Can't Read "Opt(Exp)": No Such Element in Array

1. Introduction

Photoacoustic tomography (PAT) is a promising biomedical imaging modality that offers high-resolution optical assimilation imaging of deep tissue. The hybrid acoustic detection of optical absorption overcomes the optical diffusion limitation.^1,2,3,4,v PAT forms images based on the photoacoustic (PA) effect, which was first discovered by Alexander Bell more than 100 years ago. The enquiry for photoacoustic imaging (PAI) developed very slowly until the 1990s. At this time, the evolution of high-power pulsed lasers, sensitive ultrasonic transducers, and data conquering systems triggered the rapid development of PAI. Since then, the technique has evolved rapidly and became one of the most exciting biomedical imaging techniques in this decade. In the terminal few years, PAT has been demonstrated in various preclinical and clinical applications, such as cardiology imaging,^half-dozen oncology imaging,⁷ vascular biometrics,^viii functional imaging,^9,10,xi,12 breast cancer screening,^{xiii,fourteen} and guidance of lymph node biopsy.¹⁵

In terms of audio-visual signal detection configuration, diverse ultrasonic transducer arrays, such as ring array,^16,17 linear array,^{18,19,20,21,22} and hemispheric array,^13,14 have been implemented in the PAT system to run across the need of preclinical and clinical applications. Amongst these, linear transducer arrays are probably the almost widely used. As the name implies, the piezoelectric elements of the linear transducer array are arranged in a line, thus, producing a rectangular field of view. Compared to other arrays, linear arrays are handheld operable, convenient, and very affordable. It tin can exist easily manufactured and integrated with light sources and conventional ultrasound systems.

Although linear array-based PAT is promising and has been quickly developed, it still faces challenges that impair the imaging operation of the system. The spatial resolution of a linear transducer array can be represented in three axes. Within the imaging plane shown in Fig. one(a), the axial direction is along the axis that is perpendicular to the transducer element surface, and the lateral direction is perpendicular to the axial direction. The elevational direction is orthogonal to the rectangular imaging airplane.

Fig. 1. Schematic drawing of a linear array transducer. (a) Top: Imaging plane of the linear assortment transducer. Bottom: Side view of the focal zone of the linear array transducer. (b) Light delivery scheme for side-illumination PAI.

In a linear array-based PAT, the axial resolution (Fig. 1(a)) is primarily defined past the centre frequency of the transducer, while the lateral resolution (Fig. one(a)) is determined by the element pitch of the assortment. Typically, the axial resolution equals one-half of the central audio-visual wavelength, while the lateral resolution equals ane key acoustic wavelength.^five

Along the height management, the elements of the linear array transducers are usually cylindrically focused to attain a cantankerous-exclusive imaging airplane (Fig. i(a)). For 3D PAI, the volumetric image can be obtained by stacking two-dimensional (2D) images. In this case, the linear transducer assortment has to be scanned forth the height direction. However, because of the stock-still cylindrical focus, the resulting volumetric images take a poor spatial resolution along the scanning axis. As shown in Fig. 1(a), the elevation resolution is the highest at the audio-visual focus, and information technology degrades as the object moves away from the focus. Even at the elevational focus, both the axial and lateral resolutions are better than the elevational resolution by at least three times.^5,23,24

Too the nonisotropic spatial resolution, the arrangement of the linear elements limits the light delivery to the epitome plane of the linear array-based PAT systems. Since the paradigm plane is right under the elements' surface, the lite tin can only exist delivered from the side of the probe for most linear array-based PAT systems (Fig. 1(b)). The side illumination creates boosted challenges because it is hard to command the calorie-free incident angle according to the distance/depth of the object.

Over the by few years, numerous researchers have fabricated substantial efforts to address these limitations. In this review, electric current technologies to meliorate elevation resolution and light commitment of the linear array-based PAT will be presented.

2. The Principle of PAT

Before talking well-nigh the details of each system, nosotros first innovate the principle of PAT (Fig. 2).

Fig. two. Principle of PAI.

PA signals are typically generated by shorted-pulsed lasers. Upon laser irradiation, the object will absorb the photon free energy and experience transient thermos-elastic expansion, resulting in the generation of wideband ultrasound signals. For an constructive ultrasound signal generation, the pulse duration is typically within a few nanoseconds, which is lower than both the thermal and stress confinements.²⁵ Afterwards the wideband emission, the induced acoustic waves are then detected past ultrasound transducers. Finally, the distribution of optical absorption can be obtained past performing an prototype reconstruction of the detected signals. The PA pressure level ( $p_0)$ can exist written as the post-obit equation :

where $\mathrm{\Gamma }$ is the Grueneisen parameter which increases linearly with temperature, ${\mu }_a$ is the absorption coefficient, and $F(\overrightarrow{r})$ is the local optical fluence.

The sound force per unit area propagates to the tissue surface at different time delays due to the various location of the audio source and properties of the tissue. Linear array-based PAT uses an array of ultrasound transducers to tape the audio waves. The distribution of the initial sound force per unit area or electromagnetic absorption tin exist obtained by inversely projecting back the detected audio waves. There are many approaches for PAT imaging reconstruction. Amongst them, the fourth dimension-domain back-projection reconstruction algorithms are probably the more widely used.²⁶ These methods assume a homogeneous acoustic property in tissue, and the speed of sound in the soft tissue is relatively constant at around 1.five $$ mm/ $$ $\mu$ southward.²⁷

three. Technologies for Improving the Elevation Resolution

To improve the elevational resolution of linear array-based PAT, researchers take proposed numerous solutions. They include new scanning geometries, new detection hardware designs, and advanced image reconstruction algorithms.

iii.one. Modifying the scanning geometries to meliorate the elevation resolution

Gateau et al. starting time investigated a novel scanning geometry that combined linear and rotational scanning to achieve most isotropic 3D spatial resolution.²⁸ Every bit shown in Fig. 3(a), the proposed geometry employs two movements of the linear array, including translation and rotation. The linear array was perpendicularly mounted on a linear translation stage, which was further fixed on a rotary stepper motor so that the stage could be rotated. The entire scanning setup was moved to detached positions along the contour of a polygon. Each of the translation ranges (polygon sides) was 13.five $$ mm and tangent to a circle centered on the axis of rotation. The unabridged rotation range was $180^{°}$ . A 128-chemical element linear array (5.0/7.0 $$ MHz, Acuson L7, Siemens) was used to examination this method. The spatial resolution of the PAT arrangement was measured through imaging 50 $$ mm diameter microspheres. The resulting spatial resolutions were 130 $$ $\mu$ m in-plane and 330 $$ $\mu$ thou in elevation.

Fig. iii. Different scanning geometries for improving elevation resolution. (a) The rotational scanning geometry proposed in Ref. 28. (b) The translate-tilting scanning geometry proposed in Ref. 29. (c) The bi-directional scanning geometry proposed in Ref. thirty. (d) The sample-rotational scanning geometry proposed in Ref. 31.

Upon the initial study of the combined linear and rotational scanning geometry, Gateau et al. proposed a novel single-sided access rotate-translate linear array-based PAT scanner.²⁹ In this organisation, a 128-chemical element linear array (Vermon, Tours, France) with a 15 MHz center frequency, 101 $$ $\mu$ m element pitch, and 1.5 mm cylindrical focus was applied. A motorized translation stage and goniometer stage were used to combine translation and rotation motions. The maximum travel range was 50 $$ mm for the translation phase and $90^{°}$ for the rotation stage. As shown in Fig. 3(b), the linear transducer assortment was mounted on the goniometer stage and then translated by the translation stage. To ensure that the move of the elements' centers was inside the XY-plane, the length axis of the linear array was mechanically aligned to match the rotation axis of the goniometer. During the scanning, the array was continuously and simultaneously translated and rotated from $-45^{°}$ to $4{\mathrm{five}}^{°}$ . Like to their initial study, microspheres phantom was used to test the spatial resolution of the PAT system. The spatial resolution results testify that the proposed organization has a quasi-isotropic 3D resolution of $\sim$ 170 $$ $\mu$ m. The comeback of spatial resolution in the translation direction is almost one social club of magnitude.

Also the translate-rotate scanning geometry, Schwarz et al. proposed a bi-directional scan method with 2 array positions perpendicular to each other to amend the summit resolution.^thirty As shown in Fig. 3(c), two linear scans were conducted in perpendicular directions ( $x$ - and $z$ -direction) for bi-directional scanning. A 24 $$ MHz 128 element linear transducer array (LA28.0/128, Vermon, Tours, France) with a 1.5 $$ mm focus and lxx $$ $\mu$ m pitch was first scanned along the meridian direction and was and then rotated by $\mathrm{ix}{0}^{°}$ and scanned across the same region again. Numerical simulation and experimental phantom resolution studies both demonstrated that the method yields an improved summit resolution with only minor losses in lateral resolution.

Li et al. also proposed a combined linear and rotational scanning method to achieve isotropic resolutions for linear array-based PAT.³¹ Instead of rotating or translating the array over the sample, a rotating sample and translational scanned linear assortment were adopted, as shown in Fig. 3(d). In each scan pace, a commercial linear array with 256 elements (LZ250, 21 $$ MHz center frequency, Visualsonics Inc., Canada) was get-go elevationally scanned. Then the sample was rotated around its heart in a 2 ${}^{\text{o}}$ angular step size and scanned over again until 180 ${}^{\text{o}}$ take been covered. Carbon fiber was chosen to quantify the top resolution of the proposed system, and the resolution consequence shows that this method improves the elevational resolution by 10 times in comparison with the conventional single elevational scan.

In principle, the various scanning geometries discussed above ameliorate elevation resolution past converting the elevation management into axial or lateral directions. This conversion overcomes the intrinsic limitation of the linear array transducer. However, such complicated scanning geometry frequently means a prolonged scanning time. The large data size also takes more time to process for image reconstruction.

3.2. Modifying the detection scheme to improve the elevation resolution

Without modifying the scanning geometry, Wang et al. proposed a fundamentally different approach to improve elevation resolution. The technique is based on acoustic diffraction through a thin slit, which essentially improves the receiving angle of the array along the superlative management (Fig. 4).³² The imaging system exploited an ATL/Philips L7-4 128-element linear transducer array (5 $$ MHz center frequency, 25 $$ mm peak focus) and a thin slit formed past two metallic blades with 500 $$ $\mu$ k thickness. The bottom bract was fixed in position while the acme blade was mounted on a translation stage, allowing for like shooting fish in a barrel and precise control of the slit opening (from 300 $$ $\mu$ m to 1000 $$ $\mu$ m). The thin slit diffracts the incoming PA waves along the elevation direction and enables 3D image reconstruction. Through phantom and in vivo experiments, the authors demonstrated that the slit improves the elevation resolution by upwardly to 10 times without compromising scanning time.³¹ Besides improvement in pinnacle resolution, the slit likewise improves the signal-to-noise ratio (SNR) due to a larger receiving discontinuity. Figure four displays the vascular paradigm results of a homo palm acquired by slit-based linear PAT.

Fig. 4. Slit-based linear PAT proposed in Ref. 33. (a) Schematic cartoon of the slit-based linear-array PAT organisation. (b) 3D palm vascular images acquired by the slit applied science. This piece of work past Y. Wang et al., Ref. 33 is licensed under a Artistic Commons Attribution 4.0 International License.

3.3. Imaging algorithms for improving the elevation resolution

Other than modifying the system hardware, advanced imaging algorithms can also improve the acme resolution of the linear assortment-based PAT system. Wang et al. proposed the integration of two advanced image reconstruction techniques: coherent weighting (CW) and focal-line (FL) 3D image reconstruction.^34,35

The CW algorithm calculates the coherence of received PA signals and assigns a weighting factor to the delay-and-summed signals. The value of the coherent weighting factor (CWF) ranges from 0 to i and can exist applied to the reconstructed paradigm. This factor enhances the coherently summated signals while suppressing the out-of-phase signals and randomized dissonance. The CW gene is applied in 3D through the FL reconstruction algorithm, which precisely calculates the time of inflow in 3D space. Previous studies have indicated that the FL algorithm tin can better the elevation spatial resolution up to the size of the acoustic focus (Fig. 1(b)) regardless of the axial distance of the object.³⁴ The combined CW–FL algorithm was validated through numerical simulation and was experimentally tested in both phantom and man subjects. Both of the experiments' results proved that the method tin significantly improve the acme resolution by 4 times; moreover, the method also suppresses noise and offers higher SNR.

Alshaya et al. reported another algorithm named the³⁶ Filter Delay Multiply and Sum (FDMAS) beamforming technique, which is an adaptive beamforming technique that depends on the autocorrelation between delayed radio frequency (RF) data. Due to the autocorrelation operation, the FDMAS beamforming technique cannot be applied directly in 3D PAI. Instead, the FDMAS is used to beamform the RF information in the lateral management and elevation direction separately, and then combine them. This FDMAS beamforming technique not only improved the elevation resolution out of the focal length, but as well reduced the clutter signals and background noise of the PA image. The FDMAS beamforming technique was compared with the Delay and Sum (DAS) beamforming technique in terms of spatial resolution and SNR. The improvement in the elevation resolution and SNR are nearly 30% and 13 $$ dB compared to DAS, respectively.

Table 1 summarizes different techniques used to improve the elevation resolution.³⁷ It tin can be seen that the last three methods possess the fastest speed because they require only a single translational scan, while the first 2 methods provide the best improvement in elevation resolution considering they interpret the superlative direction into axial direction during the scan. The center 2 methods convert top direction into lateral direction during the browse. Depending on the scanning method, the speed ranges from medium to deadening.

Table 1. Comparison of different methods for improving the elevation resolution in a linear array.³⁵ The table was reproduced with permission from Ref. 35.

Name	Scanning method	Speed	Modification of transducer array	Improvement in summit resolution
Rotational scanning geometry38	$\mathrm{i}\mathrm{eight}{0}^{°}$ rotational scan +translational scan at each $1.5^{°}$ interval	Slow	No	High
Translate-tilting scanning geometry29	Continuous and simultaneous rotation and translation browse	Slow	No	High
Bi-direction scanning geometry30	Two translational scans perpendicular to each other	Medium	No	Medium
Sample-rotational scanning geometry31	The sample is rotated in increments and linearly scanned	Boring	No	Medium
Slit PAT geometry32	One translational scan	Fast	Yes (slit)	High
CW–FL35	1 translational scan	Fast	No	Medium
FDMAS36	1 translational scan	Fast	No	Medium

4. Technologies for Improving Light Delivery Efficiency

Due to the linear system and cylindrical focus of the array elements, the imaging airplane of linear array transducers is a cross-sectional plane that extended along the axial management. As nosotros introduced in Sec. 2, the intensity of the PA signal primarily depends on the local light fluence and absorption coefficient. To achieve optimal PAI depth, we need to ensure that the bulk of calorie-free goes to the imaging aeroplane. In this case, coplanar light delivery and acoustic detection would be the optimal geometry. In reality, due to the geometric shape of linear array transducers, the light is typically delivered from the side of the linear array. Because of the noncoaxial calorie-free commitment and acoustic detection, a good amount of the light energy will be wasted outside of the imaging plane. The large incident angle as well increases the lite travel distance. Both efforts lead to a shallower imaging depth in side-illumination PAT systems. This conclusion is supported past Monte Carlo simulations,^39,40 which found that smaller incident angles could significantly better the light fluence in deep imaging regions.

In this department, we will first talk over technologies for improving the efficiency of side illumination, and and then introduce methods to achieve coplanar (coaxial) calorie-free delivery and audio-visual detection.

four.i. Adaptable side light delivery

Liu et al. designed and built a handheld, existent-fourth dimension PAI system with manually adjustable side light delivery.⁴¹ To optimize the light amplification by stimulated emission of radiation light commitment, a finite element simulation was employed to evaluate the influence of the incident angle and interval between the ii arms of the cobweb parcel regarding light fluence. Phantom experimental validations were performed and the results were consistent with the simulations results. These results indicated that the altitude between the 2 arms of the cobweb package played a major office in light fluence propagation.

Besides the manual adjustment, Sangha et al. reported a motorized adjustable PAT probe.⁴² The adjustable PAT holder (Fig. v) consists of an external linear stepper motor and 2 bipolar stepper motors. This holder can vertically translate the ultrasound transducer and adapt the cobweb bundle'southward rotation and bending. These adjustments could amend the optical fluence of different tissue layers, thereby increasing the penetration depth and SNR. By tuning the fiber orientation, probe-skin reflection artifacts were reduced and light distribution in the epitome acquisition airplane was improved. They validated the motorized PAT probe through Monte Carlo simulations, ex vivo imaging, and in vivo imaging. The ex vivo results showed several millimeter improvements in penetration depth, while the in vivo results showed a 62% increment in lipid SNR.

Fig. 5. The adjustable probe proposed in Ref. 42. Exploded (a), presentation (b), and constructed (c) images of the probe. Reprinted from Photoacoustics, 12, G. S. Sangha, Northward. J. Hale, C. J. Goergen, Adjustable photoacoustic tomography probe improves light commitment and epitome quality, half-dozen–13., Copyright (2018), with permission from Elsevier.

iv.2. Coaxial lite delivery and acoustic detection

Although side lite delivery is widely used in linear array-based PAT systems, coaxial light delivery and acoustic detection is still the optimal low-cal commitment method. The first coaxial organization was proposed by Montilla et al., who utilized an optically transparent acoustic reflector to separate lite illumination and audio-visual detection into two directions.⁴³ Every bit shown in Fig. 6, the glass plate is transparent to light while the audio-visual waves were reflected past $\mathrm{ix}{0}^{°}$ , achieving coaxial illumination and detection. The functioning of the system was demonstrated by imaging a mouse with a pancreatic tumor.

Fig. half dozen. Cross-sectional view of the photoacoustic enabling device (PED) blueprint.⁴³ In this pattern, a drinking glass plate was used as a light and audio combiner.

Lee et al. proposed a handheld probe in which the illuminated light beam axis coincides with the centrality of the ultrasound through a axle combiner.⁴⁴ The axle combiner doubly reflects the acoustic waves to the linear assortment transducer and the manual losses of the low-cal and audio-visual beams are low. Moreover, the laser output was shaped to a line beam by three cylindrical lenses (Fig. 7). In their small brute experiments, the lymph nodes well-nigh the skin could be detected without the demand for whatever supplementary material.⁴⁴

Fig. 7. Schemes of a handheld probe with the illuminated light beam axis coincides with the axis of the ultrasound through a beam combiner.⁴⁴

Li et al. proposed a similar handheld probe design, utilizing polymethyl methacrylate (PMMA) as an optical/acoustic coupler.²⁷ The optical/acoustic coupler reflects the lite beam two times and is permeable to audio-visual waves, achieving coaxial light delivery and acoustic detection with the optical fiber bundle and transducer probe parallel to each other. Using the handheld probe, the authors successfully imaged the sentinel lymph node (SLN) in a live rat. Li's grouping has also designed various types of meaty PA probes to improve the SNR of the organisation⁴⁵ and to detect the SLN.⁴⁶

Recently, Wang et al. ⁴⁷ reported another double-reflector pattern-based linear optical cobweb packet. Instead of the optics shown in Fig. 7, their system utilized a line output fiber bundle to illuminate the object, and so that the whole organisation is much easier to align. In this design, a meaty housing was created to combine both the transducer and fiber bundle output for convenient handheld imaging (Fig. eight). Various phantom and human in vivo experiments were performed to evaluate the efficiency of the system. 3D vascular images of the human forearm were acquired equally shown in Figs. eight(b) and 8(c). The images demonstrated that the double-reflector pattern provides a deeper imaging depth than that of side illumination.

Fig. 8. Schemes of a Double-reflector PAI system.⁴⁷ (a) The cold mirror is transparent to the near-infrared low-cal, while it reflects audio-visual waves by $90^{°}$ . The second acoustic reflection was achieved past a regular drinking glass. (b) Depth-encoded Maximum amplitude project (MAP) image of a human forearm, acquired by the side-illumination system. (c) Depth-encoded MAP image of the forearm, caused by the double-reflector organisation. White arrows show the same features and the xanthous arrow indicates the deepest vessel. This work past Y. Wang et al., Ref. 47 is licensed nether a Creative Commons Attribution 4.0 International License.

Table 2 compares different light illumination schemes. It can be seen that while the side illumination is easy to implement, it has express low-cal penetration depth. The unmarried-reflector design achieves coplanar light illumination and audio-visual detection with the minimal wave aberration, nonetheless, it is inconvenient for handheld functioning. The double-reflector organization represents the most meaty design among the 3. Even so, it is also associated with a longer audio-visual travel distance, which needs to be considered during prototype reconstruction.⁴⁷

Table 2. Comparing of various light illumination schemes.

Light delivery systems	Advantages	Disadvantages
Side illumination	Easy to implement. Minimal light and audio-visual distortion	Express imaging depth.
Unmarried-reflector illumination	Coplanar light illumination and audio detection.	Inconvenient for handheld operation
Double-reflector illumination	Compact design; Coplanar calorie-free illumination and audio detection.	Long acoustic travel distance; potential aberration from two acoustic reflectors.

5. Summary and Conclusions

Linear array-based PAT is a loftier resolution, noninvasive, and user-friendly imaging modality with extensive applications from preclinical laboratory research to clinical patient intendance. Nevertheless, due to the unique geometry design of the linear transducer array, information technology still faces engineering science challenges in terms of poor acme resolution and light delivery that would impair the imaging performance of the PAT system. In this review, we discussed the state-of-the-art of linear array-based PAT systems, introduced the implementation of the imaging system, and elaborated on the reasons for those engineering challenges. We provided a comprehensive review of existing studies and progresses to solve limitations on the summit resolution and calorie-free delivery scheme.

The elevation resolution improvement technologies can be classified into three categories based on their principles. The first category involves new scanning geometries to improve the summit resolution. Through modified scanning geometries, the meridian direction was converted into centric or lateral directions. However, in consideration of the elongated scanning and imaging reconstruction time, these techniques did not improve the top resolution effectively. The 2d category is based on a brand new engineering science that improves the height resolution past diffracting the acoustic waves through a thin slit. This method provides the highest peak resolution improvement without modifying the scanning geometry. Furthermore, the slit width tin be adjusted to achieve optimal resolution based on the imaging feature. The 3rd category is the simplest method because it improves the elevation resolution purely through imaging reconstruction. Although these algorithm-based methods do not crave whatsoever hardware modification, their elevation resolution improvement is very express.

Equally for the light delivery technologies, at that place are two major solutions: improving the side-illumination pattern and achieving coaxial light delivery and acoustic detection. To improve the side-illumination blueprint, information technology is critical to increase the light fluence inside the acoustic detection area. For the first solution, linear array-based PAT systems with adjustable light delivery angles were adult to dynamically control the illumination. Equally for the second solution, the basic principle is to use acoustic and lite combiners to separate or combine light and acoustic beams. The coaxial light delivery and acoustic detection technology has been well demonstrated in imaging beast SLNs and human vasculature. All the aforementioned technologies have greatly improved the imaging capability of the linear array-based PAT system.

To further improve the imaging quality, nosotros envision that time to come studies will combine the elevation resolution improvement techniques and low-cal delivery schemes to achieve both deeper penetration depth and higher spatial resolution in a linear array. With increasing demand in preclinical and clinical applications of PAT, we anticipate that other areas of linear-array PAT, such as low-cal source and data conquering system, will also be improved to further reduce the system size and detection sensitivity.^48,49 In the next few years, we expect to come across a broader awarding of linear array-based PAT systems.

Acknowledgment

Yuehang Wang and Ye Zhan contributed equally to this work. This written report was supported in function past the Career Catalyst Research Grant from the Susan 1000. Komen Foundation (No. CCR17481211).

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