Fig. 1. Mechanism of PARSE. (a) PA pressure detection: all-optical generation and detection of PA pressure. (b) Material mechanical response: elasticity estimation from a material’s temporal response characteristics.

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Fig. 2.
Fig. 2. Schematic of the PARSE system. (a) PARSE system: DAQ, data acquisition; BPD, balance photodetector; FP1–3, fiber ports; C1, C2, collimators; DM1, DM2, dichroic mirrors; L1, L2, focusing lenses; OL, objective lens. (b) Lateral resolution of the PARSE system. Scale bar: 200 μm.

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Fig. 3.
Fig. 3. Images of mouse heart, kidney, and liver hematoxylin- and eosin-stained sections. (a) PARSE images of three organ slices; (b) PARS images of three organ slices; (c) PARS signal profiles in three organ slices; (d) zoomed-in temporal displacement profiles; (e) rise time in slices (n = 60 for each phantom). Scale bar: 300 μm.

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Fig. 4.
Fig. 4. Images of porcine bronchial hematoxylin- and eosin-stained sections. (a) PARS image of porcine bronchial section; (b) PARSE image of porcine bronchial section; (c) microscopic image of a hematoxylin- and eosin-stained section of a porcine bronchus; (d) signal amplitude of PARS and PARSE (n = 200 for each phantom). Scale bar: 300 μm.

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Equations (9)

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n ( x , t ) = n 0 ( x ) + δ n ( x , t ) = n 0 ( x ) ( 1 + η n 0 ( x ) 2 p ( x , t ) 2 ρ v a 2 ) ,
Δ R ( t ) = | n 1 + δ n ( t ) − n 2 n 1 + δ n ( t ) + n 2 | − R = δ n ( t ) 2 R e { n 1 − n 2 } | n 1 + n 2 | − 2 R e { n 1 + n 2 } | n 1 − n 2 | | n 1 − n 2 n 1 + n 2 | 2 ,
p ( x , t ) = − ρ C L ∂ u ∂ t .
u ( t ) = ∫ K ⋅ I ( t ) d t ,
K = 2 R e { n 1 − n 2 } | n 1 + n 2 | 2 .
ρ ∂ 2 u ∂ t 2 − ( E + η ∂ ∂ t ) ∇ 2 u = μ α μ a t t Γ P 0 f ( t ) × e x p ( − μ a t t z − x 2 R 2 ) .
u ( t ) = π μ α μ a t t Γ P 0 f ( t ) 2 ρ E ( E / ρ R ) t ( E / ρ R ) t 2 + 2 η ρ R 2 t + 1 .
t max = R E / ρ .
Q e = Δ a . u S ,
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