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Photoacoustic imaging is an emerging imaging technology combining optical imaging with ultrasound. Imaging of the optical absorption coefficient and flow measurement provides additional functional information compared to ultrasound. The issue with photoacoustic imaging is its low signal-to-noise ratio (SNR) due to scattering or attenuation; this is especially problematic when high pulse repetition frequency (PRF) lasers are used. In previous research, coded excitation utilizing several pseudorandom sequences has been considered as a solution for the problem. However, previously proposed temporal coding procedures using Golay codes or M-sequences are so complex that it was necessary to send a sequence twice to realize a bipolar sequence. Here, we propose a periodic and unipolar sequence (PUM), which is a periodic sequence derived from an m-sequence. The PUM can enhance signals without causing coding artifacts for single wavelength excitation. In addition, it is possible to increase the temporal resolution since the decoding start point can be set to any code in periodic irradiation, while only the first code of a sequence was available for conventional aperiodic irradiation. The SNR improvement and the increase in temporal resolution were experimentally validated through imaging evaluation and flow measurement.
© 2016 Optical Society of America
1. Introduction
Photoacoustic (PA) imaging is an emerging imaging technology combining optical imaging with ultrasound [1–3]. A nanosecond laser pulse is irradiated into an optical absorber, which generates photoacoustic waves by thermo-elastic expansion. Photoacoustic waves possess acoustical properties that enable greater penetration depth compared to other optical imaging methods. Optical absorption properties differ from target to target, so that multi-spectral information can be used to obtain functional information such as blood oxygenation [1–3]. The issue with PA imaging is that the excitation light is attenuated because it diffuses with depth. The problem of low signal-to-noise-ratio (SNR) is eminent when a high pulse repetition frequency (PRF) laser is used because of its low pulse energy. In particular, when a low-cost laser source such as a pulsed laser diode is considered, certain signal-processing techniques are essential because the pulse energy is extremely low. Therefore, improving the SNR requires repeated irradiation through averaging; this is a major obstacle in PA real-time imaging, since it makes it hard to achieve a high frame rate, and possibly induces motion artifacts.
Non-invasive flow measurement is another type of functional information that can be obtained by calculating the target motion speed. The flow velocity represents vital information about the supply of oxygen and other nutrients, and it can be used to diagnose a variety of diseases including diabetes and cancer. Various methods have been proposed to obtain flow information, but each modality has its weakness. Doppler ultrasound can only capture large vessels such as arteries and veins. Doppler optical coherence tomography has a limited detection depth of 1mm. Electromagnetic methods are expensive and bulky [4,5]. Photoacoustic imaging is expected to overcome these problems. Capillaries, which have low blood-flow rates and micrometer-scale diameters, can be captured by photoacoustic microscopy [6–9]. Temporal resolution in flow measurement is important for identifying subtle physiological changes in biological objects. It is important to capture high-speed movement such as in the aorta, where the speed can reach 600mm/s, as well as low-speed movement such as in the capillaries, where the speed is 0.5 to 10mm/s. Most of all, the flow speed changes constantly with the heartbeat. In order to capture small velocity variations, a high frame rate must be maintained, but the maximum frame rate is restricted by the acoustic time-of-flight (TOF).
Coded excitation can be used to resolve these issues. Coded excitation enables increasing the signal intensity without compromising the measurement time. In temporal encoding, the laser pulses are irradiated with a special coding pattern without waiting for the acoustic TOF, and the encoded received radio frequency (RF) signal can be decoded with its SNR improved. Thus, a high-PRF laser system is desired to maximize the performance of coded excitation, and fortunately a low-cost, low-power laser generally has the capability to generate pulses with a much higher repetition frequency than a high-power laser. Previous studies of temporal encoding have proposed Golay codes [10,11] and aperiodic m-sequence family (such as preferred pairs of m-sequences and Gold codes) [12,13]. The problem is that those sending procedures are so complex that it is necessary to send the same sequence twice since the negative codes of the bipolar sequences must be sent separately as positive codes. Further, in the case of an aperiodic m-sequence family, the decoding artifacts could not be minimized to be zero.
We propose using a periodic and unipolar m-sequence (PUM) that can overcome the problems mentioned. Signal intensity can be enhanced by decoding periodically sent PUM using bipolar sequences, and there are no coding artifacts for a single wavelength. Moreover, the start point of the decoding has no restriction in periodically implemented sequences, which means that decoded results can be obtained for each continuous code sequence. In other words, an ultra-high frame rate, which is conventionally impossible due to the restriction of the acoustic TOF, can be achieved. Thus, the temporal resolution will be improved up to the PRF of the laser system.
This paper first introduces the concept of coded excitation and its application to flow measurement. Next, experiments are conducted to validate the proposed idea through the evaluation of SNR improvement and the potential to increase the temporal resolution. We then discuss the feasibility of multi-spectral simultaneous irradiation and provide a comparison to previously proposed codes.
2. Theory and method
2.1 Coded excitation for photoacoustic imaging
Coded excitation has been a signal processing method to improve SNR in classical ultrasound imaging [14]. To integrate coded excitation for photoacoustic imaging, laser pulses are transmitted with certain coding patterns through encoding, and the initial pulse response is recovered through decoding. The decoded signals possess a high SNR compared to single shot signals, in that the initial pulse signals will be enhanced due to autocorrelation property of pseudorandom codes. Although averaging is a classical approach to improve SNR without using coded excitation, the maximum available PRF in averaging is bounded by the acoustic TOF, the time trip from an acoustic source to the receiver. In other words, a high PRF laser cannot be used its maximum accessible PRF at some conditions. Coded excitation in temporal domain allows the laser to use its maximum PRF without signal contamination from previous pulse [10,11]. The idea of this multiple pulses separation can also be applied in spectral domain such as S-sequence or spatial Fourier encoding [15,16]. A unique character of photoacoustic imaging compared to ultrasound imaging is that multi-wavelengths data can retrieve functional information of the target. On the point, coded excitation enables multiple wavelengths simultaneous irradiation, while each wavelength has to be sent one by one in conventional technique. Thus, higher SNR could be achieved by using spectrally implemented coded excitation.
The limitation of coded excitation for photoacoustic imaging is that only positive code can be sent as light, even though coding sequences are generally bipolar, consisted by positive code and negative code. Consequently, a solution is to transmit positive and negative part of bipolar codes separately. Aperiodic code such as Golay codes or aperiodic m-sequence family have been proposed based on this idea. Those aperiodic codes work, but have complicated implementation procedures, and have less flexibility for transmission. Moreover, its SNR improvement is lower than that of periodic sequence, because a waiting time corresponding to the acoustic TOF is required between multiple sequences continuous sending. Here, we designed unipolar codes, which does not contain negative part, to enable periodic transmission. The summary of different coded excitation sequences are shown in Table 1.
Table 1. Coded excitation sequences and those characteristics.
2.2 Construction of periodic and unipolar sequences
Periodic and unipolar m-sequences (PUMs) can be derived from maximum-length sequences (m-sequences). M-sequences are bipolar sequences that can be generated with a linear feedback shift register. PUMs are unipolar sequences consisting of {1, 0}, which is selected from positive codes of bipolar m-sequences consisting of {1, −1}. For instance, the 7-bit bipolar m-sequence = {1, −1, −1, 1, 1, 1, −1} can generate a PUM = {1, 0, 0, 1, 1, 1, 0}. The code length of a PUM is , where L is the size of the linear feedback shift register used to generate the m-sequences.
As an encoding process, the laser irradiation is triggered to be a pattern of PUM with contentious periodic transmission. Thus, temporally encoded signals will be received in which the response from a single pulse will continue as a sequence based on the code. The received signals are formulated as
where h(k) is the impulse response from a single laser shot, and * denotes convolution. In the decoding process, we convolute the received radio frequency (RF) data with the corresponding bipolar sequences. In the example of the sequence M, the received signals periodically encoded with the sequence will be convoluted by the sequence M. Hence, the decoded signals areThe starting point of decoding can be set at any code in periodic irradiation. Figures 1(a) and 1(b) present the implementation flow chart and a timing diagram of the PUMs.
Fig. 1 Periodic and unipolar m-sequence. (a) Implementation flow chart. (b) Timing diagram of periodic and unipolar m-sequences. The sequences corresponding to the laser excitation timing through triggering a laser. (c) Simulation of 7-bit PUM implementation. The left figure depicts a part of the periodically sent sequences, and the decoded signals for the same temporal region are shown to the right.
2.3 Properties of periodic and unipolar sequences
The properties of periodic and unipolar sequences follow those of m-sequences. M-sequences possess good auto-correlation; the main lobe is the code length N and the level of the side lobes is −1 in periodic sending. Certain specific m-sequences with unique cross-correlation properties are defined as preferred pairs of m-sequences [17,18]. To assess a PUM, the periodic autocorrelation function is defined as
where is the k-th element of a PUM A ({1, 0}), where the main signal (n = 0) will be enhanced times, and there are no coding artifacts for a single wavelength, so that , when n ≠ 0 [Fig. 1(c)].Assuming coding artifacts are negligible, the root mean-square error (RMS) of the decoded signals for a PUM is
An image is generated by sending a single-sequence irradiation of a PUM for continuous imaging, even though three repetitions will be needed to simulate the PUM. Thus, we compare the acquisition time of a single sequence and averaging. If the time interval between two light pulses is defined as and the time between the emissions of two consecutive light pulses for repetitive irradiation is defined as , the acquisition time is . The performance of the PUM is compared to that of the averaging procedure for the equivalent measurement time. The possible number of averages within the PUM acquisition time is given byTherefore, the coding gain (), i.e. the SNR improvement compared with averaging, is given in dB byAnother attractive property of PUMs is that decoding can be started at any point in a sequence [Fig. 2]. Thus, the frame rate, which was limited by the acoustic TOF, can be maximized up to the PRF of the laser. This is equivalent to obtaining high temporal resolution. Considering its application for flow measurement, the interval of the estimated velocity can be shortened to an interval of two bits, so it is possible to observe high-speed flow and momentary velocity variations. High temporal resolution is not only useful for observing high-speed phenomena but also contributes to improving the resolution of slow movement because it is possible to observe the movement over a short distance. The temporal information contained when measuring a sequence isbecause the acoustic TOF of the last code pulse must be measured. There may thus be coding artifacts if TPUM-I is huge. However, the number of artifacts is practically negligible because the realistic time cost for the movement of the object is much greater than TPUM-I.Fig. 2 Timing diagram of PUM sequence (upper) and codes used for decoding (lower). The periodically irradiated PUM sequence is decoded by the designated starting point and sequence. (a) Decoding starts at the first bit. (b) Decoding starts at the second bit. (c) Decoding starts at the third bit.
2.4 Velocity estimation
Coded excitation for photoacoustic flow measurement can be applied to any velocity estimation method. In this paper, we estimate the velocity using 1-D cross-correlation, a classic and simple method, as the principal verification [19]. When we send pulses twice with an interval of τC, the interval of receiving signals is τC if the target is not moving at all. If the target is moving, the velocity can be estimated by
where the interval of the received signals is τC + Δt, and the speed of sound is c. 1-D cross-correlation was used to trace the movement of the object. The cross-correlation function C(τ) between two segments s(t) and s(t + τE), which are sent with an interval of τC, iswhere T is the window range. The same target is captured when C(τ) is the maximum value, and the displacement will be Δt = τ. That is why we are able to estimate the displacement of two time points. The cross-correlation interval τC can be set as needed.2.5 Experimental evaluation
Coded excitation using the proposed codes was tested to confirm its applicability using the setup in Fig. 3. A laser module with a wavelength of 532nm (Nd: YVO4, Coherent MATRIX532-8-100) was used. The laser energy was 70µJ per pulse, and the beam was expanded to 2cm in diameter. A PRF of 100kHz was used. The irradiation pattern of the PUM was generated by a PC, and that triggered the laser using a function generator. The encoded signals were captured by a 9mm hydrophone with a sampling rate of 50MHz. For the image construction, 105 receiver elements were generated by a translating stepping motor with a scanning pitch of 1mm. Each line was reconstructed from 31 elements using a delay-and-sum dynamic receive beamforming algorithm. As the imaging target, a black rubber wire was embedded into a 0.2% agar phantom, which is a cube 60mm on each side. The wire is located inside, approximately 25mm from the surface where the laser is irradiated.
Fig. 3 Experiment setup. (a) SNR improvement evaluation. A hydrophone was moved by a stepping motor to form a photoacoustic image. (b) Flow measurement. A line phantom is moved using a stepping motor at designated speed.
For the flow measurement analysis, we used a black wire moved by a stepping motor at designated speeds (−40mm/s, −20mm/s, −10mm/s, 0mm/s, 10mm/s, 20mm/s, and 40mm/s), while the hydrophone was fixed. The velocity of the moving object is calculated by measuring the displacement of two signals using 1-D cross-correlation. A 31-bit PUM sequence was employed periodically with a PRF of 100kHz, and the coded and non-coded results were compared. To emphasize the difference in the coded and non-coded cases, the acoustic TOF is assumed to be 310μs, which is the time for one PUM sequence. Even though this is not as realistic a number as the acoustic TOF, it makes it easy to compare non-coded and coded results. The interval of the 1-D cross correlation was the time for fifty PUM sequences, the window range was 100 sampling points, and 500 sampling points.
3. Results
3.1 SNR improvement
This experiment confirmed the SNR improvement of the proposed codes for single-wavelength irradiation. Code lengths of 31, 63, 127, 255, and 511 were used while comparing the theoretical values drawn from Eq. (4) [Fig. 4(a)]. Five data sets were examined for each code length. The experiment results were close to the theoretical value, but the longer the chosen code length, the more that the SNR improvement was less than the theoretical number. This was attributed to the fact that the transmission energy was not always constant although the theoretical value is based on the assumption that the same energy is transmitted though encoding.
Fig. 4 (a) Comparison of theoretical values (line) and the experiment result (cross) for PUM. (b) Photoacoustic image results. The non-coded one-shot PA image is shown at left, and the 63-bit PUM coded result is shown at right.
Figure 4(b) presents PA images without coding and with 63-bit PUM encoding. The target without coding is hard to see because the light was diffused inside the phantom. The reconstructed PA signals are extended in a lateral direction because the diameter of hydrophone used was 9mm, and this size matches the reconstructed target size. The visualized region depth in the result was deeper than the actual size of the phantom to confirm the effect of coding artifacts, but in the coded result, no coding artifact was visible as expected. These experiment results indicate that the performance of PUM coding followed the theoretical values, and justify to compare PUM to averaging or other codes through simulation and theory.
To verify the SNR improvement compared to averaging, we designed a simulation [Fig. 5]. Five point targets are placed at the depth from 20mm to 100mm with 20mm interval, and other parameters follows the experimental setting. To simulate the condition of low SNR, random white noise was added to the simulated receive data, which standard deviation was selected to the peak signal intensity of 20mm depth point. The SNR improvement of PUM is demonstrated in Fig. 5(a), in which five points were clearly visualized through 63-bit PUM coding. Figure 5(b) shows the SNR improvement using averaging with the same measurement time for a sequence of PUM sending. The maximum possible number of averaging was calculated from Eq. (5). The results indicate that the superiority of PUM over averaging becomes obvious as the higher PRF was used and deeper field-of-view was kept. To generalize the comparison, the Gain, the SNR improvement compared to averaging, are plot in Fig. 5(c).
Fig. 5 (a) Photoacoustic images with five point sources are shown as non-coding and PUM coding results. (b) The number of averaging for the same measurement time of PUM coding depends on the PUM sending PRF and the depth of field-of-view (FOV). The result of the same measurement time with 63 bit PUM coding is shown. (c) The Gain, the SNR improvement compared to averaging, is shown, while the PUM sending PRF and the depth of FOV are varied.
3.2 Flow measurement
The estimated velocity is depicted in Figs. 6(a)-6(b). When the window range of the cross-correlation was 100 sampling points, the non-coded signals could not estimate velocity well at all, and there are numerous outliers because of the poor SNR. The averaged standard deviation (SD) of the estimated velocities was 19.88mm/s. Figure 6(a) presents the results when the window range was 500 sampling points (the averaged SD of the estimated velocities was 2.13mm/s). Basically, the window range is set based on the size of the region of interest and affects the noise included during the cross-correlation process. For the same window range, coding significantly improved the SNR, so that the estimated velocity agreed well with the true designated velocity [Fig. 6(b)]. (The averaged SD of the estimated velocities was 1.24mm/s.) Moreover, the coded results for the window range of 100 sampling points took on an almost equivalent value to that of the 500 sampling points (1.14mm/s), indicating that the spatial resolution of coded signals can be higher than that of non-coded signals due to the improved SNR.
Fig. 6 Velocity estimates for (a) non-coded and (b) coded signals. The solid line plots the true values. (c) Temporal velocity change of coded signals when the object moves at 20mm/s. (d) SNR improvement of signals for moving target analysis.
In addition, we confirmed a shorter interval of temporal velocity change from the coded results [Fig. 6(c)]. The designated velocity was 20mm/s, and the velocity sampling period of the coded signals was 10μs. This frame rate clearly outweighs the frame rate of the non-coded results because the available frames in the non-coded case for the same duration with the coded results in Fig. 6(c) are 375µs, 685µs, and 995µs because the acoustic TOF was set to 310µs. The estimates varied around the designated 20mm/s. Fluctuation of the wire caused by water or other physical factors can be considered to be the cause of this phenomenon. In particular, a seesawing variation can be confirmed around 500µs to 700µs, and it can be confirmed that the estimated velocity decreased from 800µs to 1000µs. This indicates that slight flow variations, which could not be observed without coding, can be detected by high temporal resolution.
The RF signals for a movement of 20mm/s are displayed in Fig. 6(d). An SNR improvement of 7.99dB was confirmed between the non-coded and coded RF signals. This is close to the theoretical value of 9.17dB. Motion artifacts are expected because of coding, but these artifacts remain invisible. At any rate, coding artifacts are not a problem for flow measurement because coding artifacts appear in all decoded results but do not affect the cross-correlation calculation. This paper confirms that the accuracy of the velocity estimation and the temporal resolution was improved. Ultra-high temporal resolution is achieved based on the assumption that each decoded frame reflects the true frame information. Since each decoded frame contains TPUM-I long information, the spectral pattern of the coded result may change from the original single-pulse result.
4. Discussion
4.1 Application to multi-spectral photoacoustic imaging
Here, we discuss the application to multi-spectral photoacoustic imaging. Although this paper is dedicated to demonstrating the characteristics of PUMs for single-wavelength usage, this code has potential to be applied in the multi-wavelength case. Utilizing multi-spectral information in PA is quite useful in doing spectral decomposition such as computing blood oxygenation based on the absorption coefficient of hemoglobin. However, obtaining multi-spectral information normally takes time corresponding to the number of signals, because each wavelength has to be sent one by one. Several researchers have investigated coded excitation to enable simultaneous multi-spectral irradiation using the property of low cross-correlation during the decoding process [20,21]. Like other aperiodic pseudorandom sequences, PUMs inherit the property of low cross-correlation from m-sequences. The cross-correlation function is defined as
where is the k-th element of another PUM sequence B ({1, 0}); the two sequences originate from a preferred pair of m-sequences. Table 2 lists the maximum cross-correlation corresponding to the code length. The cross-correlation value will appear in images as coding artifacts, or in other words, crosstalk.Table 2. The maximum cross-correlation of periodic and unipolar sequences
In simultaneous multi-spectral irradiation, in which coded laser pulses are irradiated from different sources simultaneously, each spectral component can be acquired separately from compression using codes of the required wavelength because any specific signal can be detected by autocorrelation; other signals will be offset by cross-correlation. Therefore, the coding gain, which considers the situation of multi-spectral PA coded excitation (), is estimated using Eq. (6), which is based on the assumption that the noise is independent of the signals and that the range of cross-correlation is much smaller than the noise for evaluating SNR improvement.
Here, represents the number of signals and the number of averages in the multi-spectral PA coded excitation, and can be defined asEquation (11) shows that the gain is higher for short code lengths. In contrast, crosstalk will be generated in multi-spectral irradiation. Therefore, a longer code length is desirable for multi-spectral photoacoustic imaging. Hence, it can be concluded that finding a suitable code length is necessary based on the need.4.2 Coding gain compared to other coded excitation approaches
The performance of PUMs is compared to previously proposed codes. Here, we discuss Golay codes, the aperiodic m-sequence family, and S-sequence as representative of pseudorandom codes. Golay codes and aperiodic m-sequence family encodes in both temporal and spectral domains, while S-sequence encodes in spectral domain only [17]. The aperiodic m-sequence family are consisted by maximal-length sequences (m-sequences) and the related sequences such as Gold codes and Kasami sequences. Equations (13), (14), and (15) describe the coding gain of orthogonal Golay codes (O-Golay), the aperiodic m-sequence family (AMF), and S-sequence.
Assuming that ≅ 33.33µs (a depth of 50mm) and = 1µs, the gains of four types of codes are shown in Fig. 7. Figure 7(a) compares aperiodic sequences and periodic sequences for a single-wavelength scenario. Both codes converge to the same level, but the periodic sequence shows consistently good coding gain, while long code lengths are required for the aperiodic sequence. This trend follows in multispectral simultaneous irradiation [Fig. 7(b)]. It can be seen that for two-wavelengths simultaneous irradiation, the gains of the aperiodic m-sequence family and the orthogonal Golay codes are equivalent. For four-wavelengths simultaneous irradiation, the SNR improvement of the aperiodic m-sequence family begins to exceed that of the orthogonal Golay codes.Fig. 7 (a) Comparison of coding gain for aperiodic sequences and periodic sequences under single-wavelength irradiation. (b) Coding gain for multi-spectral irradiation. Two-wavelengths and four-wavelengths simultaneous irradiation are shown.
Compared with Golay codes, the greatest advantage of the proposed codes (periodic and unipolar sequences), is that they only need to be sent once, as compared with Golay codes that must be sent twice for a sequence. Therefore, PUMs can reduce the transmission time with high SNR improvement efficiency. On the other hand, the PUM is superior to the aperiodic m-sequence family because of its stability and low level of coding artifacts for a single wavelength. In addition, PUM does not need to send sequences twice to send the negative part of the codes, so the acoustic time-of-flight limitation need not be imposed. Thus, greater SNR improvement can be expected. S-sequence shows similar SNR improvement when a short code length was used, and the Gain was 0.51dB and 1.94dB for two-wavelengths and four-wavelengths, respectively. Since S-sequence is dedicated to spectral encoding, the code length in temporal domain does not show improvement compared to averaging. The gains of PUM always exceed those of the other three types of codes.
5. Conclusion
We proposed coded excitation for photoacoustic imaging using periodic and unipolar sequences. The resulting SNR improvement and its application for velocity measurement were confirmed by experiments. Coded excitation provides higher SNR with a short measurement time and enables more accurate velocity estimation. Subtle velocity variations can be observed, and it has the potential to expand the impact of PA flow measurement. In the future, it should be considered to integrate coded excitation into various velocity estimation methods such as those using the photoacoustic Doppler effect [8] or Doppler broadening of bandwidth [9]. Further experiments and evaluations under ex vivo or in vivo conditions should also be investigated.
Acknowledgments
This work was supported by the Japan Society for the Promotion of Science KAKENHI Grants No. 22240063 and No. 253749. In addition, this work was partly supported by the Innovative Techno-Hub for Integrated Medical Bio-imaging of the Project for Developing Innovation Systems, from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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