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Keywords:

  • optoacoustic techniques;
  • photoacoustic techniques;
  • image reconstruction;
  • burns

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information
Thumbnail image of graphical abstract

The poor elevation resolution in a linear scan (left image) is overcome by the proposed bi-directional scanning approach that yields isotropic transverse resolution (right).

Optoacoustic (photoacoustic) imaging is often performed with one-dimensional transducer arrays, in analogy to ultrasound imaging. Optoacoustic imaging using linear arrays offers ease of implementation but comes with several performance drawbacks, in particular poor elevation resolution, i.e. the resolution along the axis perpendicular to the focal plane. Herein, we introduce and investigate a bi-directional scanning approach using linear arrays that can improve the imaging performance to quasi-isotropic transverse resolution. We study the approach theoretically and perform numerical simulations and phantom measurements to evaluate its performance under defined conditions. Finally, we discuss the features and the limitations of the proposed method.


1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

Optoacoustic (photoacoustic) imaging enables high-resolution visualization of optical absorbers in biological tissue at depths beyond the operational limits of optical microscopy [1-3]. Using advanced reconstruction techniques and multi-wavelength illumination, imaging of anatomical, functional and molecular contrast has been shown in small animals in-vivo [1, 4]. Single wavelength imaging can produce images of optical absorption revealing tissue structure, including visualization of blood vessels. More generally, however, multispectral optoacoustic tomography (MSOT) can specifically detect multiple spectral signatures of intrinsic or extrinsically administered molecules and image the biodistribution of targeted fluorochromes [5, 6], fluorescent proteins [7], circulating gold-nanorods [8], vascular structures [9] and several important physiological readings, including cerebrovascular activity [10, 11], kidney perfusion [12] and tumor hypoxia [13].

The use of multi-element detector arrays has been common in enabling fast imaging performance. Real-time visualization of optical contrast has been achieved in 2D [4, 14] and 3D [15-17] by surrounding the object with a large number of detectors and parallel reading of the acoustic responses. Two-dimensional real-time optoacoustic tomography typically uses a 1D transducer array with elements arranged on an arc [8, 12, 14, 18-20], a full circle [10] or a line [21-25] around the object of interest. Typically, to suppress out-of-plane signals and achieve cross-sectional imaging, the elements are cylindrically focused to preferentially detect signals from a plane. In this way, signals outside the plane of interest are suppressed and the optoacoustic reconstruction is, in principle, reduced to a two dimension problem [4, 12]. Then, volumetric images can be obtained by scanning the transducer along the elevation axis, i.e. the direction perpendicular to the focal plane of the transducer array. In practice, however, acoustic focusing is not ideal. Acoustic cylindrical focusing generates slices with a variable width as a function of depth and frequency and does not offer ideal spatial cut-off characteristics. Moreover, the small effective detection aperture obtained by scanning a focused transducer typically leads to elevation resolution that is not as high as the lateral resolution. Importantly, even if the aperture along the elevation direction effectively increases by translating the array along this direction, the resolution remains anisotropic, due to the asymmetric size of the individual detector elements in a linear array. Optoacoustic imaging with one-dimensional focused detector arrays yields therefore anisotropic resolution.

In clinical application, the generation of images with anisotropic resolution is common. Many radiological modalities such as MRI or ultrasound imaging similarly operate using slice thickness which is significantly larger than the lateral resolution. The advantage of anisotropic resolution images is that they operate with voxels of higher effective volume, thus leading to a higher signal to noise ratio, compared to isotropic resolution images that offer slice-thickness-resolution comparable or identical to that of the lateral resolution. Nevertheless, in higher precision studies, the generation of images with isotropic resolution improves the information available and can help elucidate more complex structural or functional features.

One approach investigated to reach isotropic resolution consists of rotating linear cylindrically focused arrays around the object of interest [21, 22, 26]. This approach requires the enclosure of the sample imaged, i.e. it assumes that the object of interest is accessible from all sides, which is appropriate for small animal imaging but not suited for clinical imaging applications. Multi-bandwidth deconvolution methods [27] and model based inversion methods [28-30] have also been proposed to remedy the resolution anisotropy. These methods operate on data collected by scanning the detector along the elevation direction. In particular, modeling of the shape of the transducer elements and consecutive numerical inversion of the forward model has shown significant improvements in resolution performance [28-30].

In this work we investigate the merits of scanning a cylindrically focused linear array along two directions perpendicular to each other in order to improve upon the resolution anisotropy, which stems from the anisotropic size of the individual detector elements, typical in a linear array. The method is considered as a supplementary method to the regular use of cylindrically focused arrays employed in handheld mode. In other words, a foreseen implementation of the method is a follow up to handheld operation, when more accurate readings of the underlying tissue may be required. The implementation considered can be applied to clinical applications or imaging larger animals, as it requires access to tissue from one side only. The theoretical basis of the method is briefly presented, followed by numerical simulations that evaluate its performance. We showcase the experimental performance using measurements on phantoms and biological tissue. We conclude with a discussion of the potential and limitations of the proposed method.

2 Theory

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

The method examined herein assumes that a cylindrically focused ultrasound detector array is used for imaging. Volumetric data sets are acquired by scanning the array in elevation direction as shown in Fig. 1a. Two scans are performed along two directions perpendicular to each-other, as depicted in Fig. 1b. The 3D absorption maps reconstructed from the two perpendicular scans are represented by inline image and inline image, respectively. Typically, inline image and inline image are characterized by high lateral resolution (perpendicular to the scanning direction) and low elevation resolution (in scanning direction). To improve on this anisotropic resolution we propose to use the square root of the product t-norm of the two datasets, i.e.

  • inline image(1)

where inline image is the resulting absorption map and the operator inline image the Hadamard product, i.e. the element-wise multiplication of the two datasets. The rationale of this approach is to enforce structures that are common to both datasets and suppress others. To visualize the basics of the method, we applied Eq. (1) to two Gaussian-shaped absorption maps on a 2D plane (red and blue surfaces) shown in Fig. 1d. The square root of the product t-norm is then given by the intersection of the red and blue datasets, depicted in green.

2.1 Resolution of point-like structures

To better understand the effects of the bi-directional scanning geometry it is useful to derive the point spread for the proposed method. For that purpose it is assumed that we have a point source located at inline image, i.e. inline image and that images are reconstructed with a linear algorithm, such as for instance the backprojection algorithm [31]. Image formation can then be modeled as a convolution process of the true absorption inline image with the system's spatial impulse response (point spread function or PSF), i.e.

  • inline image,(2)

where inline image is the optoacoustic absorption map recontructed from a scan in inline image -direction inline image. For the two scans in x- and z-direction we then obtain from Eq. (2)

  • inline image(3)
  • inline image(4)

and from Eq. (1)

  • inline image(5)

To proceed with analytical calculations, the point spread functions inline image and inline image are approximated by three-dimensional normal distributions:

  • inline image(6)
  • inline image(7)

where inline image represents the standard deviation of the normally distributed PSF along the j-axis for a scan along the i-direction. Combining Eqs. (5)(7) we obtain for the point spread of the proposed reconstruction approach:

  • inline image(8)

where the normally distributed standard deviations in x-, y- and z-direction are given as:

  • inline image(9)
  • inline image(10)
  • inline image(11)

Equations (9)–(11) are general formulas that are not limited to a specific detection geometry. The formulas can be applied to cylindrical and planar imaging configurations. We assume for the following a planar detection geometry obtained by scanning a linear cylindrically focused transducer along its elevation axis, as depicted in Fig. 1a, c. Due to the limited effective aperture in elevation, the elongation of the PSF in elevation direction is significantly stronger than in lateral direction, i.e.

  • inline image(12)
  • inline image(13)

where inline image is a scaling factor representing the elongation of the PSF in elevation direction with respect to the lateral direction.

Plugging Eqs. (12) and (13) into Eqs. (9)(11), we can deduce the width of the point spread obtained with the new method as a function of the widths of the PSFs of the two perpendicular scans:

  • inline image(14)
  • inline image(15)

From Eq. (15) we see that the resolution along the acoustic axis of the transducer is not affected by the proposed reconstruction approach. The proposed reconstruction approach creates an isotropic resolution perpendicular to the acoustic axis, hereafter referred to as transverse resolution. The transverse resolution is slightly lower than the lateral resolution of a simple linear scan, but it will always be higher than the limiting resolution of inline image. On the other hand, the transverse resolution is significantly higher than the resolution in elevation direction of a simple linear scan. The larger the anisotropy of the PSF (the larger the ratio inline image ), the larger the increase in transverse resolution is compared to the resolution in elevation direction.

2.2 Resolution of line-like structures

The resolution of line-like structures can be calculated in the same way as for point-like structures. We assume a line source at an angle inline image with respect to the focal plane of the transducer for a scan in z-direction, i.e. inline image.

Following the same steps as above and employing the fact that the line source is at an angle of inline image with respect to the focal plane of the transducer for a scan in x-direction, we calculate the width of the line perpendicular to its axis after reconstruction. The cross-section of the line has a Gaussian shape with the width:

  • inline image(16)
  • inline image(17)

Thus, the resolution of line-like structures depends on the angle of the line with respect to the two perpendicular scans. At inline image and inline image the resolution is highest and equal to the point spread of a point (see Eq. (14)). The resolution decreases towards the lowest resolution at inline image where the resolution is lower by a factor of inline image, but always higher than the resolution in elevation direction.

3 Material and methods

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

3.1 Imaging system

To test the performance of the proposed method we employed a 24 MHz 128 element transducer array (LA28.0/128, Vermon, Tours, France), which has previously been applied as a handheld system for skin imaging [25]. The elements in this array are cylindrically focused in elevation direction by means of an acoustic lens with a focal distance of 7.5 mm. The size of a single detector element is 1.5 mm in elevation direction (height) and 55 µm in lateral direction (width) with a pitch of 70 µm between neighboring elements As a light source we used an optical parametric oscillator laser (Phocus II, Optotek Inc., California, USA) delivering <10 ns pulses at 10 Hz pulse repetition frequency (PRF) and tunable between 690 nm and 900 nm. The laser light was coupled into a fiber bundle with two arms that direct light to the sample, as depicted in Fig. 1c. Each of the two light sheets contained approximately 200 fibers that were arranged in two rows covering a rectangular surface of approximately 0.75 mm × 40 mm. The two light sheets were fixed at an angle of 30–40° with respect to the focal plane of the transducer. The two rectangular illumination beams were adjusted such as to cross each other within the focal plane of the transducer at a distance comparable to the focal distance of the transducer. A translation stage (M-605.2DD High-Accuracy Translation Stage, Physik Instrumente (PI), Germany) attached to a rotation stage (M-062.PD Precision connected Rotation Stage, Physik Instrumente (PI) Germany) was employed for computer controlled high precision scanning of the imaging unit along a planar surface. Signals were recorded using a custom-made 128-channel data acquisition system (DAQ) with a sampling rate of 125 MSamples/s, a dynamic range of 16 mV and 4 µV resolution.

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Figure 1. Scanning geometries. Scanning geometries investigated in this paper are (a) the simple linear scan (ls mode) and (b) the bi-directional linear scan using voxel-by-voxel addition (2lsA mode) or voxel-by-voxel multiplication (2lsM mode). For reasons of clarity the 128 elements of the transducer are reduced to 9 elements in the schematic. The two black dots represent a phantom with two microspheres. The red arrows illustrate the scanning directions. In dark gray and white a spatially fixed coordinate system is shown. (c) The high frequency linear array transducer in the center and the two light sheets to the left and right were mounted on a translation and rotation stage. (d) The square root of the product t-norm of two Gaussian-shaped datasets (red and blue) is shown in green. The saturation of the colors increases with the magnitude of the absorption maps.

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3.2 Data acquisition and reconstruction

Three different scanning modes were examined in this study.

  • linear scan – ls mode (Fig. 1a):

The imaging unit comprising fiber bundle and transducer array were translated continuously at a constant speed of 150 µm/s in elevation direction leading to the acquisition of a 2D dataset every 15 µm at a PRF of 10 Hz. Thus, for a scan of 8 mm in elevation direction the acquisition time for a simple linear scan amounts to 54 seconds. Before reconstruction, the signals were bandpass filtered (Butterworth, order 3) between 5 MHz and 45 MHz for noise removal. Images were reconstructed with the filtered backprojection algorithm in the far field approximation (i.e. only with the derivative term) as described in [25] on a reconstruction grid comprising inline image voxel with an isotropic voxel size of inline image. Maximal amplitude projections (MAP) images were used for visualization of the volumetric images.

  • bi-directional linear scan – 2lsA mode and proposed 2lsM mode (Fig. 1b):

For the bi-directional scanning modes two linear scans were performed in perpendicular directions (x-direction and z-direction) with a step size of 30 µm and reconstructed as described above. The step size was twice as big as for the ls mode for better comparability of the results since for all acquisition modes the same number of projections was used. The acquisition time of the bi-directional linear scan on a ROI of 8 mm × 8 mm amounts to 54 seconds plus an additional two seconds stemming from the time needed to rotate the transducer by 90°. In the 2lsA mode a combined image was then formed by addition of the two volumetric reconstructions. In the proposed 2lsM mode, the final image was formed by applying Eq. (1), i.e. by element-wise multiplications of the two volumetric datasets and taking the square root thereof. Since in the bi-directional scanning mode two volumetric datasets have to be reconstructed and processed, the reconstruction time is prolonged by a factor of approximately 2.5 compared to the simple linear scan.

3.3 Calibration of the bi-directional datasets

The calibration procedure of the bi-directional scanning mode is crucial for the performance of the proposed algorithm. The precision of the rotation stage used in the setup is 15 µrad, which would yield an offset of 0.12 µm over a distance of 8 mm (maximal image width), which is well below the transverse resolution of the system.

Two angles describing the tilt of the focal plane of the linear array have to be calibrated. First, if the normal to the focal plane of the transducer array is not parallel to the scanning direction, the image will be distorted in the x-z-plane. Fig. 2b shows how the image will be distorted if the angle α between the focal plane of the transducer and the scanning direction deviates from 90°, as depicted in Fig. 2a. We used the discrepancy in the angle in the reconstructed image for calibration. Second, the tilt angle inline image of the transducer surface with respect to the horizontal x-z-plane has to be calibrated. Fig. 2f shows how the image is distorted if the transducer surface is not horizontally oriented, as depicted in Fig. 2e. For a scan in z-direction the tilt of the transducer surface of an angle inline image will result in a distortion of the image in y-direction that increases linearly with x. Likewise, for a scan in negative x-direction, the distortion will increase linearly with z.

3.4 Numerical simulations

To test the proposed approach on controlled datasets, optoacoustic signals of a sample containing spherical absorbers of various diameters, ranging from 10 µm to 80 µm, were simulated for the uni- and bi-directional scanning modes. The theoretical N-shape signal of each spherical absorber [32] was filtered according to the bandwidth of the transducer used in our experiments and time-delayed according to the distance of the absorber with respect to the detector position. Each transducer element was simulated as the sum over individual point detectors located on a cylindrically focused surface (the focus being 7.5 mm away from the sensor surface) of 55 µm times 1.5 mm. Since spherical absorbers of different size have a distinct frequency content in the optoacoustic signal, spherical absorbers of various size were simulated to ensure that the applicability of the proposed reconstruction method is not limited to a specific frequency range. The microspheres were located over a large depth range from 4 mm (microsphere 4) to 10 mm (microsphere 6). Microspheres 1 and 2 were located at the same depth. Fig. 3a depicts the size of the spherical absorbers and their location in the transverse plane. In the images presented in this paper no background noise was implemented in the simulations.

3.5 Experimental measurements

Two agar phantoms and one biological tissue sample were prepared to experimentally test the resolution capabilities of the different scanning modes. Phantom 1 consisted of two 50 µm microspheres (BKPMS 45–53 µm, Cospheric, Santa Barbara, CA, USA) embedded at the same depth, approximately 450 µm apart, in a light scattering agar matrix. Phantom 2 contained four sutures of diameters ranging from 30 µm to 39 µm (NYL03DS, vetsuture, France) crossing each other at the same depth also embedded in a scattering agar matrix. The scattering agar matrix used for phantom 1 and phantom 2 was made by mixing water with 1.3% w/m agar gel (Agar for microbiology, 05039-500G, Fluka Analytical, Sigma-Aldrich, Germany) and 2% v/v intralipid-20% (Intralipid 20%, emulsion, l141-100ML, Sigma-Aldrich, Germany). Sample 3 was a fresh chicken wing from the local grocery store with a 4 mm deep skin burn induced with a cone-shaped iron rod heated to 400 °C. For imaging all samples were immersed in water to improve the acoustic coupling between the transducer and the sample.

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Figure 2. Calibration of the bi-directional datasets. The red and green dashed cross (b), channels (c, g) and curves (d, h) correspond to the images acquired with the array marked in red and dashed green (a), respectively. (a) B-directional scan of a phantom with cross structure. The focal plane of the array is at an angle α with respect to the scanning direction. (b) For both bi-directional scans the reconstructed images will be distorted in the x-z-plane, if the scanning direction is not perpendicular to the focal plane. (e) A tilt of the transducer surface with respect to the x-z-plane by an angle β will result in a distortion of the image along the y-direction (f). (c) MAP images along the y-direction of phantom 2 after the calibration had been performed (α = 3° β = 0.7°). (d) Exemplary cut through the MAP images in (c) along the white dashed line. (g) MAP images along the z-direction of phantom 2 after the calibration had been performed (α = 3° β = 0.7°). (h) Exemplary cut through the MAP images in (g) along the white dashed line. Each of the two datasets in (d, h) were normalized before plotting.

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Figure 3. Reconstruction of microspheres of various diameters for different scanning geometries. (a) Schematic of the simulated phantom. The microspheres were located at a depth of 4 mm (4), 6 mm (3), 7.5 mm (1, 2), 8 mm (5) and 10 mm (6). The diameters of the microspheres were: 40 µm (1,2), 10 µm (3), 80 µm (4), 50 µm (5) and 30 µm (6). Reconstructed images are shown for (b) the linear scanning geometry in ls mode, (c) the bi-directional scanning geometry in 2lsA mode and (d) the bi-directional scanning geometry in 2lsM mode.

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4 Results 

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

4.1 Calibration of the bi-directional scans

Fig. 2c, d and Fig. 2g, h show overlain images acquired by two perpendicular scans in the x-z-plane and x-y-plane, respectively. The red (green dashed) curves in Fig. 2d, h and channels in Fig. 2c, g correspond to the images acquired with the array marked in red (green dashed) in Fig. 2a. The overlay shows that over a range of 6 mm the crosses coincide well after the alignment of the array had been performed. The precision of the alignment was higher than the system resolution. The best results were found for inline image and inline image.

4.2 Simulations showcasing improvement of resolution in bi-directional linear scans

Fig. 3b depicts the reconstruction results for the uni-directional scan (Is mode). As expected, the microspheres are elongated along the elevation direction. Microspheres 1 and 2, which are separated by 200 µm along the z-direction, are not distinguishable, but form one large object of high intensity. Fig. 3c shows that the microspheres are better discriminated when employing the 2lsA mode. Yet, a cross-like structure is formed due to the superposition of the two perpendicular scans. In Fig. 3d the results of the 2lsM mode are shown. All microspheres are distinguishable and display a spherical shape without the cross-artifacts and independent of the distance of the absorbers from the transducer surface. In all scanning geometries the reconstructed 10 µm microsphere (microsphere 3) is hardly visible since high frequency components necessary for its reconstruction were not captured by the bandwidth of the transducer. This is also the reason microsphere 4 displays at low intensity.

A microsphere of 10 µm diameter that was located at the focal point of the transducer (7.5 mm in front of the surface) was simulated to evaluate the resolution capabilities of the three planar scanning geometries. The resolution in lateral and elevation direction was estimated from the full width at half maximum (FWHM) of the y-MAP (MAP image along the y-coordinate) of the reconstructed microsphere. To estimate the axial resolution of the three scanning modes, the FWHM of the central peak in a cut along the y-coordinate through the voxel of highest amplitude was evaluated. No obvious change in axial resolution is observed for the different scanning modes. Lateral resolution in the 2lsM mode deteriorates only slightly from 60 µm to 82 µm, whereas the resolution in elevation direction increases significantly compared to the simple linear scan from 311 µm to 82 µm. Table 1 summarizes the measured FWHM for all scanning modes and directions. From Eq. (14) we would expect an isotropic resolution of 83 µm in the 2lsM mode, as compared to a resolution of 311 µm in elevation direction and 60 µm in lateral direction. The measured resolution of 82 µm isotropic resolution coincides perfectly with the theoretical prediction.

Table 1. FWHM in the reconstructed image of a simulated 10 µm microsphere for different scanning geometries along different directions
Simulated modeFWHM in z-direction (µm)FWHM in x-direction (µm)FWHM in y-direction (µm)
ls mode311 6015
2lsA mode10410415
2lsM mode 82 8215

4.3 Resolution study using experimental data

Fig. 4 shows the results obtained with phantom 1. The experimental results are in congruence with the simulation study. The proposed reconstruction method (2lsM mode) significantly increases the resolution in elevation direction. The 2lsA mode improves the resolution as well compared to a simple linear scan. However, in the 2lsA mode the reconstructed circular microspheres were overlain by crosses stemming from the elongated shape of the microspheres in the simple linear scans.

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Figure 4. Resolution study of point-like structures for different scanning geometries. Phantom 1 was scanned and reconstructed using (a) the linear scan mode (ls mode) as well as the bi-directional linear scan modes 2lsA (b) and 2lsM (c). Figures (ac) are maximum amplitude projections (MAP) along the y-coordinate. (d) Cut through the center of the region of interest (ROI) marked by the white boxes along the z-direction. (e) Cut through the center of the ROI along the x-direction. (f) 1D cut through the center pixel of the ROI along the y-direction.

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As for the resolution study with simulated data, the resolution of different scanning geometries was estimated by the FWHM of an image of a 50 µm microsphere. The results are illustrated in Fig. 4(d–f) and Table 2. The resolution in elevation direction improves from approximately 282 µm in the simple linear scan to approximately 105 µm using the proposed 2lsM scanning mode. From Eq. (14) we would expect an isotropic resolution of 104 µm (108 µm) in the 2lsM mode, based on the resolution of 282 µm (282 µm) in elevation direction and 76 µm (79 µm) in lateral direction. The experimentally measured resolution of 104 µm (107 µm) (Table 2) is isotropic and agrees perfectly with the theoretically expected resolution. The axial resolution remained unchanged, as shown in Fig. 4(d–f) and Table 2.

Table 2. FWHM in the reconstructed image of a 50 µm microsphere for different scanning geometries along different directions
Acquisition modeFWHM in z-direction (µm)FWHM in x-direction (µm)FWHM in y-direction (µm)

ls mode

(z-scan)

282 7616

ls mode

(x-scan)

 7928217
2lsA mode14415318
2lsM mode10710415

Fig. 6 shows the improvement in resolution of line-like structures when applying the proposed scanning mode (2lsM mode). Fig. 6a reveals a blurring of sutures oriented perpendicular to the scanning direction in the ls mode. Sutures of the same diameter appear to be of different width and variable intensity. Fig. 6b, c illustrates that for both bi-directional linear scanning modes (2lsA and 2lsM) the size and intensity of the reconstructed sutures correspond better to their actual shape. The improvement in resolution is slightly angle-dependent, as expected from Eq. (16). The resolution for lines oriented perpendicular to the scanning direction, corresponding to the third peak in Fig. 6d, increases significantly, whereas the width of lines oriented at an angle of approximately 45° to the scanning direction, corresponding to the second peak in Fig. 6d, decreases only slightly.

4.4 Application to biological tissue

In a last experiment the proposed data acquisition and reconstruction method (2lsM mode) was applied to the biological tissue sample 3. Fig. 5 shows that the proposed 2lsM mode manages to produce high-resolution images in both lateral and elevation direction of the carbonized tissue. Furthermore, we see in Fig. 5d, e that the backprojection related arc artifacts above the burn indicated by the arrows in Fig. 5b, c are suppressed by the proposed algorithm. The supporting videos S1 and S2 show the outline of the cone shaped burn in three dimensions for the simple linear scan and the proposed bi-directional scan.

5 Discussion 

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

We presented a novel scanning and reconstruction approach to cope with the anisotropic resolution encountered in planar or cylindrical detection geometries using detection elements with a high aspect ratio or cylindrically focused transducer arrays. The approach consists of performing two linear scans of the same region in perpendicular directions, multiplication of the volumes and taking the square root thereof. We have theoretically derived that the proposed method yields a significantly improved resolution in elevation direction with minor losses in lateral resolution and confirmed this behavior in simulation and experiment.

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Figure 5. Reconstruction of a 4 mm deep burn. (a) Cross-sectional slice through the center of the burn. Images in the upper row show MAP images in ls mode along (b) the elevation direction and (c) the lateral direction. Images in the lower row (d, e) show the corresponding MAP images of the reconstructed volume in 2lsM mode. The resolution in elevation direction is significantly improved.

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By using the same amount of tomographic views in the different reconstruction modes, we could rule out that the improvement is due to the number of tomographic views utilized. Moreover, by comparing the novel method with simple addition of the two scans (2lsA mode), we have shown that taking the product t-norm of the data is the important step for achieving quasi-isotropic resolution. Multiplication improves the resolution because it suppresses those voxels that do not coincide in the reconstructed volumes of the perpendicular scans.

The advantages of the proposed method compared to a simple linear scan are manifold. First, the transverse resolution significantly improves when using the proposed reconstruction technique. Two distinct elongated structures that were indistinguishable and formed one object in the reconstruction of the simple linear scan could be discriminated by the proposed method. Second, noise is suppressed by the multiplication method. Since noise is uncorrelated in independent datasets it is less likely for noise structures to coincide in both datasets of the bi-directional scan. By the multiplication of the datasets, noise is suppressed. Third, arc artifacts, a common issue in backprojection algorithms, are reduced, especially for transducers that have a large aspect ratio or that are cylindrically focused and receive optoacoustic signals originating from a thin tissue layer. If a second scan is performed at an angle of 90° with respect to the first one, arc artifacts will appear in layers perpendicular to the first scan. Thus, the differently oriented arc artifacts do not coincide in the two datasets and are suppressed in the multiplication procedure.

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Figure 6. Resolution study of line-like structures for different scanning geometries. MAP images of phantom 2, containing four sutures of 30 µm diameter, are visualized for scanning modes (a) ls mode, (b) 2lsA mode and (c) 2lsM mode. (d) Cut through subfigures (ac) along the white dashed line.

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For line-like structures the increase in resolution is slightly angle-dependent. The largest increase in resolution is for lines oriented perpendicular to the scanning direction. If the line structure is oriented at an angle of 45° to both bi-directional scanning directions the resolution increases only slightly compared to the simple linear scan. Nonetheless, noise and arc artifacts are suppressed for line structures as well. The resolution of line structures could be further improved by performing more than two perpendicular scans, for example four scans with their scanning directions rotated by inline image ; inline image.

Although a linear cylindrically focused transducer array was used in this study with a planar detection geometry, the proposed method is not limited to such arrays, but will also improve reconstructions with unfocused transducers or in cylindrical detection geometries as long as the linear scans are performed in different directions. Moreover, Eqs. (9)(11) are independent of a specific scanning geometry or transducer arrangement and valid for all anisotropic point spread functions. The two scans composing the 2lsM mode do not necessarily have to be perpendicular to each other, but perpendicular orientation yields the best improvement of resolution and simplifies the alignment of volumetric datasets.

The success of the method relies on an accurate alignment of the two volumes obtained by the two linear scans prior to multiplication. The calibration of the bi-directional scans is crucial for the performance of the proposed algorithm. The axial direction with its high resolution is most sensitive to misalignment. In this work we presented a calibration method that compensates for both a tilt of the normal to the focal plane of the transducer array with respect to the scanning direction and the tilt angle of the transducer surface with respect to the horizontal x-z-plane. Once the tilt angles and the axis of rotation are calibrated, the proposed method may be applied to other bi-directional datasets without further adjustment.

The method will work well for stationary samples. In case of in vivo measurements movement has to be considered and must be accounted for since the multiplication procedure is susceptible to misalignment. Nonetheless, misalignment through movement is not an intrinsic problem of the proposed method, but all methods aiming at high resolution imaging have to deal with movement restriction.

6 Conclusion

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

To conclude, the proposed scanning geometry and reconstruction method has been shown to considerably improve the anisotropic resolution problem common to planar scanning geometries with elements featuring a high aspect ratio. Moreover, the novel ability to achieve quasi-isotropic resolution in a planar scanning geometry utilizing rather big detector elements might be of great importance in clinical imaging scenarios where SNR is a crucial factor.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information

This work was supported by the ERC Advanced Investigator Award N° 233161-MSOT. A.B. acknowledges financial support from the European Union project FAMOS (FP7 ICT, contract no. 317744).

References

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  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Theory
  5. 3 Material and methods
  6. 4 Results 
  7. 5 Discussion 
  8. 6 Conclusion
  9. Acknowledgements
  10. Supporting Information
FilenameFormatSizeDescription
jbio_201400021_sm_Author_biographies.pdf411KAuthorbiographie
jbio_201400021_sm_videoS1.avi2987KVideo 1
jbio_201400021_sm_videoS2.avi3369KVideo 1

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