On the imaging depth limit of photoacoustic tomography in the visible and first near-infrared windows

Songde Liu; Songde Liu; Tong Wang; Xinye Zheng; Yunhao Zhu; Chao Tian; Chao Tian; Chao Tian; Chao Tian

doi:10.1364/OE.513538

1. Introduction

Photoacoustic tomography (PAT) is a fast-evolving biomedical imaging modality in recent years [1–3]. In PAT, ballistic photons and diffused photons both contribute to the generation of photoacoustic signals. Therefore, PAT can break the optical diffusion limit and achieve an imaging depth greater than pure optical imaging while still maintaining high resolution and high contrast [3,4].

The imaging depth advantage of PAT has been widely recognized throughout the community. Li et al. achieved photoacoustic imaging of the whole body of small animals in vivo with a cross-sectional width of 4.8 cm without using exogenous contrast agents [5]. Ke et al. showcased an imaging depth of 6.6 cm at 650 nm using oxygenated bovine blood as the absorption target with 200 times signal averaging [6]. To enhance the imaging depth, Li et al. proposed an internal light illumination strategy combined with external ultrasound detection and extended the imaging depth to 7.5 cm in a leaf target embedded in an optically scattering medium [7]. Based on a phosphorus phthalocyanine formulation, Zhou et al. demonstrated an imaging depth of 11.6 cm at 1064 nm in chicken breast tissues with 100 times signal averaging [8]. These work well demonstrates the superior deep-tissue imaging capability of PAT from the perspective of experiments but lacks theoretical support and unified analysis. The basic question of what the fundamental imaging depth limit of PAT in biological tissues is remains unclear.

In this work, we propose and establish a unified numerical framework for estimating the imaging depth limit of PAT in the visible and first near-infrared (NIR) windows (400 nm – 1000 nm). The established framework simulates the physical process of photoacoustic imaging and consists of seven steps, including tissue modelling, photon transportation, photon to ultrasound conversion, sound field propagation, signal reception, image reconstruction, and imaging depth evaluation, as shown in Fig. 1. Based on the established framework, we study the imaging depth problem in three typical tissues, including the human breast, the human abdomen-liver tissues, and the rodent whole body and obtained corresponding imaging depth limits.

Fig. 1. Overview of the proposed framework for evaluating the imaging depth limit in PAT.

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2. Methods

2.1 Tissue modelling

The numerical models of optical, thermal, and acoustic properties of tissues are established to characterize the generation, propagation, attenuation, and reception behaviours of light and sound.

The optical properties of tissue affect the scattering and absorption behaviours of photons and thus determine the penetration depth of light and the amount of energy deposited. The optical properties of a thick tissue can be described by three optical parameters [9], including the absorption coefficient, μ_a (cm⁻¹), the scattering coefficient, μ_s (cm⁻¹), and the anisotropy factor, g. The optical absorption coefficient of a tissue, μ_a, can be modelled as a linear combination of the optical absorption coefficients of its contents, such as blood, water, fat, and melanosome [9], i.e.,

(1)$${\mu _a} = BS{\mu _{a.\textrm{oxy}}} + B({1 - S} ){\mu _{a.\textrm{deoxy}}} + W{\mu _{a.\textrm{water}}} + F{\mu _{a.\textrm{fat}}} + M{\mu _{a.\textrm{melanosome}}},$$

where μ_a_.oxy, μ_a_.deoxy, μ_a_.water, μ_a_.fat, and μ_a_.melanosome are correspond to the wavelength-dependent absorption coefficients of oxygenated blood, deoxygenated blood, water, fat, and melanosome [10], respectively; B is the whole blood volume fraction; S is the blood oxygen saturation; W is the average water content; F is the average fat content; M is the melanosome volume fraction. The optical scattering coefficient of a thick tissue, μ_s, is difficult to measure and model due to multiple scattering events. In such a case, the optical reduced scattering coefficient, ${\mu ^{\prime}_s}$, is used to describe the multiple scattering process as [9]

(2)$${\mu ^{\prime}_s} = {\mu _s}({1 - g} ),$$

where g is the anisotropy factor characterizing tissue scattering in terms of the relative forward versus backward direction of scatters. It has a representative value of 0.9. The reduced scattering coefficient, ${\mu ^{\prime}_s}$, can be modelled by the following empirical formula as [9]

(3)$${\mu ^{\prime}_s} = a{({{\lambda / {500}}} )^{ - b}},$$

where λ is the light wavelength, b is the scattering power, and a is the reduced scattering coefficient at 500 nm. The optical attenuation in tissue is the result of the combined effect of optical absorption and optical scattering and depends on the effective attenuation coefficient, defined as [11]

(4)$${\mu _{\textrm{eff}}} = \sqrt {3{\mu _a}({{\mu_a} + {{\mu_s^{\prime}}}})}.$$

The effective attenuation coefficient is generally smaller in the NIR band than in the visible band, indicating that NIR light has a greater penetration depth in tissues. The literature data on optical properties of major human and rodent tissues are summarized in Table S1.

The thermal properties of tissue affect the energy conversion efficiency from thermal energy deposited by laser to mechanical energy (sound pressure), which can be measured by the Grüneisen parameter, Γ. The Grüneisen parameter is a dimensionless quantity related to the thermal expansion coefficient, β, specific heat capacity at constant pressure, C_p, and the speed of sound, v_s, of the tissue. It can be mathematically formulated as [11]

(5)$$\Gamma = \frac{{\beta v_s^2}}{{{C_p}}}.$$

The Grüneisen parameter specifies the fraction of thermal energy deposition that couples into mechanical energy. Its value depends on the thermal property of the tissue and the temperature. As an example, the value of Γ for water at 37°C is about 0.2, indicating that about 20% of deposited thermal energy converts into sound energy. The literature data on thermal properties of different tissues in humans are summarized in Table S2.

The acoustic properties of tissue affect the propagation and attenuation of sound waves. When light-induced sound waves travel in tissue, their propagation obeys acoustic wave equations. For a lossless acoustic medium, the medium density and the sound speed need to be specified in the wave equations to predict physical phenomena, such as absorption, refraction, and scattering accompanying the propagation process. For a lossy acoustic medium, sound waves attenuate in strength during propagation due to acoustic absorption and scattering. The attenuation coefficient, α, is frequency-dependent and can be modelled as [12]

(6)$$\alpha = {\alpha _0}{f^c},$$

where f is the frequency of the sound, α₀ and c are empirical constants whose values differ from one type of tissue to another. The formula suggests that high-frequency acoustic waves attenuate more significantly in tissue during propagation. The literature data on the acoustic properties of different tissues in humans are summarized in Table S3.

2.2 Photon transportation in tissues

The simulation of photon propagation in soft tissue in this study is based on the Monte Carlo method [13,14], which is a flexible yet rigorous approach for photon transport simulation in turbid media. In the Monte Carlo method, local rules of photon transport are expressed as probability distributions, which describe the step size of photon movement between sites of photon-matter interaction and the angles of deflection in a photon's trajectory when a scattering event occurs [14]. Monte Carlo simulation can be used to model photon transportation in homogeneous media as well as multi-layered media by considering boundaries, as shown in Fig. S1.

In practical implementations, Monte Carlo simulation does not trace photons individually but considers photon packets with a specific weight (generally initialized as unity). The simulation of photon transportation goes through four steps. First, initialize the position and direction of the photon packet and launch it into the tissue. Second, determine the step size that the photon packet travels between interaction sites and propagate the photon packet by the step size in a defined direction. Third, determine the new weight and direction for the photon packet after absorption and scattering at each interaction site. Finally, terminate the photon packet if it has a sufficiently small weight after experiencing many interactions. The Monte Carlo method is a statistics-based model and, therefore, tracing more photons can provide better accuracy and spatial resolution. The simulation of photon transportation in this study is implemented by the use of the three-dimensional (3D) Monte Carlo toolbox developed by Jacques [13].

Photon transportation in soft tissue has a fundamental depth limit, called the dissipation limit, which is roughly defined as 10/μ_eff [15]. For soft tissue with a typical absorption coefficient of 0.1 cm⁻¹, a scattering coefficient of 100 cm⁻¹, and an anisotropy factor of 0.9, the dissipation limit is about 10 cm, indicating that photons will be significantly attenuated in tissue after propagating a distance of 10 cm due to optical absorption and scattering.

2.3 Photon to ultrasound conversion

Photon to ultrasound conversion involves two energy transformation phases, from light energy to heat energy and from heat energy to mechanical energy (acoustic energy). In the first phase, pulsed light energy is deposited in tissue and induces an instantaneous temperature rise, ΔT, which can be written as

(7)$$\Delta T = \frac{{{\mu _a}F}}{{\rho {C_p}}},$$

where F is the incident laser fluence, ρ is the medium density. In the second phase, the temperature rise causes thermal elastic expansion of the tissue, which can be expressed as the strain ɛ. The strain is related to the temperature rise via ɛ = βΔT. The stress (or pressure) generated by the strain is expressed as p₀ = Mɛ, where M is the bulk modulus, specifying the pressure per unit strain. Eventually, the initial acoustic pressure caused by thermoelastic expansion can be written as [16]

(8)$${p_\textrm{0}} = M\beta \Delta T = \Gamma {\mu _a}F.$$

2.4 Sound field propagation

The simulation of sound propagation in tissue is implemented using the k-Wave toolbox [17], developed by the Photoacoustic Imaging Group at University College London (UCL). In the k-Wave toolbox, the propagation of sound field in tissue is described by acoustic wave equations. When acoustic absorption and heterogeneities of the tissue are considered, the acoustic wave equations can be described by a series of coupled first-order partial differential equations based on the conservation of mass, momentum, and energy within the medium [18]. The k-Wave toolbox solves these equations using a k-space pseudospectral method [17,19,20], which can reduce computing memory and improve speed.

When sound waves propagate in a lossy tissue, frequency-dependent acoustic attenuation described in Eq. (6) is a key factor that limits the imaging depth of PAT. To illustrate this, suppose a typical tissue with α₀ = 0.5 dB MHz^−c cm⁻¹, c = 1, and ${{v}_{s}}$ = 1500 m/s. A 1-mm-diameter absorber within the tissue will generate 1 MHz centre frequency sound waves [21], which have a −10 dB propagation distance of 20 cm [15]. In contrast, a 0.1-mm-diameter absorber will generate 10 MHz centre frequency sound waves, which have a −10 dB propagation distance of only 2 cm [15]. Therefore, for high-frequency PAT imaging, acoustic attenuation becomes a dominant factor that limits the imaging depth of PAT and should be taken into consideration.

2.5 Sound signal reception

Acoustic signals in PAT need to be captured by ultrasound detectors and converted into electrical signals for digitization, processing, and storage. Different types of acoustic detectors such as piezoelectric, optical, and capacitive have been used in practical PAT imaging [22]. In this study, the most widely used piezoelectric transducer is adopted as the detector. Its performance is characterized by four parameters, including the centre frequency, bandwidth, sensitivity, and thermal noise level. The centre frequency of the detectors used in this study varies from 1 MHz to 50 MHz, covering the most common ultrasound frequency band in PAT. The one-way fractional bandwidth is fixed at 80%, a typical value for piezoelectric detectors. The sensitivity and the thermal noise level of the detector are set to 6 µV/Pa and 40 µV, respectively, which are typical values for polymer film detectors based on literature data [23,24]. As such, the noise-equivalent pressure (NEP) of the detector is about 7 Pa. To simulate the thermal noise of the detector, Gaussian random numbers with a mean value of zero and a maximum amplitude of 7 Pa are generated and added to raw photoacoustic signals in this study.

2.6 Image reconstruction

After signal reception by ultrasound detectors, approximate or exact image reconstruction algorithms are needed to map time-varying pressure signals into final photoacoustic images. A large number of tomographic reconstruction techniques are currently available for this task and can be divided into several categories such as time reversal, back projection, iterative reconstruction, and deep learning-based reconstruction [3]. In this study, the time reversal algorithm is adopted because its implementation can take advantage of the sound field propagation model and is well integrated with the k-Wave toolbox. It works by running the numerical acoustic propagation model backwards and re-transmitting the photoacoustic signals measured by each detector in temporally reversed order. The time reversal algorithm allows heterogeneous acoustic media, arbitrary detection geometries, sources outside the detection surface, and non-zero initial time derivative of the pressure, and is thus considered the least restrictive reconstruction algorithm for PAT [25].

2.7 Evaluation criterion for imaging depth limit

The last step of the established framework is to choose a proper evaluation criterion to assess the imaging depth limit. To accomplish this, we may either use raw photoacoustic signals or final photoacoustic images as the evaluation target. However, since multiple detectors are typically used in PAT imaging, the quality of the raw photoacoustic signal of individual detectors may not be able to truly reflect the imaging depth limit. For example, even if the signal of an individual detector is drowned out by noise, the finally reconstructed image may still possess reasonable image quality due to the superposition of the signals captured by different detectors. Therefore, we use final photoacoustic images as the evaluation target in this study and adopt CNR as the image quality evaluation criterion [11]. CNR can reflect the difference between the region of interest (ROI) and the region of background from reconstructed images and is a common measure for image quality assessment. It is defined as [26]

(9)$$\textrm{CNR = }\frac{{{\mu _{\textrm{ROI}}} - {\mu _{\textrm{background}}}}}{{{{\sqrt {\sigma _{\textrm{ROI}}^2 + \sigma _{\textrm{background}}^2} } / 2}}},$$

where μ_ROI and μ_background are the mean values of the ROI and the background, respectively; σ_ROI and σ_background are the standard deviations of the ROI and the background, respectively. According to the literature [26–28], a CNR value between 3 to 5 is required to ensure a reasonable distinction between the ROI and the region of background. Herein a value of 3.0 (CNR = 3.0) is employed as the evaluation criterion.

Note that the CNR of a photoacoustic image can be enhanced by increasing the laser fluence of illumination light in the linear thermal elastic regime. However, it is impossible to increase the laser fluence indefinitely due to potential laser damage. The laser fluence used in PAT generally follows the ANSI safety limit [29], which regulates the maximum permissible exposure (MPE) for the skin according to

(10)$$\textrm{MPE = }\left\{ \begin{array}{ll} {20,}&{400\textrm{ }\textrm{nm} \le \lambda \le 700\textrm{ }\textrm{nm, }}\\ {20 \times {{10}^{2({\lambda - 700} )/1000}}\textrm{, }}&{700\textrm{ }\textrm{nm} < \lambda \le 1000\textrm{ }\textrm{nm,}} \end{array} \right.$$

where λ is the laser wavelength. The MPE is a constant (20 mJ/cm²) in the visible band and increases with wavelength in the first NIR window (see Fig. S2). In the simulations and experiments in this study, the laser fluence is set to be consistent with the ANSI safety limit.

3. Results

3.1 Depth limit in linear detector array-based human breast imaging

Breast cancer is the leading cause of cancer incidence in women worldwide [30]. Non-invasive breast imaging is of great significance. To achieve high-performance imaging, it is critical to understand the imaging depth limit of PAT in the human breast. Towards this goal, we established a numerical breast model following the Methods and Table S4 and simulated the imaging depth limit of linear detector array-based breast imaging [31,32], as shown in Fig. 2(a). The simulations were performed in accordance with the settings described in Method S1.

Fig. 2. Imaging depth limit evaluation in the human breast under linear detection geometry. (a) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (b) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (c) Imaging depth limit and optical attenuation coefficient of the human breast in the visible and first NIR windows at 2 MHz detector centre frequency. (d) Dependence of imaging depth limit and acoustic attenuation coefficient on detector centre frequency. (e) Relationship between CNR and imaging depth at 730 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (f) Laser fluence map in the breast with depth. The laser wavelength is 730 nm. (g)−(j) PAT images of a spherical blood absorber at depths of 4.0 cm (fluence = 0.53 mJ/cm², CNR = 8.2), 5.0 cm (fluence = 0.18 mJ/cm², CNR = 5.4), 5.7 cm (fluence = 0.10 mJ/cm², CNR = 3.1), and 6.0 cm (fluence = 0.05 mJ/cm², CNR = 2.1), respectively. The acoustic detector is a linear array with a centre frequency of 2 MHz and is located at the top of the image. Scale bars: 2 mm. (k)−(m) Experimental PAT images at depths of 2.2 cm (CNR = 8.8), 3.8 cm (CNR = 3.3), and 4.1 cm (CNR = 2.7). The acoustic detector is a linear array with a centre frequency of 5 MHz and is located at the left side of the images.

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Figure 2(b) is a 3D map showing the simulated imaging depth limit as a function of laser wavelength and detector centre frequency. The deep imaging region is mainly concentrated in the NIR light and low acoustic frequency bands, which have weaker optical and acoustic attenuation. Figure 2(c) shows the estimated imaging depth limit and the optical attenuation coefficient of the breast in the visible and first NIR band at 2 MHz detector centre frequency (see Table S5 for specific values). The results suggest the following conclusions. First, the imaging depth limit of PAT in the human breast reaches the highest peak value of 5.7 cm at 730 nm and the second highest peak value of 5.6 cm at 795 nm, where the optical attenuation coefficients are minimum. Second, although the absorption coefficient of the blood absorber also changes with wavelength [10], its impact on the imaging depth limit is not as significant as the light attenuation coefficient of the background tissue, which has a direct inverse relationship with the imaging depth limit. Third, compared with the NIR window, the visible band suffers more significantly from light attenuation and thus has a smaller penetration depth (typically below 2 cm). These findings are consistent with the data in existing literature, where NIR wavelengths around 730 nm and 795 nm are widely used in breast imaging for enhanced penetration depth [33–35].

Figure 2(d) presents the dependence of imaging depth limit and acoustic attenuation coefficient on detector centre frequency (see Table S6 for specific values). The results show that the imaging depth limit exponentially declines with the increase of the detector centre frequency and the low-frequency band has a deeper imaging depth than the high-frequency band. This is in line with expectations considering that acoustic attenuation becomes more prominent at high frequencies. Figure 2(e) demonstrates the relationship between the contrast-to-noise ratio (CNR) and imaging depth at 730 nm and different detector centre frequencies. The values of CNR drop with the increase of imaging depth and a value of 3.0 (CNR = 3.0) corresponds to imaging depths of 6.6 cm, 5.7 cm, and 4.0 cm for 1 MHz, 2 MHz, and 5 MHz detector centre frequencies, respectively. These are the fundamental imaging depth limits of PAT in the human breast tissue at 730 nm.

To better understand the imaging depth limit in the breast, Figs. 2(f)−(j) showcase the map of laser fluence in the breast and simulated PAT images of a blood absorber located at different depths. The map of laser energy deposition density in this case can be found in Fig. S3. As expected, the PAT image quality degrades with the increase of imaging depth. The blood absorber gradually disappears in noise and becomes barely distinguishable when the imaging depth reaches a value of 5.7 cm, which corresponds to a CNR value of 3.1. This observation is consistent with the predefined image quality evaluation criterion (CNR = 3.0) in this study. Note that due to multiple backscattering, the laser fluence at the breast surface (120 mJ/cm²) is several times greater than the incident laser fluence (23 mJ/cm²), which is set according to the MPE [36,37]. As elaborated in [36], the fluence rate within the tissue near the surface significantly exceeds the incident laser fluence. The light accumulates near the surface due to backscatter, which augments the fluence rate at the surface by a factor k. This augmentation factor k increases as the total diffuse reflectance (R_d) increases, becoming linearly proportional to R_d when reflectance exceeds 0.2. In soft tissue, R_d is typically in the range of 0.2–0.6, and the fluence rate at the surface can be several folds greater than the incident laser fluence. The same is true for subsequent simulations and will not be repeated later.

To validate the simulation results, a phantom experiment was conducted (see Method S2), where a 0.2-mm-diameter blood-filled tube embedded in chicken breast tissues serves as the absorber. Figures 2(k)−(m) are experimental PAT images of the tube at depths of 2.2 cm, 3.8 cm, and 4.1 cm, respectively, which correspond to CNR values of 8.8, 3.3, and 2.7. We thus infer that a CNR value of 3.0 will give an imaging depth limit of 3.9 cm. This agrees with the simulation result of 4.0 cm at 5 MHz [Fig. 2(e)] and verifies the effectiveness of the proposed framework.

3.2 Depth limit in circular detector array-based human breast imaging

Circular detector array can overcome the limited view angle problem of linear detector array and is another widely used detection geometry in photoacoustic breast imaging [38]. To investigate the imaging depth limit of circular detector array-based breast imaging illustrated in Fig. 3(a), simulations were performed in accordance with the settings described in Method S3. Corresponding simulation results are shown in Figs. 3(b)−(e), which are the counterpart of Figs. 2(b)−(e). At 2 MHz detector centre frequency, the imaging depth limit reaches the highest peak value of 6.7 cm at 730 nm and the second highest peak value of 6.6 cm at 795 nm, where the optical attenuation coefficients are minimum. Other conclusions drawn in this simulation are generally consistent with those in the linear detector array case and are not detailed here. Note that the highest centre frequency of the detector considered is 30 MHz instead of 50 MHz used in the linear array case. This is because acoustic attenuation at frequencies beyond 30 MHz is so prominent that the photoacoustic signals generated by the absorber will experience significant attenuation after travelling a distance of the detector radius (11 cm) and are thus of little value for imaging. Figures 3(f)−(j) showcase the map of laser fluence in the breast and simulated PAT images of a blood absorber located at different depths. The map of laser energy deposition density in this case can be found in Fig. S4. A CNR value of 3.0 corresponds to an imaging depth of 6.7 cm at 730 nm and 2 MHz detector centre frequency, which indicates the imaging depth limit in the human breast is 6.7 cm in this case.

Fig. 3. Imaging depth limit evaluation in the human breast under circular detection geometry. (a) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (b) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (c) Imaging depth limit and optical attenuation coefficient of the human breast in the visible and first NIR windows at 2 MHz detector centre frequency. See Table S7 for specific values. (d) Dependence of imaging depth limit and acoustic attenuation coefficient on detector centre frequency. See Table S8 for specific values. (e) Relationship between CNR and imaging depth at 730 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (f) Laser fluence map in the breast with depth. The laser wavelength is 730 nm. (g)−(j) PAT images of a spherical blood absorber at depths of 4.5 cm (fluence = 1.26 mJ/cm², CNR = 8.7), 5.5 cm (fluence = 0.4 mJ/cm², CNR = 6.5), 6.7 cm (fluence = 0.14 mJ/cm², CNR = 3.0), and 7.5 cm (fluence = 0.04 mJ/cm², CNR = 2.1), respectively. The acoustic detector is a circular array with a centre frequency of 2 MHz and encircles the absorber. Scale bars: 2 mm.

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3.3 Depth limit in hemispherical detector array-based human breast imaging

Hemispherical detector array is well-suited for 3D imaging and is also widely used for photoacoustic breast imaging [39,40]. To investigate the imaging depth limit of hemispherical detector array-based breast imaging illustrated in Fig. 4(a), similar simulations were performed based on the 3D imaging system designed by Kruger [39] under the settings described in Method S4. Corresponding simulation results are shown in Figs. 4(b)−(e), which are the counterpart of Figs. 2(b)−(e). At 2 MHz detector centre frequency, the imaging depth limit in this case reaches the highest peak value of 6.7 cm at 730 nm and the second highest peak value of 6.6 cm at 795 nm, where the optical attenuation coefficients are minimum. Other conclusions are generally consistent with those in the linear detector array case and are not detailed here. Figures 4(f)−(j) showcase the map of laser fluence in the breast and simulated 3D PAT images of a blood absorber located at different depths. The map of laser energy deposition density in this case can be found in Fig. S5. A CNR value of 3.1 corresponds to an imaging depth of 6.7 cm at 730 nm and 2 MHz detector centre frequency, which indicates the imaging depth limit in the human breast is 6.7 cm in this case.

Fig. 4. Imaging depth limit evaluation in the human breast under hemispherical detection geometry. (a) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (b) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (c) Imaging depth limit and optical attenuation coefficient of the human breast in the visible and first NIR windows at 2 MHz detector centre frequency. See Table S9 for specific values. (d) Dependence of imaging depth limit and acoustic attenuation coefficient on detector centre frequency. See Table S10 for specific values. (e) Relationship between CNR and imaging depth at 730 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (f) Laser fluence map in the breast with depth. The laser wavelength is 730 nm. (g)−(j) PAT images of a spherical blood absorber at depths of 4.5 cm (fluence = 1.26 mJ/cm², CNR = 9.4), 5.5 cm (fluence = 0.4 mJ/cm², CNR = 5.9), 6.7 cm (fluence = 0.14 mJ/cm², CNR = 3.1), and 7.5 cm (fluence = 0.04 mJ/cm², CNR = 2.0), respectively. The acoustic detector is a hemispherical array with a centre frequency of 2 MHz and surrounds the absorber. Scale bars: 2 mm.

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3.4 Depth limit in the human abdomen-liver tissues

In addition to the human breast, PAT can potentially be used for disease diagnosis in other organs of the human body, such as the human liver [41]. We are curious about the imaging depth limit of PAT in the human abdomen-liver tissues and whether PAT could potentially be used as a non-invasive tool for the diagnosis of liver diseases in vivo. To answer this question, we established a two-layered abdomen-liver tissue model (see Methods and Table S11), where the top layer is a 2-cm-thick adult abdominal tissue [42] and the bottom layer is the liver, as illustrated in Fig. 5(a). Based on this model, a series of simulations were performed in accordance with the settings described in Method S5.

Fig. 5. Imaging depth limit evaluation in the human abdomen-liver tissues under linear detection geometry. (a) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (b) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (c) Imaging depth limit and optical attenuation coefficient in the visible and first NIR windows at 2 MHz detector centre frequency. (d) Dependence of imaging depth limit and acoustic attenuation coefficient on detector centre frequency. The imaging depth limit starts from 2.1 cm and the detector centre frequency cuts off at 15 MHz. (e) Relationship between CNR and imaging depth at 1000 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (f) Laser fluence map in the human abdomen-liver model with depth. The laser wavelength is 1000 nm. (g)−(j) PAT images of a spherical blood absorber at depths of 2.6 cm (fluence = 0.54 mJ/cm², CNR = 8.2), 3.0 cm (fluence = 0.12 mJ/cm², CNR = 4.9), 3.2 cm (fluence = 0.08 mJ/cm², CNR = 3.0), and 3.4 cm (fluence = 0.03 mJ/cm², CNR = 2.2), respectively. The acoustic detector is a linear array with a centre frequency of 2 MHz and is located at the top of the image. Scale bars: 2 mm.

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Figure 5(b) is a 3D map showing the simulated imaging depth limit in the abdomen-liver tissues as a function of laser wavelength and detector centre frequency. The deep imaging region is similarly concentrated in the NIR light and low acoustic frequency bands, which have weaker optical and acoustic attenuation. Figure 5(c) shows the optical attenuation coefficients of the abdomen and the liver and the estimated imaging depth limit from 620 nm to 1000 nm at 2 MHz detector centre frequency (see Table S12 for specific values). The optical attenuation coefficient of the liver is much higher than that of the abdomen and dominates the overall optical attenuation coefficient of this model. Therefore, the imaging depth limit is roughly inversely proportional to the optical attenuation coefficient of the liver and reaches the highest peak value of 3.2 cm at 1000 nm and the second highest peak value of 3.1 cm at 910 nm. Due to the lack of tissue data, the simulation model does not include results beyond 1000 nm. For longer wavelengths, the optical attenuation coefficient of the liver gets smaller and greater imaging depth is achievable [43].

In addition to the relationship between imaging depth limit and laser wavelength, Fig. 5(d) presents the dependence of the acoustic attenuation coefficients of the abdomen and the liver and imaging depth limit on the detector centre frequency in the range of 1 MHz to 15 MHz (see Table S13 for specific values). The results show that the imaging depth limit declines with the increase of the detector centre frequency and the low-frequency band has a deeper imaging depth than the high-frequency band. Figure 5(e) demonstrates the relationship between CNR and imaging depth at 1000 nm for different detector centre frequencies. The values of CNR drop with the increase of imaging depth and a value of 3.0 (CNR = 3.0) corresponds to imaging depths of 3.3 cm, 3.2 cm, and 2.9 cm (including the 2-cm-thick abdomen tissue) for 1 MHz, 2 MHz, and 5 MHz detector centre frequencies, respectively. These are the fundamental imaging depth limits of PAT in the human abdomen-liver tissues at 1000 nm.

To better understand the imaging depth limit in the human abdomen-liver tissues, Figs. 5(f)−(j) showcase the map of laser fluence and simulated PAT images of a blood absorber located at different depths. The map of laser energy deposition density in this case can be found in Fig. S6. The laser wavelength is 1000 nm and the linear array detector has a centre frequency of 2 MHz. As expected, the PAT image quality degrades with the increase of imaging depth. The blood absorber gradually disappears in noise and becomes barely distinguishable when the imaging depth reaches a value of 3.2 cm, which corresponds to a CNR value of 3.0. This observation is also consistent with the predefined image quality evaluation criterion (CNR = 3.0) in this study.

3.5 Depth limit in linear detector array-based rodent whole body

In addition to clinical diagnosis, PAT also has important applications in preclinical studies, such as small animal whole body imaging [44,45]. In such situations, it is important to understand the imaging depth limit. Towards this goal, we established a digital mouse model with segmented organs including the brain, the liver, the kidney, the spleen, and so on (see Fig. 6(a) and Fig. S7) from computed tomography and cryosection data according to [46]. The optical, thermal, and acoustic properties of the organs are modelled following the Methods and specific modelling data can be found in Table S14. Since the liver has a high whole blood volume fraction (see Table S1), it attenuates light more significantly and is the decisive organ limiting the imaging depth of PAT in the rodent whole body. Therefore, it is meaningful to focus on the imaging depth limit in the liver region [Fig. 6(b)]. Based on this consideration, we simulated the imaging depth limit of linear detector array-based rodent imaging near the liver illustrated in Fig. 6(c) in accordance with the settings described in Method S6.

Fig. 6. Imaging depth limit evaluation in the mouse model under linear detection geometry. (a) 3D digital mouse model with segmented organs [46]. 1: adipose. 2: bone. 3: kidney. 4: spleen. 5: stomach. 6: liver. 7: lung. 8: heart. 9: brain. (b) A cross section of the mouse in the liver region indicated by the arrow in a. 10: an artificial blood absorber for imaging depth evaluation. (c) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (d) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (e) Imaging depth limit and optical attenuation coefficient of the mouse liver in the visible and first NIR windows at 5 MHz detector centre frequency. (f) Dependence of imaging depth limit and acoustic attenuation coefficient of the mouse liver on detector centre frequency. (g) Relationship between CNR and imaging depth at 1000 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (h)−(k) Laser fluence maps in different-sized mice (torso diameter: 2.0 cm, 3.4 cm, 4.6 cm, and 5.2 cm). The dotted curves represent the boundaries of the mouse torso and organs. The laser wavelength is 1000 nm. Scale bars: 1 cm. (l)−(o) PAT images of the spherical blood absorber at depths of 1.0 cm (fluence = 13.1 mJ/cm², CNR = 8.5), 1.7 cm (fluence = 1.1 mJ/cm², CNR = 6.5), 2.3 cm (fluence = 0.2 mJ/cm², CNR = 3.0), and 2.6 cm (fluence = 0.05 mJ/cm², CNR = 2.0), respectively. The acoustic detector is a linear array with a centre frequency of 5 MHz and is placed at the top of the image. Scale bars: 0.5 mm.

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Figure 6(d) is a 3D map showing the simulated imaging depth limit in the rodent whole body as a function of laser wavelength and detector centre frequency. Similar to the linear detector array-based human breast imaging, the deep imaging region in this case is also concentrated in the NIR light and low acoustic frequency bands, which have weaker optical and acoustic attenuation. Figure 6(e) shows the estimated imaging depth limit and the optical attenuation coefficient of the mouse liver in the visible and first NIR band at 5 MHz detector centre frequency (see Table S15 for specific values). Since the optical attenuation coefficient of the liver is much greater than those of other tissues, it dominates the overall light attenuation of the mouse model and is roughly inversely proportional to the imaging depth limit, which reaches a peak value of 2.3 cm at 1000 nm. Moreover, compared with the NIR window, the visible band suffers more significantly from optical attenuation and thus has a much smaller penetration depth.

In addition to the relationship between imaging depth limit and laser wavelength, Fig. 6(f) presents the dependence of imaging depth limit and the acoustic attenuation coefficient of the liver on the detector centre frequency in the range from 1 MHz to 50 MHz (see Table S16 for specific values). The results show that the imaging depth limit declines exponentially with the increase of the detector centre frequency. However, the decline rate is not as high as that in the breast imaging case, as shown in Fig. 2(d). This is mainly because optical attenuation in this case is more significant, resulting in limited imaging depths, where acoustic attenuation is not that noticeable. Therefore, high-frequency acoustic detectors are well-suited for small animal imaging. Figure 6(g) demonstrates the relationship between CNR and imaging depth at 1000 nm and different detector centre frequencies. The values of CNR drop with the increase of imaging depth and a value of 3.0 (CNR = 3.0) corresponds to imaging depths of 2.5 cm, 2.3 cm, and 2.0 cm for 2 MHz, 5 MHz, and 10 MHz detector centre frequencies, respectively. This indicates that the largest diameter of the rodent torso that can be imaged near the liver is 4.6 cm at 1000 nm and 5 MHz.

To better understand the imaging depth limit in the rodent whole body, Figs. 6(h)−(o) showcase the maps of laser fluence in mice and simulated PAT images of a blood absorber located in the liver at different depths. The maps of laser energy deposition density in this case can be found in Fig. S8. The laser wavelength is 1000 nm and the linear array detector has a centre frequency of 5 MHz. As expected, the PAT image quality degrades with the increase of imaging depth. The blood absorber gradually disappears in noise and becomes barely distinguishable when the imaging depth reaches a value of 2.3 cm, which corresponds to a CNR value of 3.0. This observation is also consistent with the predefined image quality evaluation criterion (CNR = 3.0) in this study.

3.6 Depth limit in circular detector array-based rodent whole body

Circular detector array is also widely used for PAT imaging of small animals [47,48]. To investigate the imaging depth limit of circular detector array-based rodent whole body imaging in the liver region illustrated in Figs. 7(a) and (b), a series of simulations were performed in accordance with the settings described in Method S7. Corresponding simulation results are shown in Figs. 7(c)−(f), which are the counterpart of Figs. 6(d)−(g). The imaging depth limit reaches a peak value of 2.4 cm at 1000 nm and 5 MHz detector centre frequency, where the optical attenuation coefficient is minimum. Other conclusions drawn in this simulation are generally consistent with those in the linear detector array case and are not detailed here. Figures 7(g)−(n) showcase the maps of laser fluence in the mouse and simulated PAT images of a blood absorber located at different depths. The maps of laser energy deposition density in this case can be found in Fig. S9. A CNR value of 3.0 corresponds to an imaging depth of 2.4 cm, which indicates the largest diameter of the rodent torso that can be imaged in the liver region is 4.8 cm at 1000 nm and 5 MHz.

Fig. 7. Imaging depth limit evaluation in the mouse model under circular detection geometry. (a) A cross section of the mouse in the liver region. (b) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (c) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (d) Imaging depth limit and optical attenuation coefficient of the mouse liver in the visible and first NIR windows at 5 MHz detector centre frequency. See Table S17 for specific values. (e) Dependence of imaging depth limit and acoustic attenuation coefficient of the mouse liver on detector centre frequency. See Table S18 for specific values. (f) Relationship between CNR and imaging depth at 1000 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (g)−(j) Laser fluence maps in different-sized mice (torso diameter: 2.0 cm, 3.4 cm, 4.8 cm, and 5.2 cm). The dotted curves represent the boundaries of the mouse torso and organs. The laser wavelength is 1000 nm. Scale bars: 1 cm. (k)−(n) PAT images of the spherical blood absorber at depths of 1.0 cm (fluence = 43 mJ/cm², CNR = 8.9), 1.7 cm (fluence = 6.0 mJ/cm², CNR = 7.0), 2.4 cm (fluence = 0.9 mJ/cm², CNR = 3.0), and 2.6 cm (fluence = 0.4 mJ/cm², CNR = 2.1), respectively. The acoustic detector is a circular array with a centre frequency of 5 MHz and encircles the mouse. Scale bars: 0.5 mm.

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3.7 Depth limit in hemispherical detector array-based rodent whole body

Hemispherical detector array is widely used for 3D rodent whole body imaging in PAT [49,50]. To investigate the imaging depth limit of hemispherical detector array-based rodent imaging in the liver region illustrated in Figs. 8(a) and (b), a series of simulations were performed based on the 3D imaging system reported in [49,50] following the settings described in Method S8. Corresponding simulation results are shown in Figs. 8(c)−(f), which are the counterpart of Figs. 6(d)−(g). The imaging depth limit in this case reaches a peak value of 1.5 cm at 1000 nm and 5 MHz detector centre frequency, where the optical attenuation coefficient is minimum. Other conclusions are generally consistent with those in the linear and circular detector array cases and are not detailed here. Figures 8(g)−(n) showcase the maps of laser fluence in the mouse and simulated 3D PAT images of a blood absorber located at different depths. The maps of laser energy deposition density in this case can be found in Fig. S10. A CNR value of 3.0 corresponds to an imaging depth of 1.5 cm at 1000 nm and 5 MHz detector centre frequency, which indicates the imaging depth limit is 1.5 cm in this case.

Fig. 8. Imaging depth limit evaluation in the mouse model under hemispherical detection geometry. (a) A cross section of the mouse in the liver region. (b) Schematic. d_o: optical penetration depth; d_a: acoustic penetration depth. (c) Dependence of imaging depth limit on laser wavelength and detector centre frequency. (d) Imaging depth limit and optical attenuation coefficient of the mouse liver in the visible and first NIR windows at 5 MHz detector centre frequency. See Table S19 for specific values. (e) Dependence of imaging depth limit and acoustic attenuation coefficient of the mouse liver on detector centre frequency. See Table S20 for specific values. (f) Relationship between CNR and imaging depth at 1000 nm for different detector centre frequencies. The scattered dots represent simulation data and the curves are their smooth fits. (g)−(j) Laser fluence maps in different-sized mice (torso diameter: 1.6 cm, 2.4 cm, 3.0 cm, and 3.4 cm). The dotted curves represent the boundaries of the mouse torso and organs. The laser wavelength is 1000 nm. Scale bars: 1.0 cm. (k)−(n) PAT images of the spherical blood absorber at depths of 0.8 cm (fluence = 21 mJ/cm², CNR = 8.0), 1.2 cm (fluence = 6 mJ/cm², CNR = 5.5), 1.5 cm (fluence = 3.2 mJ/cm², CNR = 3.0), and 1.7 cm (fluence = 1.5 mJ/cm², CNR = 2.2), respectively. The acoustic detector is a hemispherical array and has a centre frequency of 5 MHz. Scale bars: 0.5 mm.

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4. Discussions

To the best of our knowledge, the simulation models for the evaluation of the imaging depth limit in PAT have rarely been reported thus far. In 2010, Telenkov and Mandelis tried to define the achieved maximum imaging depth of PAT with the system noise floor [23]. The authors built theoretical models to estimate the thermal noise level and the peak voltage of excited acoustic pressure response at given depths. A signal-to-noise (SNR) value was calculated based on the above-estimated results. However, no image reconstruction was performed to quantify the imaging depth limit, and the theoretical models are far too simple to accurately simulate the physical process of PAT, which consists of tissue modelling, photon transportation, photon to ultrasound conversion, sound field propagation, signal reception, image reconstruction, and imaging depth evaluation.

Table 1 summarizes the evaluated imaging depth limits of PAT in the human breast, the human abdomen-liver tissues, and the rodent whole body using the proposed framework. In this study, we only provide a validation study for the linear array-based human breast imaging simulation due to hardware limitations. However, the specifications of most imaging configurations studied in this paper were specially set to be closely related to reported experimental studies so that the simulated results can be validated with reported literature data. Generally, the imaging depth limit depends on both the acoustic properties of the detector and the optical properties of the light. Using a 2 MHz centre frequency detector, the maximum imaging depth limits in the human breast and the human abdomen-liver tissues are about 6.7 cm at 730 nm and 3.2 cm at 1000 nm, respectively. Using a 5 MHz centre frequency detector, the maximum imaging depth limit in the liver region of a mouse is about 2.4 cm at 1000 nm. These simulation findings are well supported by reported literature data (see Table S21) and can provide useful guidance for practical imaging experiments. Nevertheless, the simulated imaging depth limit of PAT in the human abdomen-liver tissues is expected to be validated on human subjects following the approval of corresponding protocols in the future.

Table 1. Fundamental imaging depth limits of PAT in different tissues.

View Table

In the human breast imaging simulations, the centre frequencies of the transducers used in the different configurations are 2 MHz. As discussed in Section 2.4, acoustic attenuation is not a dominant factor that limits the imaging depth for low-frequency PAT imaging. The circular array-based imaging configuration shows a larger imaging depth limit than the linear array-based imaging configuration owing to a larger beam diameter, while the imaging depth limit of the hemispherical array-based imaging configuration is the same as that of the circular array-based imaging configuration due to the same beam diameter. In the rodent whole-body imaging simulations, the centre frequencies of the transducer used in the different configurations are 5 MHz, and the impact of acoustic attenuation should be accounted for. The circular array-based imaging configuration shows a similar imaging depth limit to the linear array-based imaging configuration for two reasons. First, the former has a larger beam size compared to the latter, which is beneficial for increasing the imaging depth limit. Second, the acoustic penetration depth of the former is greater than that of the latter, which will decrease the imaging depth limit. The impact of a larger beam size and a greater acoustic penetration depth cancel each other out to a large extent. The imaging depth limit of the hemispherical array-based imaging configuration is significantly smaller than that of the circular array-based imaging configuration due to a smaller beam size and a greater acoustic penetration depth.

To achieve maximum imaging depth in real experiments, we can use NIR light to illuminate biological tissues for better photon penetration and low-frequency detectors to receive photoacoustic signals for enhanced sensitivity. As shown in [9], most biological tissues show lower reduced scattering coefficients in the NIR range than in the visible. According to the data reported in [51,52], the scattering coefficient of hemoglobin in the NIR range is slightly higher than that in the visible. However, the absorption coefficient of hemoglobin in the NIR range is significantly lower than that in the visible. As a result, the μ_eff of hemoglobin generally decreases with the wavelength shifts from the visible to the NIR range, which leads to an exponential growth of local laser fluence in the NIR range when hemoglobin is treated as the background tissue. Although the blood absorber has a relatively lower absorption coefficient in the NIR range, the exponential growth of local laser fluence still leads to a higher temperature rise, implying a greater imaging depth. Therefore, the suggestion still holds, indicating that using NIR light to illuminate biological tissues is beneficial for maximizing the imaging depth.

In addition, there are other commonly used approaches such as signal averaging and contrast agent administration for imaging depth enhancement. Signal averaging can suppress background noise and thus improve the CNR value. Therefore, the imaging depth limit can be improved by increasing the number of signal averaging times. For example, the imaging depth limit in the human breast at 730 nm and 2 MHz can be extended from 5.7 cm to 8.0 cm with 250 times signal averaging (see Fig. S11). Contrast agent administration can improve the CNR by boosting the amplitude of photoacoustic signals [44,53,54] and thus can also be used for imaging depth enhancement. By using contrast agents such as small molecule dyes and gold and carbon nanostructures with higher optical absorption coefficients [53], the imaging depth limit can be enhanced. For example, the imaging depth limit in the human breast at 730 nm and 2 MHz using a linear detector array can be extended from 5.7 cm to 7.5 cm by using a contrast agent with a higher optical absorption coefficient (see Fig. S11).

This study may have the following limitations. First, due to the lack of tissue data beyond 1000 nm, the simulation in the second NIR window is not included in the current study. Second, the tissue properties employed in this study are based on literature data and may not be completely comprehensive and accurate. Third, some tissue data in the visible and first NIR window are not readily available in literature and, therefore, the data of similar tissues are used as a surrogate (see Table S14). This may potentially lead to evaluation discrepancies to some degree. Nevertheless, the proposed numerical framework and obtained general conclusions in this study are of universal significance and can provide useful guidance for practical experiments, such as wavelength selection, acoustic detector design, system optimization, and experimental phenomena interpretation.

5. Conclusions

The general conclusion we can draw from the study is that the imaging depth limit of PAT in biological tissues is the result of the synergistic effect of light and sound. For a fixed acoustic frequency, the imaging depth limit is inversely proportional to the optical attenuation of tissues and is generally greater in the NIR band than the visible. For a particular optical wavelength, the imaging depth limit declines exponentially with the increase of acoustic frequency due to frequency-dependent acoustic attenuation and is generally greater in the low-frequency band. Therefore, using NIR light for illumination and low-frequency detectors for signal reception is beneficial for deep tissue PAT imaging. System geometry also has an impact on the imaging depth limit. For example, in rodent whole body imaging, ring illumination can provide better photon penetration into the mouse body and improve the imaging depth.

Funding

National Natural Science Foundation of China (12174368, 61705216, 62122072); National Key Research and Development Program of China (2022YFA1404400); Anhui Provincial Department of Science and Technology (18030801138, 202203a07020020); Natural Science Foundation of Anhui Province (2308085QA21); University of Science and Technology of China (YD2090002015); Institute of Artificial Intelligence at Hefei Comprehensive National Science Center (23YGXT005).

Acknowledgments

We thank Xiaoxiao Ma for assisting with the preparation of the schematics and Chenxi Zhang for proofreading the manuscript.

Disclosures

The authors declare no conflicts of interest.

Data availability

All data are available within the Article and Supplementary Files, or available from the corresponding author upon reasonable request. Photon transportation is simulated using the freely available Monte Carlo toolbox developed by Jacques [13]. Sound field propagation and image reconstruction are implemented using the freely available k-Wave toolbox developed by the Photoacoustic Imaging Group at University College London [17]. Other codes are available from the corresponding authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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On the imaging depth limit of photoacoustic tomography in the visible and first near-infrared windows

Abstract

1. Introduction

2. Methods

2.1 Tissue modelling

2.2 Photon transportation in tissues

2.3 Photon to ultrasound conversion

2.4 Sound field propagation

2.5 Sound signal reception

2.6 Image reconstruction

2.7 Evaluation criterion for imaging depth limit

3. Results

3.1 Depth limit in linear detector array-based human breast imaging

3.2 Depth limit in circular detector array-based human breast imaging

3.3 Depth limit in hemispherical detector array-based human breast imaging

3.4 Depth limit in the human abdomen-liver tissues

3.5 Depth limit in linear detector array-based rodent whole body

3.6 Depth limit in circular detector array-based rodent whole body

3.7 Depth limit in hemispherical detector array-based rodent whole body

4. Discussions

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (8)

Tables (1)

Equations (10)

Optics Express

	Laser wavelength (nm)	Laser fluence (mJ/cm²)	Detector centre frequency (MHz)	Detection geometry	Depth limit (cm)
Human breast	730	23	2	Linear	5.7
				Circular	6.7
				Hemispherical	6.7
Human abdomen-liver tissues	1000	80	2	Linear	3.2
Rodent	1000	80	5	Linear	2.3
				Circular	2.4
				Hemispherical	1.5