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Ultrasound Tomography
Ultrasound in Med. & Biol., Vol. -, No. -, pp. 1–11, 2016 Copyright Ó 2016 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter
http://dx.doi.org/10.1016/j.ultrasmedbio.2016.06.028
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Original Contribution CALIBRATED LINEAR ARRAY-DRIVEN PHOTOACOUSTIC/ULTRASOUND TOMOGRAPHY MILAN OERI, WOLFGANG BOST, STEFFEN TRETBAR, and MARC FOURNELLE Fraunhofer Institute for Biomedical Engineering (IBMT), Medical Ultrasound Group, St. Ingbert, Germany (Received 29 February 2016; revised 25 May 2016; in final form 29 June 2016)
Abstract—The anisotropic resolution of linear arrays, tools that are widely used in diagnostics, can be overcome by compounding approaches. We investigated the ability of a recently developed calibration and a novel algorithm to determine the actual radial transducer array distance and its misalignment (tilt) with respect to the center of rotation in a 2-D and 3-D tomographic setup. By increasing the time-of-flight accuracy, we force in-phase summation during the reconstruction. Our setup is composed of a linear transducer and a rotation and translation axis enabling multidimensional imaging in ultrasound and photoacoustic mode. Our approach is validated on phantoms and young mice ex vivo. The results indicate that application of the proposed analytical calibration algorithms prevents image artifacts. The spatial resolution achieved was 160 and 250 mm in photoacoustic mode of 2-D and 3-D tomography, respectively. (E-mail: [email protected]) Ó 2016 World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound tomography, Photoacoustic tomography, Transducer calibration, Linear transducers, Image artifacts, Combined imaging.
based on the presence of acoustic impedance rather than attenuation maps.
INTRODUCTION Linear ultrasound transducer for tomography In biomedical research, tomographic imaging of the anatomy and physiology of small animals and human extremities is often performed using cost-intensive modalities, for example, magnetic resonance imaging, positron emission tomography and computed tomography (Lewis et al. 2002; Koba et al. 2011). In addition to their expense, however, these technologies are sometimes based on ionizing radiation and are not always sensitive to the imaging of vasculature. On the contrary, ultrasound imaging enables non-invasive, non-ionizing visualization of tissue and organs providing scalable resolution. Furthermore, full-view (i.e., 360 ) ultrasound (US) tomography enables isotropic spatial resolution through detection of a signal from a surface surrounding the target object and thus enhances the quality of reconstructed cross-sectional images of the investigated target. Tomographic US can be performed in either transmission or pulse-echo mode. Here, we focus on the latter configuration, which enables visualization of tissue interfaces
Photoacoustic imaging Photoacoustic (PA) tomography is an emerging imaging modality that can be combined with US to obtain additional information on the optical absorption of the same target object. The underlying principle is based on the conversion of absorbed light into acoustic waves that can be detected just as conventional ultrasound and is referred to as the photoacoustic effect. Thus, PA is capable of visualizing vasculature (Fournelle et al. 2009; Laufer et al. 2012; Zhang et al. 2006) and tumor angiogenesis (Ku et al. 2005) and has already made its way into pre-clinical studies of breast cancer diagnosis (Kruger et al. 2013; Piras et al. 2009). Existing tomographic photoacoustic detection configurations are based on single elements (Sun et al. 2009) and curved (Brecht et al. 2009; Gamelin et al. 2008; Oraevsky and Karabutov 2000; Yang et al. 2009) or planar (Geateau et al. 2013; Kruger et al. 2003; Kuzhushko et al. 2004; Yin et al. 2004) arrangements. Geometric detection approaches to tomography Because in vivo studies require control of animal parameters (e.g., motion, respiration), investigations should
Address correspondence to: Milan Oeri, Fraunhofer Institute for Biomedical Engineering (IBMT), Ensheimer Strasse 48, 66386 St. Ingbert, Germany. E-mail: [email protected] 1
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be as short as possible. Transducer arrays are, thus, more likely to be applied to tomography as parallel detection reduces acquisition times. Although tomographic and concave detection geometries address the radial propagation nature of acoustic waves, they remain custom-made and cost-intensive systems. Linear transducer arrays are commercially available and hence attractive for US and PA imaging. Medical linear ultrasound transducers were introduced for thermoacoustic tomography by Kruger et al. in 2003. A linear ultrasound transducer has been found to be suitable for a whole-body photoacoustic tomography system for small animal imaging (Geateau et al. 2013). For tomographic imaging, the localization of transducer elements and the orientation of transducer arrays with respect to the center of the system are crucial. To date, several calibration methods or phantoms, such as wedge-pattern phantoms and wires (Abeyskera and Rohling 2011; Fenster and Downey 2000), acoustical trackers based on constrainment of emitter and receiver (Meyer and Biocca 1992) by coincident alignment and free-hand tracking methods based on optical or electromagnetic technologies (Arbel et al. 2004; West and Maurer 2004), have been used to align or calibrate acoustic detectors, for example, for 3-D freehand imaging (Mercier et al. 2005). However, these techniques can be cost intensive and lack the ability to determine the exact radial transducer array position and in-plane tilt (x/y-plane) in a tomographic setup, that is, with rotating probes or samples. Other calibrations are based on pointlike phantoms and a manual, iterative adjustment of the transducer position. The position is varied until a certain criterion, for example, maximum amplitude,
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is passed (Brecht et al. 2009; Geateau et al. 2013). However, imprecise knowledge of the transducer positions, and especially of the tilt, yields inaccurate time-of-flight (TOF) assumptions, preventing an adequate phase-adjusted summation of signals during the reconstruction that degrades the image. Analytical calibration algorithm I (2-D) In a previous study (Oeri et al. 2015), we described the impact of transducer alignment on the image quality achieved and illustrated a calibration algorithm for ultrasound and photoacoustic tomography accurately delivering the actual radius r and transducer array tilt d. The method is based on a system of linear equations (SLE) in which photoacoustic measurements from several angular positions are supplied as input (Fig 1, left). Owing to the misalignment of the transducer, the tomographic reconstruction of a small target yields an image artifact, where the signal information is distributed on a circular shape. Figure 1 (right) illustrates the obtained circular image artifact for a simulated transducer misalignment of 2 , an error in the radial distance of 1.5 mm and 18 angular positions (20 increments). A detailed description of the artifact, its derivation thereby and its impact on image quality is given by Oeri et al. (2015). The angular transducer position can be described by the combination of a rotation and translation matrix (R and T), in which the radial distance r and tilt d cannot be measured precisely and thus remain unknowns (cf. Fig. 1). On that basis, we set up an overdetermined SLE of the form Axzb with respect to i different angular measurement positions to extract the tilt and radial distance:
Fig. 1. Misalignment of transducer and image artifact. The transducer misalignment can be expressed by rotation and translation matrices (left), where a radial deviation and transducer tilt are present (left). Uncorrected transducer misalignment yields the circular distribution of signals fractions (right) that is used to derive the transducer tilt and actual radial distance.
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C1 1F1 4 « Ci 1Fi
E1 1H1 « Ei 1Hi
3 2 3 21 tan d 5 « 5$4 r=cos d 21 ðxtomo 1ytomo Þ=cos d 3 2 2ðD1 1G1 Þ 5 « (1) z4 2ðDi 1Gi Þ
The coefficients were simplified as follows: C 5 2xi cos q1yi sin q D 5 2xi sin q2yi cos q E 5 r cos q
F 5 2xi sin q2yi cos q G 5 xi cos q2yi sin q (2) H 5 r sin q
Practically, we obtained (1) by acquiring PA images of a point-like target from different angular positions, as illustrated in the flowchart in Figure 2 (step 1). In this approach, (xi,yi) are the coordinates of the peak value in the reconstructed image in the local system S1 (steps 2 and 3). Once the actual transducer tilt and radial distance were obtained (step 4), the reconstruction could be adapted to the actual measurement setup in terms of TOF correction (step 5). Owing to its mathematical nature, the proposed method objectifies system calibration. The latter was proven by repeating the calibration three times. The variations obtained for the two calibration parameters d and r were not significant (,1%). However, because the unique solution to the overdetermined system is given by
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the minimization in the sense of least squares, the accuracy increases with the number of measurements. We compared the deviation of the solution for three different increments (5 , 10 and 40 ). Within this range, the deviation of the radius and tilt was determined to be 0.8%. Here, we extend prior work to the imaging of small animals and apply the proposed calibration algorithm herewith generating stacked 2-D slices along the scanning axis. The performance of the calibration algorithms developed was evaluated both on a thin suture and on young mice ex vivo, illustrating their applicability to biomedical research and small animal imaging. Characterization of misalignments in a 3-D setup In the next step, we investigated transducer misalignments and resulting artifacts with a 90 -rotated orientation of the linear transducer array; that is, the lateral dimension of the transducer axis parallel to z (cf. Fig. 3). The modified arrangement was aimed at obtaining 3-D data and further reducing the acquisition duration. Because of the changed arrangement, solely one detection element contributed information (A-Scan) per angular position and plane. A new calibration algorithm that is suitable for this modified detection geometry was derived. The performance of the calibration was evaluated on a thin suture phantom. METHODS Experimental setup The experimental setup (cf. Fig. 4) comprised an illumination component, an acoustic array probe immersed in water and motorized rotation and translation stages including integrated encoders. Measurements were performed with a 5-MHz piezoelectric transducer providing a 6-dB bandwidth of 80% and a pitch of 300 mm (LA 5.0/128-633, Vermon, Tours, France). US images were acquired through plane wave imaging. Photoacoustic stimulation was provided by a Nd:YAG laser delivering short pulses (10 ns) at a repetition rate of 20 Hz and a wavelength of 1064 nm (H700, Quanta
Fig. 2. Flowchart calibration algorithm. Flowchart of the calibration algorithm for tomographic setups, based on linear ultrasound transducers and photoacoustics. SLE 5 system of linear equations.
Fig. 3. Three-dimensional tomography with linear arrays. Three-dimensional setup with modified view. The lateral transducer direction is oriented parallel to the z-axis.
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Systems, Solbiate Olono, Italy). Light was coupled into afiber whose ending is divided. Each ending had a 30-mm-wide aperture (Fig. 5). A slight tilt superimposed the light in the detection plane, over a distance of 15 mm, yielding a rectangular illumination pattern of 2 3 30 mm. The pulse energy was measured to be 40 mJ. The fluence delivered to the sample was approximately 67 mJ/cm2, well below the limitation for skin exposure of 100 mJ/ cm2 at 1064 nm in clinical settings according to the American National Standards Institute and Laser Institute of America. Different types of target objects were used to evaluate image quality. A thin, black suture (NYL02DS, Vetsuture, Paris, France) having a diameter of approximately 25 mm served as a point-like source in the detection plane. The suture was used as a calibration phantom prior to the biological measurement. A 3-D printed phantom holder was used to perform the calibration measurements (Fig. 4). The holder was made from opaque synthetic material (VeroWhite, Stratasys, Rheinmuenster, Germany) and was attached to the rotating shaft, which is part of a high-precision rotation stage (PI M-061 PD, Physik Instrumente, Karlsruhe, Germany). The latter provides an angular resolution of 0.001 and, thus, has no noticeable influence on the calibration. Two solid rods stabilize the holder and ensure the spanning of the suture. The holder
Fig. 4. Experimental setup. Experimental calibration setup with a linear ultrasound transducer and attached fiber bundles (1). The setup is immersed into a water tank. Rotation of the target object (2), which is clamped in a phantom holder (3), is achieved by a motorized rotation stage (4). A 3D-printed transducer and fiber bundle holder provides in-plane illumination.
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Fig. 5. Combined imaging. Experimental 2-D stack tomography for the combined photoacoustic and ultrasound (PA/US) investigation of young mice.
mounting on the tip of the shaft was designed such that samples could be easily exchanged without affecting the measurement setup. 2-D stack tomography In our first setup (Fig. 4), the transducer remained fixed, while the target object was rotated in 10 (calibration) and 20 (animal) steps. We assume the speed of sound in water to be constant at 1480 m/s, whereas for further investigations of biological tissue, we approximated the speed of sound as 1540 m/s. Because all methods relying on the TOF are highly sensitive to speed-of-sound variations, we performed the calibration with a target immersed in a water environment outside the sample. This configuration (Fig. 5) holds for small animal imaging; it minimizes artifacts caused by transducer rotation and reduces the system size that otherwise would be based on a transducer rotating arm. Because a 128-element transducer array is rotated instead of a single detector, the number of rotation steps can be reduced. However, the precision of the calibration method (Fig. 1) increases with the number of acquisition angles (overdetermined SLE), which is why we increase the rotation steps during the calibration process. Thus, a thin suture is rotated by 10 (36 steps) and data are reconstructed in the local field-of-view (FOV) in front of the array. The actual lateral transducer tilt d with respect to the center of rotation and the radial distance r were determined using the aforementioned method. After calibration, the suture was removed for the animal holder to be placed. We investigated young mice ex vivo (1–2 days old) that were fixed prone and later rotated and elevated to obtain 2-D stack images. Subsequent of tomographic PA and US data were acquired with the latest generation of our 128-channel beamforming research platform
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DiPhAS (Digital Phased Array System, Fraunhofer IBMT, St. Ingbert, Germany). Data were sampled at 40 MHz and bandpass filtered with a 4-MHz bandwidth with respect to the center frequency of the ultrasound transducer of 5 MHz. No further signal averaging was performed to reduce the acquisition time. Scan strategy The scan strategy was based on a motor-driven 20 stepwise rotation of the animal holder and parallel data acquisition yielding a set of 18 measurements and fullaperture tomographic data. Once data for one plane were stored, the motorized translation stage (PI M-061, Physik Instrumente, Karlsruhe, Germany) moved the probe in an elevational direction with a step size of 1 mm. All in all, we obtained data to form a stack of 30 images in ultrasound and 20 images in photoacoustic mode. Reconstruction algorithm A delay-and-sum reconstruction (DAS) was applied to form both tomographic photoacoustic and ultrasound images in a circular compounding mode. The algorithm is based on the computation of TOFs ti between a defined grid element (pixel) and the corresponding detector element, that is, solely the backward direction (pixel-toreceiver) in photoacoustic mode, for i 5 1,.,n angular detection positions according to the equation f ðx; yÞ 5
n X
pi ðt i ðx; yÞÞ
(3)
i51
Herein, f(x,y) denotes the reconstructed value of one pixel in the field of view. Pressure values p of the raw data obtained were summed with respect to the TOFs. Ultrasound images were likewise derived, but with ti denoting the entire duration of both the forward (emitter-to-FOV) and backward directions. Characterization of artifacts in 3-D tomography In the second setup (cf. Fig. 3), we modified the transducer view; that is, we oriented the lateral direction of the array vertically (parallel to the rotation axis). The constant diameter of the investigated suture enabled comparison of cross-sectional images obtained in the 2-D and 3-D setups. We considered the limited elevational aperture of the transducer array and applied an angular increment of 2 . With respect to its comparably large operating distance, the transducer covered a sufficient area and resulted in a well-sampled field of view. In return, no vertical movement of the probe was necessary, because the lateral transducer aperture enabled whole-body animal imaging. In addition to prior work, in which we studied the impact of transducer misalignments in two dimensions, artifacts arising as a result of misalignments in
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the modified setup were modeled (array orientation deviation from parallel alignment, radial uncertainty). We therefore simulated the (erroneous) reconstruction of a small absorber with the transducer having certain misalignments in three dimensions. Figure 6 (top) depicts the transducer orientation in the 3-D tomographic setup. The red lines indicate the angular position of the linear transducer during tomographic measurements. The dashed line represents the axis of rotation. In contrast to an ideal alignment, in experimental setups the transducer is inevitably slightly misaligned, and the assumed radial distance is inaccurate. We illustrated the impact of TOF correction by the artifacts resulting from two misalignments: radial displacement (Fig. 6, top left) and transducer tilt (Fig. 6, top right). The misalignments are indicated by arrows. The first case yields the circularly shaped artifact (blue circles) in place of the point source (black dot). The artifact is comparable to that of the 2-D stack-tomography (Fig 1, right). Furthermore, misalignment in orientation (tilt) yields an artifact for out-ofcenter point-like sources (Fig. 6, right). The erroneously reconstructed pattern (blue circles) varies significantly from the true point source location (black dot) affecting the volumetric image quality. Thus, we focus on the derivation of the actual radial distance of the transducer array throughout z to enable 3-D imaging. Analytical calibration algorithm II (3-D) To derive the actual radial distance of the transducer array with respect to the rotation axis (dashed line, Fig. 6), we rotated a spanned 150-mm-thin suture by 360 and detect PA signal peaks for each rotation step. Figure 7 illustrates experimentally measured distances (blue) according to the determined PA source peaks in each A-Scan. Artifacts arising at certain angles are due to the phantom holder rods and were removed prior to the calibration. Generally, the determined distance Biz varies in the vertical direction z 5 1, ., 128 (transducer elements) if a lateral transducer tilt is present (Fig. 6, top right) and with the angular position i 5 1,.,n. In a first step, we simplified the 3-D Biz to a 2-D value bi by taking only data from the central array element into account. Furthermore, we expressed the measured distance b between the PA source s and the detection element at angle i as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 bi 5 ðxi 2xs Þ 1ðyi 2ys Þ (4) The definition of the detector position was brought into polar coordinates with respect to the angle of rotation ai and in dependence on the actual radial distance r: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bi 5 ðr cos ai 2xs Þ2 1ðr sin ai 2ys Þ2 (5)
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Fig. 6. Transducer alignments. Simulated transducer alignments (red lines) with respect to the center of rotation (dashed line) in a 3-D setup. Misalignments are inevitably present (indicated by arrows), degrading image quality (here: radial deviation [top left] and tilt [top right]). The corresponding, artificially reconstructed point source formations (blue circles) are shown below in comparison to the result of an ideal alignment (black dots).
Fig. 7. Radius deviation. Experimentally obtained distances of a photoacoustic source to one transducer element (2 increment). Peak position of the envelope is determined to obtain distances to derive the radial distance in 3-D configurations. Few artifacts (marked in red) were produced by the phantom holder rods and were filtered prior to computation of the system of linear equations.
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An overdetermined SLE in the form Ax z b was derived based on several angular measurements i 5 1, ., n: 3 2 2 2 23 2 23 2 1 22 cos a1 22 sin a1 b1 xs 1ys 1r 5 $4 4« 5 z4 « 5 « « xs r 1 22 cos an 22 sin an b2n ys r (6) The solution to (6) gives the actual radial distance in one plane r64 (central transducer element 64) based on rotation of the investigated PA source. As pointed out later, we computed the remaining radial distances in plane z 5 1, ., 63, 65,.,128 based on r64 and the determined transducer tilt along z. Again, the solution to the overdetermined system is given by minimization. The accuracy increased with the number of measurements. We used a 3-D DAS algorithm to reconstruct photoacoustic and ultrasound data on the observed object based on the analytical calibration of the system. In contrast to the 2-D reconstruction in 2-D stack tomography, we addressed 3-D wave propagation and took signals of all elements on the cylindrical detection system into account to reconstructed one voxel. RESULTS Evaluation of algorithm I First, we present the results for the conventional 2-D stack imaging setup. We imaged a thin, optical absorber (suture) to derive the transducer tilt and radial distance to the rotation center. The measured data were reconstructed according to the actual transducer positions (tilt: 1.5 , radial distance: 31.34 mm).
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The reconstructed image that is exemplarily illustrated for one stack along the scanning plane in Figure 8 (left) serves as the control for the system calibration step. The isotropic spatial in-plane resolution was 160 mm. Figure 8 (right) illustrates the impact of the calibration on image resolution. During reconstruction, we applied a slight deviation of the radial transducer distance of 100 mm from the determined, value disregarding the present transducer tilt. The lack of calibration yields artifacts and degrades image quality. Combined PA/US imaging of small animals In the next step, we examined young mice (1–2 days old) with both photoacoustic and ultrasound tomography (PA/US) using prior system calibration. Exemplarily, Figure 9 depicts 5 of 30 stack images (ultrasound) that anatomically range from the thoracic part to the cranial part of the mouse. Such tissues as lung lobes, heart, supplying vessels and facial bone structure can be distinguished. We also compared images obtained with prior calibration to those obtained under a slight transducer radius deviation of 11.5 mm with respect to the center of rotation and from what is determined by applying the calibration algorithm (31.34 mm). The red, dashed arrow in Figure 9 (slice top left) points to incomplete structure boundaries compared with the same slice to the right (arrow 4). In addition to ultrasound, we performed photoacoustic tomography on the same mouse. The corresponding images are illustrated in Figure 10. The reconstructed anatomic views correlate with the US images, as expected. Moreover, PA represents information on their
Fig. 8. Reconstruction of point source. Left: Reconstructed, photoacoustic cross-sectional image of a thin suture (25 mm) as a result of the transducer calibration algorithm yielding a transducer tilt d 5 1.5 and the actual radial distance r 5 31.34 mm. Right: Reconstruction without prior calibration (i.e., 100-mm deviation from actual radial distance, no tilt), illustrating the impact of the linear array calibration.
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Fig. 9. Ultrasound stack images of mouse ex vivo. Calibrated, linear array-based ultrasound tomography of a 1- to 2-dayold mouse as cross-sectional images. The images reveal morphological information on the thoracic and cranial parts of the mouse investigated. Thorax: spinal cord (1), right and left lobes of lung (2), heart (3), sternum (4), right foreleg (5), left vena cava superior (6), aortic vessels (7), left subclavian vein (8). Head: cranium (9), right ear (10), facial cheekbone (11), mouse (12), maxilla (13). Uncalibrated, the image suffers from artifacts as incomplete structure boundaries (cf. red arrow).
Fig. 10. Photoacoustic stack images of mouse ex vivo. Calibrated photoacoustic tomography of a 1- to 2-day-old mouse as axial cross-sectional images. The images reveal additional information on the absorption of light at wavelength 1064 nm.
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Fig. 11. Combined photoacoustic/ultrasound images of mouse ex vivo. Calibrated, combined photoacoustic (colored) and ultrasound tomography of a 1- to 2-day-old mouse. The images correlate optical absorption and acoustic information on the thoracic region ex vivo. The photoacoustic data correlate well with the ultrasound images.
optical absorption in each plane. Although the US images revealed tissue surfaces, bone structures and large structures, the PA images obtained visualized lightabsorbing structures. We also fused US and PA images, combining acoustic and optical information in a single frame. Figure 11 depicts the combined images in the lung (left) and upper thorax (right). Photoacoustic signals according to their intensity composition in the color map on the right side were blended over the ultrasound images. 3-D imaging: evaluation of calibration approach II In a second setup, we modified the transducer view (i.e., 90 rotation) and derived the actual transducer array
position using a newly developed method. We first imaged a 150-mm-thin suture and derived the actual radial distance of the detecting elements with respect to the rotation center by applying the calibration algorithm proposed in eqn (1). The actual radial distance of the center element (No. 64) to the rotation axis could be determined precisely as illustrated by the reconstructed control in Figure 12 (right). Imaging of the eccentrically arranged thin suture from one angle and the entire linear detector array and the determination of the distances dependent on z (lateral transducer direction) enabled us to determine the tilt dz as 0.05 (Fig. 13). With respect to the determined radial distance of the center detector element, we were able to derive the radial distances dependent on z.
Fig. 12. Three-dimensional image of suture and 2-D slice serving as control. Tomographic, photoacoustic 3-D image of a 150-mm suture (left) serving as a control of the calibration method prior to animal studies. An in-plane resolution of 250 mm is determined from a cross-sectional view (right) in front of transducer element 64.
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Fig. 13. Transducer orientation in z. Distance from detector array aligned parallel to z. The slope gives the transducer tilt angle dz with respect to the rotation axis. Together with the computed radial distance, the transducer position is adapted to the actual measurement setup, herewith preventing the reconstructed image from degradation.
The system calibration parameters obtained were used during 3-D DAS reconstruction. We evaluated the performance of the modified calibration for 3-D tomography of the 150-mm suture. The reconstructed 3-D PA image (Fig. 12) of the suture proved the suitability of the method for calibration of the modified transducer arrangement and the ability to perform 3-D imaging based on a linear array. A cross-sectional image illustrates a spatial in-plane resolution in the range of 250 mm. DISCUSSION A newly developed calibration algorithm tailored to the application of linear transducer arrays to PA/US tomography in a 2-D stack imaging setup was applied to mice ex vivo and proved its feasibility for enhancing image quality, providing a spatial resolution of 160 mm. The results obtained prove that the calibration algorithm enables accurate determination of the position of transducer array elements in a tomographic PA/US setup. The images of the mice relate acoustic information of tissue surfaces, bone structures and larger blood vessels to their spectral absorbing characteristics at 1064 nm. This calibration approach is rather valid for slight misalignments with respect to the transducer orientation (,10 tilt), as strong tilts would obviously first require a mechanical correction. The linear transducer arrays applied decrease the required number of rotation steps compared with the rotation of single detector elements and thus yield shorter acquisition times. A new calibration algorithm adapted to a 3-D setup based on linear arrays was derived, yielding the actual radial transducer distance to the center of rotation, and it detected possible transducer misalignments in the lateral direction. A 3-D delay-and-sum
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reconstruction addressed the spherical nature of acoustic waves. We reconstructed 3-D data from a thin suture, yielding a resolution of 200 mm, and thereby illustrated the calibration method in the 3-D setting. However, in our setup, the shape of the reconstructed point-like source is less isotropic than in the 2-D stack imaging setup. This is not due to the algorithm itself, but rather to the influence of the supporting rods (Fig. 4, shadowing effect). The illumination here is parallel to the z-axis (Fig. 3). Thus, the comparably thin in-plane illumination pattern is impeding sufficient illumination at some angular positions. In contrast, in the 2-D setup, sufficient light is delivered to the sample and a wide aperture accepts acoustic signals. In the 3-D setup, this could be overcome by delivering light from several angles. Although single element detection and 2-D stack tomography with linear arrays take tens of minutes, a complete 3-D scan can be performed, in principle, in 3–5 min based on a 128-channel acquisition platform. In both methods, as found through our simulations and experimental results, prior calibration is crucial. We presented two approaches to both detection geometries providing an increased TOF accuracy during the reconstruction of PA/US images based on linear transducers in a 2-D or 3-D arrangement. Possible application fields include tomography of small animals and human extremities such as digital joints. Although we only investigated the calibration together with delay-and-sum beamforming reconstruction, it could as well be used for model-based inversion reconstructions (MBIR) relying on optimization algorithms to iteratively reconstruct an image corresponding to the spatial distribution of investigated physical parameters (absorption of optical energy in the OA setting). In that way, first estimates based on artificial data can be iteratively updated by including a TOF model yielding stepwise improvement of the reconstructed image. CONCLUSIONS We described and evaluated analytical calibration algorithms tailored to 2-D/3-D tomography based on a 128-element linear ultrasound transducer. The applied calibrations are intended to determine misalignments such as transducer tilt and radial uncertainty of the transducer array with respect to its center of rotation. The proposed calibration methods are applicable to ultrasound and photoacoustic tomography (PA/US). We evaluated performance on a thin suture and young mice ex vivo. Moreover, we compared the calibrated imaging system with an uncalibrated system and thereby proved the calibration can shield PA/US tomography from image artifacts caused by time-of-flight misinterpretations. Thus, by applying the proposed calibration methods as
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an alternative to hitherto applied mechanical positioning or time-consuming iterative approaches, we obtained an image resolution of 160–200 mm depending on the applied setup, that is, 2-D stack imaging versus 3-D tomography. Acknowledgments—The authors acknowledge funding by the European Union under the FP7 Project IACOBUS (Grant FP7-HEALTH 305760).
REFERENCES Abeyskera JM, Rohling R. Alignment and calibration of dual ultrasound transducers using a wedge phantom. Ultrasound Med Biol 2011;37: 271–279. Arbel T, Morandi X, Comeau RM, Collins DL. Automatic non-linear MRI-ultrasound registration for the correction of intra-operative brain deformations. Comput Aided Surg 2004;9:123–136. Brecht HP, Su R, Fronheiser M, Ermilov SA, Conjusteau A, Oraevsky AA. Whole-body three-dimensional optoacoustic tomography system for small animals. J Biomed Opt 2009;14: 064007. Fenster A, Downey DB. Three-dimensional ultrasound imaging. Annu Rev Biomed Eng 2000;2:457–475. Fournelle M, Hewener H, G€unther C, Fonfara H, Welsch H, Lemor R, Cox B. Free-hand 3D optoacoustic imaging of vasculature. Proc IEEE Ultrason Symp 2009;116–199. Gamelin J, Aguirre A, Maurudis A, Huang F, Castillo D, Wang LV, Zhu Q. Curved array photoacoustic tomographic system for small animal imaging. J Biomed Opt 2008;13:024007. Geateau J, Caballero MA, Dima A, Ntziachristos V. Three-dimensional optoacoustic tomography using a conventional ultrasound linear detector array: whole-body tomographic system for small animals. Med Phys 2013;40:013302. Koba W, Kim K, Lipton ML, Jelicks L, Das B, Herbst L, Fine E. Imaging devices for use in small animals. Semin Nucl Med 2011;41: 151–165. Kruger RA, Kiser WL Jr, Reinecke DR, Kruger GA. Thermoacoustic computed tomography using a conventional linear transducer array. Med Phys 2003;30:856–860.
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Kruger RA, Kuzmiak CM, Lam RB, Reinecke DR, Del Rio SP. Dedicated 3D photoacoustic breast imaging. Med Phys 2013;40: 113301. Ku G, Wang X, Xie X, Stoica G, Wang LV. Imaging of tumor angiogenesis in rat brains in vivo by photoacoustic tomography. Appl Opt 2005;44:770–775. Kuzhushko V, Khoklova T, Zharinov A, Pelivanov I, Solomantin V, Karabutov A. Focused array transducer for two-dimensional optoacoustic tomography. J Acoust Soc Am 2004;116:1498–1506. Laufer J, Johnson P, Zhang E, Treeby B, Cox B, Pedley B, Beard P. In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy. J Biomed Opt 2012;17:056016. Lewis JS, Achilefu S, Garbow JR, Laforest R, Welch MJ. Small animal imaging: Current technology and perspectives for oncological imaging. Eur J Cancer 2002;38:2173–2188. Mercier L, Lango T, Lindseth F, Collins LD. A review of calibration techniques for freehand 3-D ultrasound systems. Ultrasound Med Biol 2005;31:143–165. Meyer K, Biocca FA. A survey of position trackers. Presence Teleoperator Virtual Environ 1992;1:173–200. Oeri M, Bost W, Fournelle M. Analytical calibration of linear transducer arrays for photoacoustic tomography. Proc SPIE 2015;953390:1–9. Oraevsky AA, Karabutov A. Ultimate sensitivity of time-resolved optoacoustic detection. Proc SPIE 2000;3916:228–239. Piras D, Xia W, Steenbergen W, van Leeuwen TG, Manohar S. Photoacoustic imaging of the breast using the Twente Photoacoustic Mammoscope: Present status and future perspectives. IEEE J Select Top Quantum Electronics 2009;16:730–739. Sun Y, Sobel E, Jiang H. Quantitative three-dimensional photoacoustic tomography of the finger joints: An in vivo study. J Biomed Opt 2009;14:064002. West JB, Maurer CR. Designing optically tracked instruments for image-guided surgery. IEEE Trans Med Imaging 2004;23: 533–545. Yang X, Maurudis A, Gamelin J, Aguirre A, Zhu Q, Wang LV. Photoacoustic tomography of small animal brain with a curved array transducer. J Biomed Opt 2009;14:054007. Yin B, Xing D, Wang Zeng Y, Tan Y, Chen Q. Fast photoacoustic imaging system based on 320-element linear transducer array. Phys Med Biol 2004;49:1339–1346. Zhang HF, Maslov K, Li ML. In vivo volumetric imaging of subcutaneous microvasculature by photoacoustic microscopy. Opt Express 2006;14:9317.
http://dx.doi.org/10.1016/j.ultrasmedbio.2016.06.028
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Original Contribution CALIBRATED LINEAR ARRAY-DRIVEN PHOTOACOUSTIC/ULTRASOUND TOMOGRAPHY MILAN OERI, WOLFGANG BOST, STEFFEN TRETBAR, and MARC FOURNELLE Fraunhofer Institute for Biomedical Engineering (IBMT), Medical Ultrasound Group, St. Ingbert, Germany (Received 29 February 2016; revised 25 May 2016; in final form 29 June 2016)
Abstract—The anisotropic resolution of linear arrays, tools that are widely used in diagnostics, can be overcome by compounding approaches. We investigated the ability of a recently developed calibration and a novel algorithm to determine the actual radial transducer array distance and its misalignment (tilt) with respect to the center of rotation in a 2-D and 3-D tomographic setup. By increasing the time-of-flight accuracy, we force in-phase summation during the reconstruction. Our setup is composed of a linear transducer and a rotation and translation axis enabling multidimensional imaging in ultrasound and photoacoustic mode. Our approach is validated on phantoms and young mice ex vivo. The results indicate that application of the proposed analytical calibration algorithms prevents image artifacts. The spatial resolution achieved was 160 and 250 mm in photoacoustic mode of 2-D and 3-D tomography, respectively. (E-mail: [email protected]) Ó 2016 World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound tomography, Photoacoustic tomography, Transducer calibration, Linear transducers, Image artifacts, Combined imaging.
based on the presence of acoustic impedance rather than attenuation maps.
INTRODUCTION Linear ultrasound transducer for tomography In biomedical research, tomographic imaging of the anatomy and physiology of small animals and human extremities is often performed using cost-intensive modalities, for example, magnetic resonance imaging, positron emission tomography and computed tomography (Lewis et al. 2002; Koba et al. 2011). In addition to their expense, however, these technologies are sometimes based on ionizing radiation and are not always sensitive to the imaging of vasculature. On the contrary, ultrasound imaging enables non-invasive, non-ionizing visualization of tissue and organs providing scalable resolution. Furthermore, full-view (i.e., 360 ) ultrasound (US) tomography enables isotropic spatial resolution through detection of a signal from a surface surrounding the target object and thus enhances the quality of reconstructed cross-sectional images of the investigated target. Tomographic US can be performed in either transmission or pulse-echo mode. Here, we focus on the latter configuration, which enables visualization of tissue interfaces
Photoacoustic imaging Photoacoustic (PA) tomography is an emerging imaging modality that can be combined with US to obtain additional information on the optical absorption of the same target object. The underlying principle is based on the conversion of absorbed light into acoustic waves that can be detected just as conventional ultrasound and is referred to as the photoacoustic effect. Thus, PA is capable of visualizing vasculature (Fournelle et al. 2009; Laufer et al. 2012; Zhang et al. 2006) and tumor angiogenesis (Ku et al. 2005) and has already made its way into pre-clinical studies of breast cancer diagnosis (Kruger et al. 2013; Piras et al. 2009). Existing tomographic photoacoustic detection configurations are based on single elements (Sun et al. 2009) and curved (Brecht et al. 2009; Gamelin et al. 2008; Oraevsky and Karabutov 2000; Yang et al. 2009) or planar (Geateau et al. 2013; Kruger et al. 2003; Kuzhushko et al. 2004; Yin et al. 2004) arrangements. Geometric detection approaches to tomography Because in vivo studies require control of animal parameters (e.g., motion, respiration), investigations should
Address correspondence to: Milan Oeri, Fraunhofer Institute for Biomedical Engineering (IBMT), Ensheimer Strasse 48, 66386 St. Ingbert, Germany. E-mail: [email protected] 1
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be as short as possible. Transducer arrays are, thus, more likely to be applied to tomography as parallel detection reduces acquisition times. Although tomographic and concave detection geometries address the radial propagation nature of acoustic waves, they remain custom-made and cost-intensive systems. Linear transducer arrays are commercially available and hence attractive for US and PA imaging. Medical linear ultrasound transducers were introduced for thermoacoustic tomography by Kruger et al. in 2003. A linear ultrasound transducer has been found to be suitable for a whole-body photoacoustic tomography system for small animal imaging (Geateau et al. 2013). For tomographic imaging, the localization of transducer elements and the orientation of transducer arrays with respect to the center of the system are crucial. To date, several calibration methods or phantoms, such as wedge-pattern phantoms and wires (Abeyskera and Rohling 2011; Fenster and Downey 2000), acoustical trackers based on constrainment of emitter and receiver (Meyer and Biocca 1992) by coincident alignment and free-hand tracking methods based on optical or electromagnetic technologies (Arbel et al. 2004; West and Maurer 2004), have been used to align or calibrate acoustic detectors, for example, for 3-D freehand imaging (Mercier et al. 2005). However, these techniques can be cost intensive and lack the ability to determine the exact radial transducer array position and in-plane tilt (x/y-plane) in a tomographic setup, that is, with rotating probes or samples. Other calibrations are based on pointlike phantoms and a manual, iterative adjustment of the transducer position. The position is varied until a certain criterion, for example, maximum amplitude,
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is passed (Brecht et al. 2009; Geateau et al. 2013). However, imprecise knowledge of the transducer positions, and especially of the tilt, yields inaccurate time-of-flight (TOF) assumptions, preventing an adequate phase-adjusted summation of signals during the reconstruction that degrades the image. Analytical calibration algorithm I (2-D) In a previous study (Oeri et al. 2015), we described the impact of transducer alignment on the image quality achieved and illustrated a calibration algorithm for ultrasound and photoacoustic tomography accurately delivering the actual radius r and transducer array tilt d. The method is based on a system of linear equations (SLE) in which photoacoustic measurements from several angular positions are supplied as input (Fig 1, left). Owing to the misalignment of the transducer, the tomographic reconstruction of a small target yields an image artifact, where the signal information is distributed on a circular shape. Figure 1 (right) illustrates the obtained circular image artifact for a simulated transducer misalignment of 2 , an error in the radial distance of 1.5 mm and 18 angular positions (20 increments). A detailed description of the artifact, its derivation thereby and its impact on image quality is given by Oeri et al. (2015). The angular transducer position can be described by the combination of a rotation and translation matrix (R and T), in which the radial distance r and tilt d cannot be measured precisely and thus remain unknowns (cf. Fig. 1). On that basis, we set up an overdetermined SLE of the form Axzb with respect to i different angular measurement positions to extract the tilt and radial distance:
Fig. 1. Misalignment of transducer and image artifact. The transducer misalignment can be expressed by rotation and translation matrices (left), where a radial deviation and transducer tilt are present (left). Uncorrected transducer misalignment yields the circular distribution of signals fractions (right) that is used to derive the transducer tilt and actual radial distance.
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C1 1F1 4 « Ci 1Fi
E1 1H1 « Ei 1Hi
3 2 3 21 tan d 5 « 5$4 r=cos d 21 ðxtomo 1ytomo Þ=cos d 3 2 2ðD1 1G1 Þ 5 « (1) z4 2ðDi 1Gi Þ
The coefficients were simplified as follows: C 5 2xi cos q1yi sin q D 5 2xi sin q2yi cos q E 5 r cos q
F 5 2xi sin q2yi cos q G 5 xi cos q2yi sin q (2) H 5 r sin q
Practically, we obtained (1) by acquiring PA images of a point-like target from different angular positions, as illustrated in the flowchart in Figure 2 (step 1). In this approach, (xi,yi) are the coordinates of the peak value in the reconstructed image in the local system S1 (steps 2 and 3). Once the actual transducer tilt and radial distance were obtained (step 4), the reconstruction could be adapted to the actual measurement setup in terms of TOF correction (step 5). Owing to its mathematical nature, the proposed method objectifies system calibration. The latter was proven by repeating the calibration three times. The variations obtained for the two calibration parameters d and r were not significant (,1%). However, because the unique solution to the overdetermined system is given by
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the minimization in the sense of least squares, the accuracy increases with the number of measurements. We compared the deviation of the solution for three different increments (5 , 10 and 40 ). Within this range, the deviation of the radius and tilt was determined to be 0.8%. Here, we extend prior work to the imaging of small animals and apply the proposed calibration algorithm herewith generating stacked 2-D slices along the scanning axis. The performance of the calibration algorithms developed was evaluated both on a thin suture and on young mice ex vivo, illustrating their applicability to biomedical research and small animal imaging. Characterization of misalignments in a 3-D setup In the next step, we investigated transducer misalignments and resulting artifacts with a 90 -rotated orientation of the linear transducer array; that is, the lateral dimension of the transducer axis parallel to z (cf. Fig. 3). The modified arrangement was aimed at obtaining 3-D data and further reducing the acquisition duration. Because of the changed arrangement, solely one detection element contributed information (A-Scan) per angular position and plane. A new calibration algorithm that is suitable for this modified detection geometry was derived. The performance of the calibration was evaluated on a thin suture phantom. METHODS Experimental setup The experimental setup (cf. Fig. 4) comprised an illumination component, an acoustic array probe immersed in water and motorized rotation and translation stages including integrated encoders. Measurements were performed with a 5-MHz piezoelectric transducer providing a 6-dB bandwidth of 80% and a pitch of 300 mm (LA 5.0/128-633, Vermon, Tours, France). US images were acquired through plane wave imaging. Photoacoustic stimulation was provided by a Nd:YAG laser delivering short pulses (10 ns) at a repetition rate of 20 Hz and a wavelength of 1064 nm (H700, Quanta
Fig. 2. Flowchart calibration algorithm. Flowchart of the calibration algorithm for tomographic setups, based on linear ultrasound transducers and photoacoustics. SLE 5 system of linear equations.
Fig. 3. Three-dimensional tomography with linear arrays. Three-dimensional setup with modified view. The lateral transducer direction is oriented parallel to the z-axis.
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Systems, Solbiate Olono, Italy). Light was coupled into afiber whose ending is divided. Each ending had a 30-mm-wide aperture (Fig. 5). A slight tilt superimposed the light in the detection plane, over a distance of 15 mm, yielding a rectangular illumination pattern of 2 3 30 mm. The pulse energy was measured to be 40 mJ. The fluence delivered to the sample was approximately 67 mJ/cm2, well below the limitation for skin exposure of 100 mJ/ cm2 at 1064 nm in clinical settings according to the American National Standards Institute and Laser Institute of America. Different types of target objects were used to evaluate image quality. A thin, black suture (NYL02DS, Vetsuture, Paris, France) having a diameter of approximately 25 mm served as a point-like source in the detection plane. The suture was used as a calibration phantom prior to the biological measurement. A 3-D printed phantom holder was used to perform the calibration measurements (Fig. 4). The holder was made from opaque synthetic material (VeroWhite, Stratasys, Rheinmuenster, Germany) and was attached to the rotating shaft, which is part of a high-precision rotation stage (PI M-061 PD, Physik Instrumente, Karlsruhe, Germany). The latter provides an angular resolution of 0.001 and, thus, has no noticeable influence on the calibration. Two solid rods stabilize the holder and ensure the spanning of the suture. The holder
Fig. 4. Experimental setup. Experimental calibration setup with a linear ultrasound transducer and attached fiber bundles (1). The setup is immersed into a water tank. Rotation of the target object (2), which is clamped in a phantom holder (3), is achieved by a motorized rotation stage (4). A 3D-printed transducer and fiber bundle holder provides in-plane illumination.
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Fig. 5. Combined imaging. Experimental 2-D stack tomography for the combined photoacoustic and ultrasound (PA/US) investigation of young mice.
mounting on the tip of the shaft was designed such that samples could be easily exchanged without affecting the measurement setup. 2-D stack tomography In our first setup (Fig. 4), the transducer remained fixed, while the target object was rotated in 10 (calibration) and 20 (animal) steps. We assume the speed of sound in water to be constant at 1480 m/s, whereas for further investigations of biological tissue, we approximated the speed of sound as 1540 m/s. Because all methods relying on the TOF are highly sensitive to speed-of-sound variations, we performed the calibration with a target immersed in a water environment outside the sample. This configuration (Fig. 5) holds for small animal imaging; it minimizes artifacts caused by transducer rotation and reduces the system size that otherwise would be based on a transducer rotating arm. Because a 128-element transducer array is rotated instead of a single detector, the number of rotation steps can be reduced. However, the precision of the calibration method (Fig. 1) increases with the number of acquisition angles (overdetermined SLE), which is why we increase the rotation steps during the calibration process. Thus, a thin suture is rotated by 10 (36 steps) and data are reconstructed in the local field-of-view (FOV) in front of the array. The actual lateral transducer tilt d with respect to the center of rotation and the radial distance r were determined using the aforementioned method. After calibration, the suture was removed for the animal holder to be placed. We investigated young mice ex vivo (1–2 days old) that were fixed prone and later rotated and elevated to obtain 2-D stack images. Subsequent of tomographic PA and US data were acquired with the latest generation of our 128-channel beamforming research platform
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DiPhAS (Digital Phased Array System, Fraunhofer IBMT, St. Ingbert, Germany). Data were sampled at 40 MHz and bandpass filtered with a 4-MHz bandwidth with respect to the center frequency of the ultrasound transducer of 5 MHz. No further signal averaging was performed to reduce the acquisition time. Scan strategy The scan strategy was based on a motor-driven 20 stepwise rotation of the animal holder and parallel data acquisition yielding a set of 18 measurements and fullaperture tomographic data. Once data for one plane were stored, the motorized translation stage (PI M-061, Physik Instrumente, Karlsruhe, Germany) moved the probe in an elevational direction with a step size of 1 mm. All in all, we obtained data to form a stack of 30 images in ultrasound and 20 images in photoacoustic mode. Reconstruction algorithm A delay-and-sum reconstruction (DAS) was applied to form both tomographic photoacoustic and ultrasound images in a circular compounding mode. The algorithm is based on the computation of TOFs ti between a defined grid element (pixel) and the corresponding detector element, that is, solely the backward direction (pixel-toreceiver) in photoacoustic mode, for i 5 1,.,n angular detection positions according to the equation f ðx; yÞ 5
n X
pi ðt i ðx; yÞÞ
(3)
i51
Herein, f(x,y) denotes the reconstructed value of one pixel in the field of view. Pressure values p of the raw data obtained were summed with respect to the TOFs. Ultrasound images were likewise derived, but with ti denoting the entire duration of both the forward (emitter-to-FOV) and backward directions. Characterization of artifacts in 3-D tomography In the second setup (cf. Fig. 3), we modified the transducer view; that is, we oriented the lateral direction of the array vertically (parallel to the rotation axis). The constant diameter of the investigated suture enabled comparison of cross-sectional images obtained in the 2-D and 3-D setups. We considered the limited elevational aperture of the transducer array and applied an angular increment of 2 . With respect to its comparably large operating distance, the transducer covered a sufficient area and resulted in a well-sampled field of view. In return, no vertical movement of the probe was necessary, because the lateral transducer aperture enabled whole-body animal imaging. In addition to prior work, in which we studied the impact of transducer misalignments in two dimensions, artifacts arising as a result of misalignments in
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the modified setup were modeled (array orientation deviation from parallel alignment, radial uncertainty). We therefore simulated the (erroneous) reconstruction of a small absorber with the transducer having certain misalignments in three dimensions. Figure 6 (top) depicts the transducer orientation in the 3-D tomographic setup. The red lines indicate the angular position of the linear transducer during tomographic measurements. The dashed line represents the axis of rotation. In contrast to an ideal alignment, in experimental setups the transducer is inevitably slightly misaligned, and the assumed radial distance is inaccurate. We illustrated the impact of TOF correction by the artifacts resulting from two misalignments: radial displacement (Fig. 6, top left) and transducer tilt (Fig. 6, top right). The misalignments are indicated by arrows. The first case yields the circularly shaped artifact (blue circles) in place of the point source (black dot). The artifact is comparable to that of the 2-D stack-tomography (Fig 1, right). Furthermore, misalignment in orientation (tilt) yields an artifact for out-ofcenter point-like sources (Fig. 6, right). The erroneously reconstructed pattern (blue circles) varies significantly from the true point source location (black dot) affecting the volumetric image quality. Thus, we focus on the derivation of the actual radial distance of the transducer array throughout z to enable 3-D imaging. Analytical calibration algorithm II (3-D) To derive the actual radial distance of the transducer array with respect to the rotation axis (dashed line, Fig. 6), we rotated a spanned 150-mm-thin suture by 360 and detect PA signal peaks for each rotation step. Figure 7 illustrates experimentally measured distances (blue) according to the determined PA source peaks in each A-Scan. Artifacts arising at certain angles are due to the phantom holder rods and were removed prior to the calibration. Generally, the determined distance Biz varies in the vertical direction z 5 1, ., 128 (transducer elements) if a lateral transducer tilt is present (Fig. 6, top right) and with the angular position i 5 1,.,n. In a first step, we simplified the 3-D Biz to a 2-D value bi by taking only data from the central array element into account. Furthermore, we expressed the measured distance b between the PA source s and the detection element at angle i as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 bi 5 ðxi 2xs Þ 1ðyi 2ys Þ (4) The definition of the detector position was brought into polar coordinates with respect to the angle of rotation ai and in dependence on the actual radial distance r: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bi 5 ðr cos ai 2xs Þ2 1ðr sin ai 2ys Þ2 (5)
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Fig. 6. Transducer alignments. Simulated transducer alignments (red lines) with respect to the center of rotation (dashed line) in a 3-D setup. Misalignments are inevitably present (indicated by arrows), degrading image quality (here: radial deviation [top left] and tilt [top right]). The corresponding, artificially reconstructed point source formations (blue circles) are shown below in comparison to the result of an ideal alignment (black dots).
Fig. 7. Radius deviation. Experimentally obtained distances of a photoacoustic source to one transducer element (2 increment). Peak position of the envelope is determined to obtain distances to derive the radial distance in 3-D configurations. Few artifacts (marked in red) were produced by the phantom holder rods and were filtered prior to computation of the system of linear equations.
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An overdetermined SLE in the form Ax z b was derived based on several angular measurements i 5 1, ., n: 3 2 2 2 23 2 23 2 1 22 cos a1 22 sin a1 b1 xs 1ys 1r 5 $4 4« 5 z4 « 5 « « xs r 1 22 cos an 22 sin an b2n ys r (6) The solution to (6) gives the actual radial distance in one plane r64 (central transducer element 64) based on rotation of the investigated PA source. As pointed out later, we computed the remaining radial distances in plane z 5 1, ., 63, 65,.,128 based on r64 and the determined transducer tilt along z. Again, the solution to the overdetermined system is given by minimization. The accuracy increased with the number of measurements. We used a 3-D DAS algorithm to reconstruct photoacoustic and ultrasound data on the observed object based on the analytical calibration of the system. In contrast to the 2-D reconstruction in 2-D stack tomography, we addressed 3-D wave propagation and took signals of all elements on the cylindrical detection system into account to reconstructed one voxel. RESULTS Evaluation of algorithm I First, we present the results for the conventional 2-D stack imaging setup. We imaged a thin, optical absorber (suture) to derive the transducer tilt and radial distance to the rotation center. The measured data were reconstructed according to the actual transducer positions (tilt: 1.5 , radial distance: 31.34 mm).
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The reconstructed image that is exemplarily illustrated for one stack along the scanning plane in Figure 8 (left) serves as the control for the system calibration step. The isotropic spatial in-plane resolution was 160 mm. Figure 8 (right) illustrates the impact of the calibration on image resolution. During reconstruction, we applied a slight deviation of the radial transducer distance of 100 mm from the determined, value disregarding the present transducer tilt. The lack of calibration yields artifacts and degrades image quality. Combined PA/US imaging of small animals In the next step, we examined young mice (1–2 days old) with both photoacoustic and ultrasound tomography (PA/US) using prior system calibration. Exemplarily, Figure 9 depicts 5 of 30 stack images (ultrasound) that anatomically range from the thoracic part to the cranial part of the mouse. Such tissues as lung lobes, heart, supplying vessels and facial bone structure can be distinguished. We also compared images obtained with prior calibration to those obtained under a slight transducer radius deviation of 11.5 mm with respect to the center of rotation and from what is determined by applying the calibration algorithm (31.34 mm). The red, dashed arrow in Figure 9 (slice top left) points to incomplete structure boundaries compared with the same slice to the right (arrow 4). In addition to ultrasound, we performed photoacoustic tomography on the same mouse. The corresponding images are illustrated in Figure 10. The reconstructed anatomic views correlate with the US images, as expected. Moreover, PA represents information on their
Fig. 8. Reconstruction of point source. Left: Reconstructed, photoacoustic cross-sectional image of a thin suture (25 mm) as a result of the transducer calibration algorithm yielding a transducer tilt d 5 1.5 and the actual radial distance r 5 31.34 mm. Right: Reconstruction without prior calibration (i.e., 100-mm deviation from actual radial distance, no tilt), illustrating the impact of the linear array calibration.
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Fig. 9. Ultrasound stack images of mouse ex vivo. Calibrated, linear array-based ultrasound tomography of a 1- to 2-dayold mouse as cross-sectional images. The images reveal morphological information on the thoracic and cranial parts of the mouse investigated. Thorax: spinal cord (1), right and left lobes of lung (2), heart (3), sternum (4), right foreleg (5), left vena cava superior (6), aortic vessels (7), left subclavian vein (8). Head: cranium (9), right ear (10), facial cheekbone (11), mouse (12), maxilla (13). Uncalibrated, the image suffers from artifacts as incomplete structure boundaries (cf. red arrow).
Fig. 10. Photoacoustic stack images of mouse ex vivo. Calibrated photoacoustic tomography of a 1- to 2-day-old mouse as axial cross-sectional images. The images reveal additional information on the absorption of light at wavelength 1064 nm.
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Fig. 11. Combined photoacoustic/ultrasound images of mouse ex vivo. Calibrated, combined photoacoustic (colored) and ultrasound tomography of a 1- to 2-day-old mouse. The images correlate optical absorption and acoustic information on the thoracic region ex vivo. The photoacoustic data correlate well with the ultrasound images.
optical absorption in each plane. Although the US images revealed tissue surfaces, bone structures and large structures, the PA images obtained visualized lightabsorbing structures. We also fused US and PA images, combining acoustic and optical information in a single frame. Figure 11 depicts the combined images in the lung (left) and upper thorax (right). Photoacoustic signals according to their intensity composition in the color map on the right side were blended over the ultrasound images. 3-D imaging: evaluation of calibration approach II In a second setup, we modified the transducer view (i.e., 90 rotation) and derived the actual transducer array
position using a newly developed method. We first imaged a 150-mm-thin suture and derived the actual radial distance of the detecting elements with respect to the rotation center by applying the calibration algorithm proposed in eqn (1). The actual radial distance of the center element (No. 64) to the rotation axis could be determined precisely as illustrated by the reconstructed control in Figure 12 (right). Imaging of the eccentrically arranged thin suture from one angle and the entire linear detector array and the determination of the distances dependent on z (lateral transducer direction) enabled us to determine the tilt dz as 0.05 (Fig. 13). With respect to the determined radial distance of the center detector element, we were able to derive the radial distances dependent on z.
Fig. 12. Three-dimensional image of suture and 2-D slice serving as control. Tomographic, photoacoustic 3-D image of a 150-mm suture (left) serving as a control of the calibration method prior to animal studies. An in-plane resolution of 250 mm is determined from a cross-sectional view (right) in front of transducer element 64.
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Fig. 13. Transducer orientation in z. Distance from detector array aligned parallel to z. The slope gives the transducer tilt angle dz with respect to the rotation axis. Together with the computed radial distance, the transducer position is adapted to the actual measurement setup, herewith preventing the reconstructed image from degradation.
The system calibration parameters obtained were used during 3-D DAS reconstruction. We evaluated the performance of the modified calibration for 3-D tomography of the 150-mm suture. The reconstructed 3-D PA image (Fig. 12) of the suture proved the suitability of the method for calibration of the modified transducer arrangement and the ability to perform 3-D imaging based on a linear array. A cross-sectional image illustrates a spatial in-plane resolution in the range of 250 mm. DISCUSSION A newly developed calibration algorithm tailored to the application of linear transducer arrays to PA/US tomography in a 2-D stack imaging setup was applied to mice ex vivo and proved its feasibility for enhancing image quality, providing a spatial resolution of 160 mm. The results obtained prove that the calibration algorithm enables accurate determination of the position of transducer array elements in a tomographic PA/US setup. The images of the mice relate acoustic information of tissue surfaces, bone structures and larger blood vessels to their spectral absorbing characteristics at 1064 nm. This calibration approach is rather valid for slight misalignments with respect to the transducer orientation (,10 tilt), as strong tilts would obviously first require a mechanical correction. The linear transducer arrays applied decrease the required number of rotation steps compared with the rotation of single detector elements and thus yield shorter acquisition times. A new calibration algorithm adapted to a 3-D setup based on linear arrays was derived, yielding the actual radial transducer distance to the center of rotation, and it detected possible transducer misalignments in the lateral direction. A 3-D delay-and-sum
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reconstruction addressed the spherical nature of acoustic waves. We reconstructed 3-D data from a thin suture, yielding a resolution of 200 mm, and thereby illustrated the calibration method in the 3-D setting. However, in our setup, the shape of the reconstructed point-like source is less isotropic than in the 2-D stack imaging setup. This is not due to the algorithm itself, but rather to the influence of the supporting rods (Fig. 4, shadowing effect). The illumination here is parallel to the z-axis (Fig. 3). Thus, the comparably thin in-plane illumination pattern is impeding sufficient illumination at some angular positions. In contrast, in the 2-D setup, sufficient light is delivered to the sample and a wide aperture accepts acoustic signals. In the 3-D setup, this could be overcome by delivering light from several angles. Although single element detection and 2-D stack tomography with linear arrays take tens of minutes, a complete 3-D scan can be performed, in principle, in 3–5 min based on a 128-channel acquisition platform. In both methods, as found through our simulations and experimental results, prior calibration is crucial. We presented two approaches to both detection geometries providing an increased TOF accuracy during the reconstruction of PA/US images based on linear transducers in a 2-D or 3-D arrangement. Possible application fields include tomography of small animals and human extremities such as digital joints. Although we only investigated the calibration together with delay-and-sum beamforming reconstruction, it could as well be used for model-based inversion reconstructions (MBIR) relying on optimization algorithms to iteratively reconstruct an image corresponding to the spatial distribution of investigated physical parameters (absorption of optical energy in the OA setting). In that way, first estimates based on artificial data can be iteratively updated by including a TOF model yielding stepwise improvement of the reconstructed image. CONCLUSIONS We described and evaluated analytical calibration algorithms tailored to 2-D/3-D tomography based on a 128-element linear ultrasound transducer. The applied calibrations are intended to determine misalignments such as transducer tilt and radial uncertainty of the transducer array with respect to its center of rotation. The proposed calibration methods are applicable to ultrasound and photoacoustic tomography (PA/US). We evaluated performance on a thin suture and young mice ex vivo. Moreover, we compared the calibrated imaging system with an uncalibrated system and thereby proved the calibration can shield PA/US tomography from image artifacts caused by time-of-flight misinterpretations. Thus, by applying the proposed calibration methods as
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an alternative to hitherto applied mechanical positioning or time-consuming iterative approaches, we obtained an image resolution of 160–200 mm depending on the applied setup, that is, 2-D stack imaging versus 3-D tomography. Acknowledgments—The authors acknowledge funding by the European Union under the FP7 Project IACOBUS (Grant FP7-HEALTH 305760).
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