Photoacoustic tomography extracted from speckle noise in acoustically inhomogeneous tissue

Dan Wu; Chao Tao; Xiaojun Liu

doi:10.1364/OE.21.018061

1. Introduction

Photoacoustic tomography (PAT) has been receiving growing attention in the last decade [1–17], since it combines good acoustic resolution in deep tissue with the optical absorption contrast. It has been widely applied to small animal imaging [1, 3], vasculature visualization [4, 5], osteoarthritis assessment [6–8], drug delivery monitoring [9], and so on. Recently, Sun et al. applied PAT to evaluate the tissue denaturation induced by high-intensity focused ultrasound treatment [10]. Nie et al. imaged monkey brain [11] using PAT. Xia et al. [12] and Wang et al. [13] developed the three-dimensional PAT systems. PAT is usually limited to the biological tissues with relatively homogeneous acoustical properties [17]. Many efforts, including ultrasound tomography [18], time reversal method [19, 20], statistical reconstruction [21], and coherence factor optimization [22] have been done to improve the PAT in inhomogeneous tissue. However, these studies usually need known some prior knowledge of tissue inhomogeneity [19,21] or only consider some relatively simple scenario of tissue inhomogeneous, such as speed inhomogeneity [18, 22] or single scattering [20].

Biological tissue is essentially a kind of acoustically stochastic medium. A large number of acoustically stochastic scatterers with the size comparable to wavelength could generate multiple scattering and randomly distort the propagation of photoacoustic (PA) signal. This random multiple scattered field is usually referred to as speckle noise [23]. Speckle noise inherently exists in acoustical inhomogeneous tissue. It could bring about artifacts and distortion, and thus degrade image quality [19,21]. Therefore, speckle noises coming from acoustically inhomogeneous tissue are usually considered as nuisance and ignored in classical PAT. Speckle noise remains challenging the PAT.

In this study, an ultrasound-photoacoustics (US-PA) scheme is proposed to break the limitation of PAT in acoustically inhomogeneous tissue. An ultrasonic (US) method is used to determine the Green's function of inhomogeneous. Then, with the known Green’s function, we extend the PAT to speckle environment. Finally, we use the proposed method to improve the limited-view PAT by extracting the back-propagating information from the speckle noise.

2. Theory

Figure 1 represents the scenario considered in this study. The region of interest (ROI) is located below the surface of the tissue. A transducer array is attached on the surface to pick up the PA signal coming from the tissue. The randomly distributed circles represent scatterers deep in the tissue which scatter PA signals and give rise to speckle noise. In a PAT system, laser beam is expanded, diffused, and then irradiated on the tissue uniformly [1, 15]. After tissues are illuminated by pulsed laser, thermal expansion induced an initial acoustic sources q(r₀, t₀), which is positive proportional to optical energy absorption deposition A(r₀), i.e., q(r₀, t₀) ~A(r₀)∂H(t₀)/∂t₀ [17]. H(t₀) is the temporal profile of the laser pulse. The generated PA pressure p(r_d, t) at position r_d and time t (0 ≤ t ≤ T) is

p (r_{d}, t) = \int_{0}^{T} d t_{0} ∭_{R} q (r_{0}, t_{0}) g (r_{d}, t | r_{0}, t_{0}) d r_{0},

where g(r_d, t | r₀, t₀) is the Green’s function of medium, through which PA wave is propagating from r₀ to r_d. There are two paths, along which PA wave can reach the ultrasound transducer. Part of PA signal (p_d₁ in Fig. 1) is propagating though the homogeneous tissue. Part of PA signal (p_d₂ shown in Fig. 1) is scattered and reflected (p_s in Fig. 1) by the speckle tissue. Therefore, the Green's function g(r_d, t | r₀, t₀) also consists of two terms g(r_d, t | r₀, t₀) = g_h(r_d, t | r₀, t₀) + g_s(r_d, t | r₀, t₀), where g_h and g_s correspond to the homogeneous and speckle tissues, respectively. We can rewrite Eq. (1) as

Fig. 1 The sketch of the scenario considered. Scatters (circles) are randomly distributed in tissue. A 16-element transducer array is utilized to send and record ultrasound, and record generated photoacoustic signals.

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p (r_{d}, t) = \int_{0}^{T} d t_{0} ∭_{R} q (r_{0}, t_{0}) [g_{h} (r_{d}, t | r_{0}, t_{0}) + g_{s} (r_{d}, t | r_{0}, t_{0})] d r_{d} .

Time reversing the detected PA signal p_d(r_d, t) to p_d(r_d, T – t) and reemitting the reversed signals p_d(r_d, T – t), we have the time reversal field p_TR(r₀, t),

p_{T R} (r_{0}, t) = \int_{0}^{T} d t_{1} \iint_{Σ} d r_{d} p_{d} (r_{d}, T - t_{1}) [g_{h} (r_{0}, t | r_{d}, t_{1}) + g_{s} (r_{0}, t | r_{d}, t_{1})],

where T is the length of recorded PA signals. According to time reversal invariance [20, 24, 25], we have p_TR(r₀, t) ≈p(r₀, T–t) and the time reversal wave will eventually focus toward the originally PA sources, i.e., p_TR(r₀, T) ~A(r₀). The optical absorption distribution can be reconstruction from the detected PA signal by integrating Eq. (3). Therefore, Eq. (3) provides an algorithm to reconstruct PA image from the detected PA signal. For the homogeneous tissue with the known velocity of sound c, the Green’s function is given as g₀(r_d, t | r, t₁) = δ(t–t₁–|r₀–r_d|/c)/4π|r₀–r_d|. However, for the acoustically inhomogeneous tissue, the Green’s function g_s(r_d, t | r, t₁) is unknown, the reconstruction of PAT become difficult. This is the reason that the applications of PAT are often prohibited from acoustically inhomogeneous tissue [17].

If the Green’s function g_s(r_d, t | r, t₁) is determined, PAT can be extracted from speckle noise. Fortunately, US technique depends primarily on acoustic heterogeneity and it could provide the information of acoustically inhomogeneous properties of tissues [23, 26]. Therefore, US technique could determine the Green’s function of inhomogeneous tissue and thus make up the limitation of PAT in speckle tissue. This is the basic idea of our US-PA scheme:

Firstly, in order to estimate the Green’s function of speckle tissue, an N-element US transducer array is employed to emit and receive ultrasound, as shown in Fig. 1. A US pulse with a waveform u(t) is transmitted by the i-th (i = 1, 2, …, N) element of transducer array. The scattered field reflected by the speckle tissue is detected by the same transducer array, where the signals recorded by the j-th (j = 1, 2, …, N) element are denoted as h(j, i, t). Repeating the US pulse emitting and receiving for each element of the transducer array, we obtain N × N impulse responses h(j, i, t) (i, j, = 1, 2, …, N) between each pair of elements. With these impulse responses, the Green's function g_s can be represented in frequency domain by [26]

G_{s} (r_{d}^{(i)}, r, ω) = \int_{r_{d}^{(j)} \in Σ} ϕ (ω) H_{s} (j, i, ω) G_{h}^{*} (r_{d}^{(j)}, r, ω) d S,

where G_s(r_d⁽ⁱ⁾, r, ω) and G_h(r_d⁽^j⁾, r, ω) are the Fourier transformation of the Green’s function g_s(r_d⁽ⁱ⁾, t | r, t₁) and g_h(r_d⁽^j⁾, t | r, t₁), r_d⁽ⁱ⁾ is the position of the i-th transducer element, Σ is the surface of transducer array, and H_s(j, i, ω) is the Fourier transform of impulse responses h(j, i, t). ϕ(ω) = U*(ω) is a signal-shaping filter that accounts for the imprint of the source-time excitation function, where U(ω) is the Fourier transformation of the US pulse u(t). The superscript * denotes complex conjugation,

For a discrete ultrasound array, the integral in Eq. (4) can be approximated by the summation,

G_{s} (r_{d}^{(i)}, r, ω) \approx \sum_{j = 1}^{N} ϕ (ω) H_{s} (j, i, ω) G_{h}^{*} (r_{d}^{(j)}, r, ω) .

Then, the Green’s function g_s(r_d⁽ⁱ⁾, t | r, t₁) is evaluated by applying the inverse Fourier transformation on G_s(r_d⁽ⁱ⁾, r, ω).

Secondly, the ROI is illuminated by laser pulse and the excited PA signal is detected by the same US transducer. With the recorded PA signals and the estimated Green's function g(r_d, t | r, t₁) = g_h(r_d, t | r, t₁) + g_s(r_d, t | r, t₁), we can extract PAT images from the speckle noise by integrating Eq. (3).

The proposed US-PA scheme takes the advantages of both the US technique and PAT technique, which make it possible to extract PAT from acoustically inhomogeneous tissue. Moreover, the validities of the Green’s function estimation [Eq. (5)] and the image reconstruction [Eq. (3)] do not depend on the prior knowledge of tissue and the complexity of the medium perturbation. Therefore, this US-PA scheme could be generally applied to various scenarios, like scattering from stochastic tissue.

3. Results

Numerical experiments are carried out to validate of the proposed method. As shown in Fig. 1, the randomly distributed white circles represent acoustic scatterers with a diameter of 1.6 mm. The two dark gray circles at the center of the ROI denote optical absorbers with a diameter of 2.0 mm. The relative optical energy absorption deposition A(r₀) of optical absorbers is 1.0, while A(r₀) of the medium is 0.0. The center of the shallow absorber is 3.0 mm distance from the US transducer and the deep one is 7.0 mm distance from the US transducer. In the following discussion, the deep absorber indicates the absorber, which is far from the US transducer, while the shallow absorber means the one, which is close to the transducer, as shown in Fig. 1. The acoustic parameters of the medium are c = 1500 m/s and ρ = 1000 kg/m³. An US transducer array with 16 elements (N = 16) is utilized to transmit and record US pulse for the Green’s function estimation. The same transducer array is also used to detect PA signals generated by laser pulse.

US pulse with a central frequency of 3.5 MHz is emitted by the transducer array. The response signals h(j, i, t) within time duration 50 µs are recorded. The Green's function G_s is estimated from the impulse response signals according to Eq. (5). PA signals from the optical absorbers are recorded, as shown in Fig. 2(a). With the known Green's function and detected photoacoustic signals, images are reconstructed according to Eq. (3).

Fig. 2 Extracting PA images from speckle noise. (a) The detected PA field. (b) The image by excluding speckle noise. (c) Image by including speckle noise.

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For the sake of comparison, PA images are also reconstructed by only using the direct signal p_d₁ propagating through homogeneous tissue. In this situation, the speckle signal is ignored and the reconstruction equation [Eq. (3)] degraded to p_TR(r₀, t) = ∫dt₁ ∫∫_Σdr_dp_d(r_d, T – t₁)g_h(r₀, t | r_d, t₁). Using the summation instead of the integral in the above equation, we have

p_{T R} (r_{0}, T) ~ \sum_{i = 1}^{N} w (i, r_{0}) p_{d}^{(i)} (| r_{d}^{(i)} - r_{0} | / c),

where p_d⁽ⁱ⁾ is the PA signal recorded by the i-th transducer element. w(i, r₀) is the weighting factors taking into account the angular sensitivity of transducer array. This factor can be determined through experimental measurement or theoretical calculation [27]. For the sake of simplicity, we let w(i, r₀) = 1 in the following simulation. By ignoring speckle noise, the reconstruction equation is degraded to the widely used delay and sum method [28].

As shown in Fig. 2(b), when the speckle signal is ignored for the image reconstruction, the image of absorbers is seriously distorted due to the absence of the backside PA signals [29–31]. Moreover, although the two absorbers have the same optical absorber coefficient, they are presented significantly intensity difference in the reconstructed image [31]. The reconstructed intensity of the deep absorber is only about 60% of that of the shallow one. This is because that the US linear array with a finite length does not enclose the ROI and can only capture the forward-propagating photoacoustic waves (e.g., p_d₁ in Fig. 1), which results in the limited-view PAT. The incomplete PA data will induce artifacts, distortion [20, 30], and false intensity contrast of absorbers located in different depth [31].

Figure 2(c) illustrates the PA image extracted from speckle noise by using the proposed method. When speckle noises are involved for imaging reconstruction, the distortion is restrained and the false intensity contrast between the two absorbers is decreased. The image quality is better than that without speckle noise. This phenomenon could be explained that the backside information carried by the speckle noise improves the image quality. As we have discussed, the US linear array only capture the forward-propagating photoacoustic waves (p_d₁) and the speckle signal (e.g., p_s). The back-propagating PA wave (p_d₂) is missed. However, after the random scattering by stochastic tissue, the information carried by the back-propagating PA wave (p_d₂) is distorted, but it remains existence in the speckle noise (p_s). They cannot be utilized by the classical PAT scheme due to the absence of the Green’s function of heterogeneous tissue. However, the US-PA scheme utilizes the US method to determine the Green’s function of speckle tissue and make up the PAT limitation. It allows us to extract the backside information of the ROI encoded in speckle noise for the image reconstruction. Therefore, the image quality is improved.

Multiple scattering induced by stochastic tissue expands a narrow pulse signal to a speckle noise with a long duration. The influence of signal length on the image quality is important. Figure 3 present the relationship between signal length and image quality, where the full width at half maximum (FWHM) and the maximum amplitude ratio γ between two absorbers are chosen to quantify distortion and false contrast, respectively. As shown in Fig. 3(a), when only direct wave (the first 5µs of signal p_d) are employed for the image reconstruction, the FWHM of the deep absorber is only about 0.8 mm [Fig. 3(a)], which has far deviated from its actual diameter 2.0 mm. Moreover, the image intensity of the deeper absorber is much lower than that of the shallow one [Fig. 3(b)]. When more and more low-order scattering wave (about the first 20 µs of the detected PA signal) are included for imaging, the FWHM is approaching toward the actual value [Fig. 3(a)] and the false contrast between two absorbers are decreased [Fig. 3(b)]. Finally, the further increasing of signal length will only lead to relatively minor improvement. It could because the high-order scattering wave is generally much weaker than the direct wave and the low-order scattering wave.

Fig. 3 Influence of signal length on the image quality. (a) FWHM. (b) Amplitude ratio between the two absorbers.

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The length of US array not only determines the estimation of Green’s function but also the recording of PA signal. Figure 4 presents the performance of the US-PA scheme with various transducer array lengths. In general, the image extracted from the signals including the speckle noise is better than those by ignoring speckle noise. Moreover, both FWHM and amplitude ratio are improved with the length of the transducer array. This change can be explained from two aspects. First, a longer US array will capture more direct wave, which decrease the distortion and false contrast induced by the incomplete data [20, 30, 31]. Second, a longer US array will increase the accuracy in approximating the Green's function. Additionally, it is noticed that when the transducer array is short (< 20 mm), the image size of the shallow absorber is better if speckle signal is not included. This could be the result of the estimation error of the Green’s function due to the short US transducer. A shorter US array will decrease the accuracy in approximating the Green's function. This error could bring additional distortion to the reconstructed image.

Fig. 4 Influence of transducer array length on the performance of the US-PA method. (a) FWHM. (b) Amplitude ratio between the two absorbers.

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4. Summary

An US-PA imaging scheme is proposed to break the limitation PAT in acoustically inhomogeneous tissue. The US technique is carried out to determine the Green's function between each transducer element and the ROI. By utilizing US to make up the PAT limitation in acoustically heterogeneous tissue, PA images could be extracted from speckle noise with the determined Green’s function. Studies show that the method can effectively decrease the distortion and false intensity contrast in limited-view PA images. The information extracted from the speckle noise significantly improves the image quality. The US-PA method does not depend on the prior knowledge of tissue and the complexity of the medium perturbation. Moreover, the estimation of Green’s function and the detection of PA signal are performed by the same ultrasound transducer. Therefore, the proposed scheme could be easily integrated into a classical PAT system and improve PAT in acoustically inhomogeneous tissue.

Acknowledgments

This work was supported by the National Basic Research Program of China under Grant No. 2012CB921504, the Natural Science Foundation of China under Grant Nos. 11274167 and 11274171, and SRFDP Grant No. 20120091110001.

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Photoacoustic tomography extracted from speckle noise in acoustically inhomogeneous tissue

Abstract

1. Introduction

2. Theory

3. Results

4. Summary

Acknowledgments

References and links

Cited By

Figures (4)

Equations (6)

Optics Express