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. Author manuscript; available in PMC: 2023 Dec 2.
Published in final edited form as: IEEE Trans Med Imaging. 2022 Dec 2;41(12):3544–3551. doi: 10.1109/TMI.2022.3188739

Deep Learning-powered Bessel-beam Multi-parametric Photoacoustic Microscopy

Yifeng Zhou 1, Naidi Sun 1, Song Hu 1
PMCID: PMC9767649  NIHMSID: NIHMS1854918  PMID: 35788453

Abstract

Enabling simultaneous and high-resolution quantification of the total concentration of hemoglobin (CHb), oxygen saturation of hemoglobin (sO2), and cerebral blood flow (CBF), multi-parametric photoacoustic microscopy (PAM) has emerged as a promising tool for functional and metabolic imaging of the live mouse brain. However, due to the limited depth of focus imposed by the Gaussian-beam excitation, the quantitative measurements become inaccurate when the imaging object is out of focus. To address this problem, we have developed a hardware-software combined approach by integrating Bessel-beam excitation and conditional generative adversarial network (cGAN)-based deep learning. Side-by-side comparison of the new cGAN-powered Bessel-beam multi-parametric PAM against the conventional Gaussian-beam multi-parametric PAM shows that the new system enables high-resolution, quantitative imaging of CHb, sO2, and CBF over a depth range of ~ 600 μ m in the live mouse brain, with errors 13–58 times lower than those of the conventional system. Better fulfilling the rigid requirement of light focusing for accurate hemodynamic measurements, the deep learning-powered Bessel-beam multi-parametric PAM may find applications in large-field functional recording across the uneven brain surface and beyond (e.g., tumor imaging).

Keywords: Bessel beam, deep learning, multi-parametric photoacoustic microscopy

I. Introduction

OVER the past decades, photoacoustic microscopy (PAM) has been proven to be a promising imaging modality for biomedical research due to its ability to provide functional and physiological imaging in vivo at the microscopic level [1]-[4]. Recent developments of multi-parametric PAM have enabled simultaneous quantification of the total concentration of hemoglobin (CHb), oxygen saturation of hemoglobin (sO2), blood flow, and the associated tissue oxygen metabolism [5]-[7]—carving out a unique technical niche for PAM.

In the multi-parametric PAM, the microscopic resolution is typically achieved by focusing a Gaussian-shaped laser beam into a micron-level spot, where a tradeoff between the lateral resolution and the depth of focus exists due to light diffraction. As a result, when the region of interest (RoI) is out of focus, the resolution and signal-to-noise ratio (SNR) degrade rapidly. Moreover, since the quantitative measurements of blood oxygenation and hemodynamics relies heavily on the resolution and SNR [8], they become inaccurate in the out-of-focus region, placing a practical limit on the application of multi-parametric PAM.

The out-of-focus issue can be addressed by performing two-dimensional raster scanning at multiple depths (i.e., z-stack imaging). However, the image acquisition time increases proportionally, making it inapplicable to studies requiring high imaging speed. An electrically tunable lens can be used to speed up this process by quickly shifting the light focus axially [9], [10]; however, its response time is not sufficient to follow the MHz laser repetition rate. Alternatively, three-dimensional contour scanning has been developed to address the out-of-focus issue caused by uneven tissue surfaces [8], [11], [12]. However, this approach requires the addition of a motorized linear stage along the vertical axis and the development of sophisticated signal processing for online detection of the surface contour and real-time feedback to the motorized linear stage. More importantly, it cannot address the out-of-focus issue due to the limited depth of focus associated with the Gaussian-beam excitation. On the other hand, Bessel-beam excitation has been widely utilized to extend the depth of focus in intravital light microscopy [13]-[16], and was recently adapted for PAM [17]-[20]. However, the previous studies were mainly focused on structural imaging, leaving its utility in functional and quantitative imaging unexplored. Moreover, side lobes in the Bessel beam are known to induce image artifacts. Although deconvolution is an effective method to remove them, it imposes a high requirement on the SNR [21]. Also, the point spread function (PSF) of the imaging system may vary spatially due to tissue scattering and/or motion artifacts [22], which limit the effectiveness of deconvolution.

Deep learning is a class of machine learning techniques that uses multilayered neural networks for automated data analysis, and has been widely used in biomedical image processing [23]-[25]. In fluorescence microscopy, deep learning has been used to address the out-of-focus issue associated with the Gaussian-beam excitation [26], [27]. Also, in light-sheet microscopy, it has shown superior performance over the conventional blind deconvolution in suppressing side lobe-induced artifacts [28]. Moreover, in PAM, it has shown promises in reconstructing undersampled data [29], [30], improving spatial resolution [31], [32], enhancing penetration depth [33], and reducing motion artifacts [34].

In this article, we report a conditional generative adversarial network (cGAN)-powered Bessel-beam excitation-based multi-parametric PAM to address the out-of-focus issue. First, in vivo data concurrently acquired with the Gaussian-beam and Bessel-beam excitation were used to train a cGAN model adapted from Isola et al. [35], which had been demonstrated to be easy to use and not application-specific, for suppressing the side lobes and enhancing the depth of focus. Then, a side-by-side comparison of multi-parametric PAM with the Gaussian-beam and Bessel-beam excitation was carried out to examine if the Bessel-beam multi-parametric PAM was able to achieve accurate structural and functional imaging over an extended depth range. Finally, cortex-wide imaging was performed over the live mouse brain to demonstrate the promise of the cGAN-powered Bessel-beam multi-parametric PAM for large-field functional recording over the uneven brain surface.

II. Methods

A. Experimental Setup

Figure 1(a) shows the schematic of our experimental setup. The Bessel-beam multi-parametric PAM utilizes a nanosecond-pulsed laser (GLPM-10-Y13, IPG Photonics; wavelength: 532 nm). Individual pulses coming out of this laser are switched between two optical paths by an acousto-optic modulator (AOM; AOMO 3080-122, Crystal Technology). When the AOM is off, the laser light passes it without diffraction (i.e., 0th order) and is coupled into a polarization-maintaining single-mode optical fiber (PM-SMF, HB450-SC, Fibercore) through a fiber coupler (CFC-11X-A, Thorlabs). The stimulated Raman scattering (SRS) in the PM-SMF red-shifts the laser wavelength from 532 nm to 558 nm [36], [37]. Then, a bandpass filter (CT560/10bp, Chroma) is used to isolate the 558-nm component. When the AOM is on, ~60% of the 532-nm light will be diffracted (i.e., 1st order) into the second optical path, where no wavelength conversion is implemented. Due to the low energy, the ~40% undiffracted light does not undergo the SRS-based wavelength conversion and thus is rejected by the bandpass filter. Thus, pulse-by-pulse switching of the laser wavelength can be realized by alternating the AOM. The two optical paths are merged by using a dichroic mirror (DM; FF538-FDi01, Semrock), and the dual-wavelength beam is coupled into a PM-SMF to maintain the linear polarization.

Fig. 1.

Fig. 1.

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Photoacoustic microscopy (PAM) setup. (a) Schematic of the multi-parametric PAM system. The boxed inset illustrates the laser excitation scheme designed for simultaneous image acquisitions with the Gaussian beam and Bessel beam. AOM, acousto-optic modulator; FC, fiber coupler; PM-SMF, polarization-maintaining single-mode fiber; BPF, bandpass filter; DM, dichroic mirror; EOM, electro-optic modulator; PBS, polarizing beamsplitter; OL, objective lens; CL, correction lens; UT, ultrasonic transducer; WT, water tank; DAQ, data acquisition. (b) Experimentally measured PSFs of the Gaussian and Bessel beams. (c) Cross-sectional profiles of the Gaussian and Bessel PSFs, whose full width at half maximum (FWHM) values are quantified to be 3.1 and 2.5 μm, respectively.

After collimation of the dual-wavelength beam, an electro-optic modulator (EOM, model 350-80, Conoptics) is used to rotate the polarization. When a low voltage (i.e., 0 V) is applied to the EOM, the laser beam goes through a polarizing beamsplitter (PBS, PBS121, Thorlabs) and is magnified by a pair of relay lenses. When a high voltage (i.e., 260 V) is applied to the EOM, the laser beam is reflected by the PBS, and a pair of axicon lenses (AX2520-A, Thorlabs) is used to convert the collimated Gaussian beam into a ring-shaped beam for generating the Bessel beam. As a result, the EOM switches the beam profile between the Gaussian and Bessel beam pulse by pulse. The boxed inset in Fig. 1(a) illustrates the laser excitation scheme. By triggering the AOM and EOM at 10 and 20 kHz, respectively, the pulse train emitted by the laser operating at a 40-kHz pulse repetition rate is packaged into multiple 4-pulse packets, each of which consists of one 532-nm Gaussian pulse, one 532-nm Bessel pulse, one 558-nm Gaussian pulse, and one 558-nm Bessel pulse. In the end, an objective lens (OL, AC254-050-A, Thorlabs) focuses all the beams onto the imaging object through a correction lens (CL, LA1207-A, Thorlabs) and the central opening of a ring-shaped ultrasonic transducer (UT, inner diameter: 1.1 mm; outer diameter: 3.0 mm; focal length: 4.4 mm; center frequency: 40 MHz; 6-dB bandwidth: 69%). The optically excited ultrasonic waves are detected by the ring transducer, amplified by a 45-dB amplifier (HD28082, HD Communications), filtered by a 60-MHz low-pass filter (BLP-70+, Mini Circuits), and acquired by a high-speed data acquisition board (DAQ, ATS9350, AlazarTech) at 500 MS/s.

For raster scanning, the object to be imaged is mounted on a two-axis scanner, which consists of two motorized linear stages (L-509, Physik Instrumente). For acoustic coupling, the UT and CL are immersed in a water tank and a thin layer of ultrasound gel (Aquasonic CLEAR, Parker Laboratories) is applied between the object and a piece of transparent polyethylene membrane at the bottom of the water tank. A field-programmable gate array (PCIe-7842r, National Instruments) is programmed to synchronize the laser, AOM, EOM, motorized linear stage, and DAQ during the image acquisition.

The PSFs of Gaussian and Bessel beams captured by a camera (DMK 27BUP031, Imaging Source) are shown in Fig. 1(b). The cross-sectional profiles of the white dashed lines in Fig. 1(b) are shown in Fig. 1(c), based on which the FWHM values of the Gaussian and Bessel PSFs are estimated to be 3.1 and 2.5 μm, respectively. For microsphere phantom and mouse brain imaging, the pulse energies of the Gaussian beam are set to 10 and 100 nJ, respectively. The corresponding pulse energies of the Bessel beam are three times higher, because of the existence of side lobes. According to Fig. 1(b), the main lobe of Bessel beam accounts for ~20% of the total energy.

B. cGAN Model

The architecture of the cGAN used in this work is shown in Fig. 2(a), which is based on a previously reported cGAN model [35]. In our application, the random jitter function is disabled to avoid scaling and cropping because each pixel in the image has a fixed step size. The input image of the generator is acquired with the Bessel beam and consists of 256 × 256×n pixels, where n is the number of optical wave-lengths used for PAM imaging. The input of the discriminator consists of two images with the same size (e.g.) 256 × 256×n pixels), where the first image is the output from generator and the second is the target image (i.e., the ground truth) acquired with the Gaussian beam in the focal plane. Both the generator and discriminator are optimized using the Adam algorithm [38], and the learning rate is 0.0002. Given the 10-kHz repetition rate of the laser packet and 1-Hz B-scan rate, a B-scan contains 10,000 A-lines. Since the input image of the cGAN is set to be 256 × 256 pixels (i.e., 256 A-lines, each of which has 256 pixels), each B-scan is divided into 10,000/256 « 40 images.

Fig. 2.

Fig. 2.

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Conditional generative adversarial network (cGAN) model. (a) Architectures of the generator and discriminator in the cGAN. (b) and (c) are the loss curves derived from data acquired in the microsphere phantom and mouse brain, respectively. The red, black, and blue curves represent the loss curves with full, three times less, and ten times less training dataset, respectively. The solid curve and the shading represent the mean and the standard deviation of the loss function over the testing dataset, respectively. The periodic white and gray background represents the occurrence of each epoch, and the number of each epoch is labeled on the top of the plot.

Because the microsphere phantom and the mouse brain have very different structures, their cGAN models are independently trained based on their own datasets. For in vivo imaging of the mouse brain, the step size of each B-scan along the slow axis is set to ~2.8 μm. Thus, 710 B-scans are collected over a 2 × 2 mm2 region of interest, where 670 B-scans (i.e., 26,800 images) are used for training and 40 B-scans (i.e., 1,600 images) for testing. The same ROI was imaged at multiple depths—from −300 to 300 μm with respect to the focal plane (i.e., 0 μm) by adjusting the depth using a linear stage with an axial step size of 75 μm. For the cGAN training, the input images are acquired with the Bessel beam at different depths and the target image (i.e., the ground truth) is that acquired with the Gaussian beam in the focal plane. The phantom data are acquired in a similar manner. However, the numbers of images for both training and testing are four times less than those used for the in vivo cGAN model, because the phantom structure is much simpler.

The loss functions of the cGAN models trained based on the microsphere phantom and mouse brain data are shown in Fig. 2(b) and Fig. 2(c), respectively. The loss function is defined by the mean absolute error between the target image and the output of the generator. The batch size is set to 1. Each training has 10 epochs, each of which contains 100 iterations. For a full dataset, 5–6 epochs are sufficient to train the model, where each epoch takes ~90 minutes. Ten epochs represent a good tradeoff between the accuracy and time consumption. In each iteration, 67 and 268 images are used to train the phantom and in vivo models, respectively. Reducing the training dataset by three times can still yield a similar accuracy after ~10 epochs, while ten times less dataset requires more epochs.

Once the training is completed, it takes the cGAN model ~45 ms to process an input image. For a 2 × 2 mm2 region of interest, each B-scan contains ~40 images. Thus, it takes the model ~1.8 s to process a B-scan. As a result, it takes ~21 minutes to process the entire dataset that contains 710 B-scans. The time expense scales linearly with the size of the input dataset.

The cGAN models used in this study are implemented using Python 3.7 in Keras with a TensorFlow backend. The operating system is Window 10. The workstation contains an Intel i7-7800X CPU, NVIDIA GTX 1080 Ti GPU, and 32 GB RAM.

III. Results

A. Phantom Study

First, to characterize the performance of the cGAN-powered Bessel-beam multi-parametric PAM, a phantom study was performed, where 3-μm polystyrene black dyed microspheres (24292-15, Polysciences) were dissolved in deionized water (20%, v/v) to serve as the phantom.

Figure 3(a) shows the PAM images of the microsphere phantom acquired with the Gaussian-beam and Bessel-beam excitation (before and after the cGAN-based processing), respectively. As shown in the top row, the images acquired with the Gaussian-beam excitation show a significant degradation in the resolution when the microspheres are out of focus, while the microsphere images acquired with the Bessel-beam excitation maintain a near-constant resolution and sNR across the entire depth range (middle row). Moreover, with the aid of cGAN-based post-processing, the artifacts induced by the side-lobes of Bessel beam are effectively removed (bottom row). The cross-sectional profiles of a representative microsphere imaged with the Gaussian- and Bessel-beam excitation (before and after the cGAN-based processing) are shown in Fig. 3(b), from which the FWHM values under the three different settings (i.e., Gaussian-beam excitation, Bessel-beam excitation, and Bessel-beam excitation plus cGAN-based processing) are estimated to be 3.7, 4.5, and 4.0 μm, respectively. In addition, 20 individual microspheres at each depth are selected to quantify the average FWHM values. Figure 3(c) shows the FWHM value as a function of the distance from the focal plane. In this phantom study, the cGAN-powered Bessel-beam PAM demonstrates an extended depth of focus (600 μm) with excellent image quality.

Fig. 3.

Fig. 3.

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Characterization of the performance of the cGAN-powered Bessel-beam multi-parametric PAM. (a) PAM images of microspheres acquired with the Gaussian-beam and Bessel-beam excitation (before and after the cGAN-based processing), respectively, over a depth range of −300 μm to 300 μm with respect to the focal plane (i.e., 0 μm). Scale bar: 20 μm. PA: photoacoustic. (b) Cross-sectional profiles of a representative microsphere imaged with the Gaussian beam and Bessel beam (before and after the cGAN-based processing), as indicated along the white dashed line in (a). The FWHM values of the cross-sectional profiles are 3.7, 4.5, and 4.0 μm for the Gaussian-beam excitation, Bessel-beam excitation, and Bessel-beam excitation plus cGAN-based post-processing, respectively. (c) FWHM value as a function of the distance from the focal plane. At each depth, 20 microspheres are selected for the quantification. The shading represents the standard deviation.

B. In Vivo Study

To examine whether the cGAN-powered Bessel-beam multi-parametric PAM can ensure accurate structural and functional imaging over an extended depth range compared to the Gaussian-beam multi-parametric PAM in vivo, a side-by-side comparison and a cortex-wide recording were carried out in the live mouse brain. Male CD-1 mice (14 weeks old, Charles River Laboratories) were used for the experiments. Under general anesthesia (vaporized isoflurane: 2% for induction and 1.5% for maintenance), the body temperature of the animal was kept at 37°C by a heating pad (DCT-15, Kent Scientific). Then, an open-skull window was created by using a dental drill (K.8350-H.30, Foredom) with a 1/4 RA drill bit (H1.21.005, Carbide Instrument) under a stereo microscope (SM-3B, AmScope), and the drilling was paused every 30 seconds to avoid overheat of the skull. Before imaging, ultrasound gel was applied between the cranial window and the membrane at the bottom of the water tank. All experimental procedures were carried out in conformity with the animal protocol approved by the Institutional Animal Care and Use Committee at Washington University in St. Louis.

Figure 4(a) shows the structural PAM images acquired over a depth range of −300 μm to 300 μm with respect to the focal plane. The four rows of images were obtained with the Gaussian beam, Bessel beam, Bessel beam plus cGAN, and Bessel beam plus blind deconvolution, respectively. The deconvolution was performed by using the MATLAB function, deconvblind, and the experimentally acquired PSF in Fig. 1(b) serves as an initial estimate in the deconvolution. Zooming in on the green boxed regions in Fig. 4(a) clearly shows that combining Bessel-beam excitation and cGAN-based processing outperformed Bessel-beam excitation alone or with blind deconvolution, as shown in Fig. 4(b). For quantitative comparison, the structural similarity (SSIM) and 2-D correlation coefficient against the ground truth image acquired with Gaussian beam in the focal plane (i.e., 0 μm depth) were computed by using the MATLAB functions, ssim and corr2, respectively. As shown in Fig. 4(c), the SSIM and 2-D correlation coefficient between the ground truth image and the image acquired with the cGAN-powered Bessel-beam PAM were constantly higher than those acquired with Bessel-beam excitation without or with blind deconvolution across the 600-μm depth range, indicating the superior performance of this hardware-software combined approach. Further, a side-by-side comparison of the cross-sectional profiles of representative microvessels is presented in Fig. 4(d). The profiles obtained with the Bessel-beam excitation plus cGAN nicely follow those obtained with the Gaussian-beam excitation in the focal plane. In contrast, the microvascular profiles obtained with the Bessel-beam excitation alone or plus the blind deconvolution show more significant deviation.

Fig. 4.

Fig. 4.

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(a) PAM images of the mouse brain vasculature obtained with the Gaussian beam, Bessel beam, Bessel beam plus cGAN, and Bessel beam plus blind deconvolution (abbreviated as deconvolution in the figure), respectively, over a depth range of −300 μm to 300 μm with respect to the focal plane (i.e., 0 μm). Scale bar: 500 μm. PA: photoacoustic. (b) Close-ups of the green boxed regions in (a). Scale bar: 200 μm. (c) The SSIM and 2-D correlation coefficient values of individual images with reference to the image acquired with the Gaussian beam in the focal plane. (d) Comparison of the cross-sectional profiles of representative microvessels, as indicated along the cyan lines in (b).

Figure 5(a) shows the multi-parametric images of the same dataset. The top three rows are CHb, sO2, and CBF acquired by the Gaussian-beam multi-parametric PAM at different depths, and the bottom three rows are corresponding images acquired by the Bessel-beam multi-parametric PAM and post-processed by the cGAN. It can be observed that the multi-parametric PAM measurements made with the Gaussian-beam excitation quickly deviate from that in the focal plane, which is in contrast to the Bessel-beam case. The reason is that the validity of the multi-parametric measurements relies highly on the spatial resolution and SNR, as shown by our recent findings [8]. For the Gaussian beam, the optical spot spreads rapidly when out of focus, resulting in a fast-decaying SNR. On the other hand, the Bessel beam is non-diffractive. The focal spot size remains almost unchanged over a considerable range along the propagation direction. After processing with the cGAN, the degradations of resolution and SNR are much slower. Fig 5(b) shows the percentage errors of the CHb, sO2, and CBF measurements in 20 vessel segments as a function of depth for both systems (Gaussian vs. Bessel). For the sO2 measurement, the Bessel-beam multi-parametric PAM shows an error of <3.5% over an extended depth range of 600 μm, ~13.3 times lower than the measurement error of the Gaussian-beam multi-parametric PAM. For the CHb and CBF measurements, even when the measurements were taken 300 μm away from the focal plane, the Bessel-beam multi-parametric PAM can still provide accurate readouts (percentage errors are ~4.4% and ~4.1% for CBF and CHb, respectively), which are much more reliable than the Gaussian-beam system (percentage errors are ~255% and ~210% for CBF and CHb, respectively).

Fig. 5.

Fig. 5.

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(a) Multi-parametric PAM images of CHb, sO2 and CBF acquired with the Gaussian-beam and Bessel-beam excitation, respectively, over a depth range of −300 μm to 300 μm with respect to the focal plane. Scale bar: 500 μm. (b) Percentage errors in the measurements of CHb, sO2, and CBF as a function of the distance from the focal plane. The shading represents the standard deviation.

Figure 6 shows cortex-wide imaging of the mouse brain by the Bessel-beam and Gaussian-beam multi-parametric PAM. Figure 6(a) shows the images of vascular structure, CHb, sO2, and CBF over a ~ 4 × 6 mm2 field of view acquired by the cGAN-powered Bessel-beam multi-parametric PAM. The close-ups of the blue dashed box in the lower right corner of the cortex-wide images are shown right next to the column. Figure 6(b) shows corresponding images acquired by the Gaussian-beam multi-parametric PAM. Figure 6(c) is the ground truth image of the boxed region acquired by moving it into the focal plane of the Gaussian beam. As expected, the Gaussian-beam multi-parametric PAM can get reasonable measurement in the center of the brain due to small deviation from the focal plane. However, on the two sides of the brain, the measurement becomes invalid as the deviation increases. On the other hand, the Bessel-beam multi-parametric PAM with the cGAN-based post-processing maintains a reliable quantification across the entire width of the mouse cortex, as confirmed by the ground truth. Such an extended depth of focus would enable many new biological and physiological studies, especially where imaging over a large field of view with an uneven surface is needed.

Fig. 6.

Fig. 6.

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Cortex-wide multi-parametric PAM images of the vascular structure, CHb, sO2, and CBF acquired by (a) Bessel-beam and (b) Gaussian-beam excitation, respectively. PA: photoacoustic. The close-up of the blue boxed area is shown on the right-hand side. (c) Multi-parametric PAM images of the same region acquired with Gaussian beam in the focal plane. Scale bars: 500 μm.

IV. Conclusion

In conclusion, we have developed a new multi-parametric PAM system based on the Bessel-beam excitation and cGAN-based deep learning. Side-by-side comparison in the live mouse brain shows the advantages of the Bessel-beam excitation over the conventional Gaussian-beam excitation in maintaining accurate hemodynamic quantifications over the extended depth of focus. By combining the Bessel-beam excitation and cGAN-based processing to address the out-of-focus issue in PAM, we demonstrate that the hardware-software combined approach improves not only the quality of structural images but also the accuracy of functional measurements. This new technique may find useful applications in large-field volumetric imaging of biological tissues with uneven surfaces, such as the brain [6] and the tumor [4]. Also, it can be integrated with the real-time contour scan we previously developed [8] to further improve the tolerance of multi-parametric PAM for out-of-focus issues.

Acknowledgments

This work was supported in part by the National Institutes of Health (NS099261, NS120481) the National Science Foundation (2023988), and the Chan Zuckerberg Initiative DAF—an advised fund of Silicon Valley Community Foundation (2020-226174)

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