Concentric-ring arrays for forward-viewing ultrasound imaging

Abstract.

Purpose

Current ultrasound (US)-image-guided needle insertions often require an expertized technique for clinicians because the performance of tasks in a three-dimensional space using two-dimensional images requires operators to cognitively maintain the spatial relationships between the US probe, the needle, and the lesion. This work presents forward-viewing US imaging with a ring array configuration to enable needle interventions without requiring the registration between tools and targets.

Approach

The center-open ring array configuration allows the needle to be inserted from the center of the visualized US image, providing simple and intuitive guidance. To establish the feasibility of the ring array configuration, the design parameters causing the image quality, including the radius of the center hole and the number of ring layers and transducer elements, were investigated.

Results

Experimental results showed successful visualization, even with a hole in the transducer elements, and the target visibility was improved by increasing the number of ring layers and the number of transducer elements in each ring layer. Reducing the hole radius improved the region’s image quality at a shallow depth.

Conclusions

Forward-viewing US imaging with a ring array configuration has the potential to be a viable alternative to conventional US image-guided needle insertion methods.

1. Introduction

Percutaneous needle insertion under medical image guidance [e.g., computed tomography, magnetic resonance imaging, ultrasound (US) imaging] has been increasingly used for cancer diagnoses and treatments, such as biopsies and focal ablations, nerve blocks, drainages, and drug deliveries. Among the various interventions, US image-guided needle insertion offers the advantages of real-time imaging, low cost, safety, and portability, and it is commonly utilized in those procedures. A major issue with US-guided needle insertion is efficient and accurate targeting, which is required in those procedures for safety and efficacy. For instance, liver ablations require high targeting accuracy to ensure the safety margin of the ablation and to obtain efficacious treatment results.^1–3 Furthermore, shortening the procedure time can ultimately decrease the overall cost of the procedure and potentially allow clinicians, technologists, and nurses to increase their overall productivity by performing more procedures per unit of time.⁴ As a specific cause of the loss of accuracy and efficiency with current US-guided techniques, the performance of three-dimensional (3D) tasks using two-dimensional (2D) images requires clinicians to cognitively maintain the spatial relationships between the US probe, the needle, and the lesion as well as manage hand-eye coordination, which is very operator dependent.^5,6 In cases in which targets are located under sensitive anatomical obstructs, such as a complex vascular network, needle placement must often be performed out of the plane of the target. When this occurs, the lesion and the entire needle do not appear on the screen together, and the operator must guide the needle in multiple planes without visualizing the entire device. This may require multiple corrections of the needle trajectory, leading to an increased risk of complications, such as bleeding and increased procedure time.

A reliable approach to acquiring such sophisticated skills is practicing in a specialized training protocol, such as utilizing a tissue-mimicked phantom or simulation system.^7–9 Although the learning curve for acquiring the skills is effectively improved through specialized training, clinicians still need to spend a certain amount of time due to the awkward procedure. There are numerous products for assisting US-guided needle insertion accurately and intuitively to tackle the issue. A US needle guide is widely used in clinical procedures and enables locating the needle from the probe side stably at a certain angle through a guide slot attached to the probe. However, because the needle is physically fixed to the probe at a certain angle, the reachable area of the needle is limited, and subsequently, the flexibility of manipulation for clinicians is degraded. When comparing needle insertion with the needle guide and the free-hand technique, there was no significant difference in terms of improving targeting and procedure time.¹⁰ As for computer-assisted approaches, tracking systems, such as electromagnetic tracking and image-based tracking algorithms, can be implemented to register a US image and needle, allowing for the virtual display of the needle path on the US image.^11–15 Although this approach can visually aid the navigation of the needle trajectory, special training is required for clinicians to become familiar with the tracking system, often with the use of special needles. Additionally, navigation accuracy depends on the reliability of the registration and the tracking algorithm, limiting the applicable workspace and tools’ materials, which may disrupt the current workflow. In another approach, US-guided needle insertion robot systems aimed at an autonomous procedure was developed.^16–21 Although robotic systems can perform accurate needle placements without relying on the clinician’s skill, many of them require tracking systems and image processing algorithms for the accurate alignment of the needle and US images, which increases the system complexity, bloat, and cost, leaving additional technical challenges unresolved. Thus, there is an unmet need for a simple and intuitive imaging system that allows for flexible needle intervention without any registration process.

We hypothesize that synchronizing the intended needle trajectory with the direction of the visualizing US image can provide simple and intuitive guidance. As mentioned above, the clinician needs to perform 3D tasks using 2D images while maintaining the spatial relationships between the US probe, the needle, and the lesion through the tools’ manipulations with both of their hands as well as managing hand-eye coordination, which creates a crucial cognitive load. Given that both needle manipulation and US imaging can be performed with one platform, the cognitive load can be improved. We assume that the needle should be inserted from the center of the US image, although conventional US probes, such as linear-array transducers, do not have a space to allow for inserting the needle physically. Therefore, we developed a ring-arrayed forward-viewing (RAF) US imaging system.^22,23 This system comprises concentric-ring arrayed transducer elements and a needle manipulation holder, as shown in Fig. 1. This configuration allows clinicians to insert the needle into the center of the transducer. Additionally, arbitrary forward-views corresponding to the needle posture adjusted by clinicians can be visualized by measuring its rotational angle. A similar concept, circular ring arrays, was proposed for forward-looking catheter-based imaging used for intravascular US applications.^24,25 Our focus is on a larger and deeper-scale target, such as liver and kidney intervention guidance. More importantly, the required hole size for needle manipulation is significantly larger than that for the catheter. The forward-looking catheter-based imaging system has a $430\text{-}\mu \mathrm{m}$ center hole for a guidewire, whereas needle manipulation requires a few millimeters for those diagnoses and treatments. For instance, the size of a commercial needle probe for radiofrequency ablation ranges from 15 gauge ($\phi 1.8\mathrm{mm}$) to 22 gauge ($\phi 0.7\mathrm{mm}$). Given that the needle’s posture is adjusted manually inside the ring array during the operation, the hole needs some margin in addition to the clearance of the needle shaft diameter. Thus, this paper aims to investigate the feasibility of a concentric ring array with a large hole for needle intervention through simulations and experiments.

Fig. 1.

Conceptual illustration of the RAF-viewing US imaging system.

2. Methods

2.1. Ring Array Configuration

A ring array configuration can generate an arbitrary 2D plane because this configuration allows it to transmit and receive US beams in a 3D volume. For US-guided needle intervention, visualizing a 2D B-mode image matching the direction of the needle insertion may be intuitive guidance. However, this configuration may decrease the contrast and resolution and produce side lobes compared with a conventional linear array due to a lack of transmission and receiving US beams at the center of the ring. Therefore, it is necessary to compensate for the effect of the insufficient signal on image quality by optimizing the ring array configuration. In this study, we considered the following design parameters for the ring array configuration: (1) the hole radius $R_h$, (2) the outer radius of the whole ring array $R_o$, (3) the total number of transducer elements $E$, (4) the number of ring layers $N_e$, and (5) the number of transducer elements in each ring layer $M_e$, as shown in Fig. 2. Assuming that the transducer elements are equally spaced on the array plane, the position of each transducer element ${\mathit{e}}_{\mathit{i}}$ is defined in the polar coordinate system as follows:

$$\begin{gathered} {\mathit{e}}_{\mathit{i}}(r,\theta )=(R_h+n_e{d}_r,m_e{d}_{\theta }) \\ {n}_e=1\dots N_e \\ {m}_e=1\dots M_e \\ E=n_e{m}_e, \end{gathered}$$ (1)

where $d_r$ is the pitch distance of each transducer element along the radial direction, $d_{\theta }$ is the pitch angle of each transducer in each ring layer, and $n_e$ and $m_e$ are the layer number and transducer element number in the ring layer, respectively. $d_r$ and $d_{\theta }$ are defined as follows:

$$d_r=\frac{R_o-R_h}{N_e},$$ (2)

$$d_{\theta }=\frac{2\pi }{M_e}.$$ (3)

Fig. 2.

Design parameters of the ring-array configuration.

Through simulations and experimental studies, we evaluated the contrast and resolution of a reconstructed image by varying those design parameters using the proposed beamforming algorithms described below.

2.2. Beamforming

For intuitive US-guided intervention, we assumed that it was useful to visualize the coronal plane ($\mathrm{x}\mathrm{z}$ plane) and sagittal plane ($\mathrm{y}\mathrm{z}$ plane) along the direction of needle insertion, as shown in Fig. 3. The targeted plane is reconstructed from the received radio frequency (RF) data using delay-and-sum (DAS) beamforming.^26–29 The round-trip time of the wavefront from an element #$i$ of the ring-arrayed configuration ${\mathit{e}}_{\mathit{i}}=(e_{ix},e_{iy},e_{iz})$ to an intended reconstruction pixel at 3D coordinate $\mathit{P}=(p_x,p_y,p_z)$ is defined as follows:

$${\tau }_i(\mathit{P})=\frac{2\Vert \mathit{P}-{\mathit{e}}_{\mathit{i}}\Vert }{c},$$ (4)

where $c$ is the speed of sound in the medium and $\Vert ·\Vert$ means the Euclidean distance. Then, the DAS beamforming equation is described as follows:

$$y_{\mathrm{DAS}}(t)=\sum _{i=1}^E{x}_i(t+{\tau }_i(\mathit{P})),$$ (5)

where $y_{\mathrm{DAS}}(t)$ is the output of beamforming, $t$ is the time index, and $x_i(t)$ is the received row signal. To suppress the effects of side lobes due to the ring array configuration, we apply the apodization weight $w_i$ that allows for weighting the received signal corresponding to the distance on the $\mathrm{x}\mathrm{y}$ plane between the element and the pixel of interest. Then, the apodization weight $w_i$ is designed with a Gaussian window based on the Euclidean distance ratios between the element and reconstruction pixel position to the outer radius of the ring array as follows:

$$w_i=\exp \left(\frac{-(1-\frac{\sqrt{{(p_x-e_{ix})}^2+{(p_y-e_{iy})}^2}}{R_o})}{2{\sigma }^2}\right).$$ (6)

Fig. 3.

3D visualization of coronal ($\mathrm{x}\mathrm{z}$) and sagittal ($\mathrm{y}\mathrm{z}$) planes with ring-arrayed transducer elements.

In this paper, the $\sigma$ of the Gaussian window is experimentally set to eight. Note that $w=1$ when not applying the apodization weight. Then, the equation of beamforming with DAS while applying the apodization weight is described as follows:

$$y_{\mathrm{DAS}+\mathrm{APD}}(t)=\sum _{i=1}^E{w}_i{x}_i(t+{\tau }_i(\mathit{P}))=\sum _{i=1}^E\exp \left(\frac{-(1-\frac{\sqrt{(p_x-e_{ix}{)}^2+(p_y-e_{iy}{)}^2}}{R_o})}{2{\sigma }^2}\right)x_i(t+{\tau }_i(\mathit{P})).$$ (7)

The DAS-based algorithm was implemented as a baseline for the RAF US imaging, and some advanced beamforming algorithms could be incorporated into the proposed algorithm to compensate for the lack of received RF data due to the created hole. In this study, the coherence factor (CF) was utilized.³⁰ CF can be used combined with DAS, which contributes to side lobe level reduction and contrast enhancement, and it is represented as follows:

$$\mathrm{CF}(t)=\frac{{|{\sum }_{i=1}^E{x}_i(t+{\tau }_i(\mathit{P}))|}^2}{E{\sum }_{i=1}^E{|x_i(t+{\tau }_i(\mathit{P}))|}^2}.$$ (8)

The output of the combined DAS and CF with the combined DAS while applying the apodization weight and CF is given as follows:

$$\begin{gathered} y_{\mathrm{DAS}+\mathrm{CF}}(t)=\mathrm{CF}(t)y_{\mathrm{DAS}}(t)=\frac{{|{\sum }_{i=1}^E{x}_i(t+{\tau }_i(\mathit{P}))|}^2}{E{\sum }_{i=1}^E|x_i(t+{\tau }_i(\mathit{P})){|}^2}\sum _{i=1}^E{x}_i(t+{\tau }_i(\mathit{P}))y_{\mathrm{DAS}+\mathrm{APD}+\mathrm{CF}}(t) \\ =\mathrm{CF}(t)y_{\mathrm{DAS}+\mathrm{APD}}(t)=\frac{{|{\sum }_{i=1}^E{x}_i(t+{\tau }_i(\mathit{P}))|}^2}{E{\sum }_{i=1}^E{|x_i(t+{\tau }_i(\mathit{P}))|}^2}\sum _{i=1}^E{w}_i{x}_i(t+{\tau }_i(\mathit{P})), \end{gathered}$$ (9)

$$\text{where}{w}_i=\exp \left(\frac{-(1-\frac{\sqrt{(p_x-e_{ix}{)}^2+(p_y-e_{iy}{)}^2}}{R_o})}{2{\sigma }^2}\right).$$ (10)

With the proposed beamforming, the coronal plane ($\mathrm{x}\mathrm{z}$ plane) and sagittal plane ($\mathrm{y}\mathrm{z}$ plane) are reconstructed, as shown in Fig. 3.

2.3. System Architecture for Data Collection

For collecting the RF signals in the proposed ring array configuration, a 3D printer-based data collection platform was developed with a 3D printer (MP Mini Delta 3D Printer, Monoprice, USA), as shown in Fig. 4. The platform was built based on a delta configuration with a three-degree-of-freedom parallel structure and placed on a single element transducer with high motion precision in the 3D space.^22,28,31 Prebeamforming RF data were collected with the single-element transducer (element dimension: 0.25 in., focal depth: 0.5 in., center frequency: 6 MHz) and research US system (Vantage 128, Verasonics, USA). The US system control, data acquisition, signal processing, and 3D printer control were performed with MATLAB (MATLAB, Mathworks, USA). The controller of the 3D printer worked based on g-code commands. With this platform, we generated the scan trajectory of the single-element transducer along the concentric ring and collected the RF data during the scan. This virtually enabled the array’s single transmit/receive channels in the arbitrary ring configuration.

Fig. 4.

Experimental setup: (a) customized 3D printer for collecting RF data and (b) data acquisition and reconstruction way.

3. Simulations

3.1. Simulation Setup

Simulations were carried out in the field II simulator running on MATLAB.^32,33 Each single element arrayed on the concentric ring transmitted and received US beams in sequence. Beamforming was performed with the received signals in each single element. In the transmission, the transducers generated a Gaussian-windowed one-cycle sinusoidal burst at 6 MHz. The signal sampling frequency was 40 MHz. The speed of sound was assumed to be $1540\mathrm{m}/\mathrm{s}$ during the simulations. Envelope detection using the Hilbert transform was performed on all images, and the resulting lines were normalized and logarithmically compressed to form the final image. The utilized simulated phantom was composed of a spherical point target located at a depth of 60 mm, an anechoic cylinder with a diameter of 10 mm along the $\mathrm{y}$-axis located at a depth of 70 mm, and a hyperechoic cylinder mimicking a needle with a diameter of 1 mm along the $\mathrm{z}$-axis at the center of the $\mathrm{x}\mathrm{z}$ plane, as shown in Fig. 5. For evaluating the quality of beamforming with the point target, signal-to-noise ratio (SNR) was measured using the following equation:²⁹

$$\mathrm{SNR}=20{\log }_{10}\left\{\frac{|A_{\mathrm{Max}}|}{{\sigma }_{\text{noise}}}\right\},$$ (11)

where $A_{\mathrm{Max}}$ and ${\sigma }_{\text{noise}}$ are the peak signal amplitudes at each point target and the standard deviation of image amplitudes in an experimentally chosen noise region where the region was away from the effect of side lobes. Furthermore, the full width at half maximum (FWHM) was calculated to evaluate beamforming resolution with the point target. For evaluating the contrast of the anechoic target and needle, a contrast-to-noise ratio (CNR) was measured as follows:³⁴

$$\mathrm{CNR}=\frac{|{\mu }_{\mathrm{tar}}-{\mu }_{\mathrm{bck}}|}{\sqrt{{\sigma }_{\mathrm{tar}}^2-{\sigma }_{\mathrm{bck}}^2}},$$ (12)

where ${\mu }_{\mathrm{tar}}$ and ${\mu }_{\mathrm{bck}}$ represent the mean image intensities in a small region inside the target and the surrounding background, respectively, and ${\sigma }_{\mathrm{tar}}$ and ${\sigma }_{\mathrm{bck}}$ are the corresponding variances. Regarding the CNR of the anechoic cylinder, both cross-sections of the coronal plane ($\mathrm{x}\mathrm{z}$ plane) and sagittal plane ($\mathrm{y}\mathrm{z}$ plane) were evaluated.

Fig. 5.

Reconstructed images showing (a) coronal plane ($\mathrm{x}\mathrm{z}$-plane) and (b) sagittal plane ($\mathrm{y}\mathrm{z}$-plane), and lateral resolution under varying (c) the beamforming methods, (d) the hole radius $R_h$, (e) the number of ring layers $M_e$, and (f) the number of the elements in each ring layer $N_e$. Red, green, and blue dashed frames show the region of interest for the CNRs of coronal and sagittal cross-sections of anechoic cylinders and needle, respectively. The yellow dashed line marks the cross-section to assess the lateral resolution.

3.2. Effect of the Beamforming Method

First, we compared the DAS and DAS + CF beamforming algorithms with and without applying the proposed apodization weight. In this simulation, the configuration of the ring array was fixed with $R_h=2.5$, $M_e=32$, and $N_e=72$. A linear array transducer consisting of 128 elements (element width = 0.2 mm, height = 5 mm) with a pitch of 0.2 mm and a fixed focus at 10 mm was utilized for obtaining ground truth data.

Figure 6 shows the reconstruction images using varying beamforming methods, and the SNR, FWHM, and CNR in each of the conditions are listed in Table 2(a). The results show that combining DAS and CF with the apodization weight improved all SNRs, FWHMs, and CNRs compared with other beamforming methods. A combination of DAS and CF was able to suppress the side lobes and background noise in the ring array configuration. Moreover, applying the apodization weight improved the CNR of the anechoic target. This ring array configuration received the signals two dimensionally and reconstructed the slice image with those signals. The apodization weight was used to reduce the signal received by the transducer element located far from the intended pixel location in the elevational and lateral directions, which contributed to improving the contrast. Therefore, in the following sections, we use the combination as the beamforming method.

Fig. 6.

Reconstructed images under varying beamforming methods: (a) DAS, (b) DAS with applying the apodization weight, (c) combination of DAS and CF, (d) combination of DAS and CF with the apodization weight, and (e) linear array configuration.

Table 2.

Image metric varying (a) beamforming, (b) radius of hole, (c) number of ring layers, and (d) number of transducer elements in each ring layer in the simulation.

	Beamforming				Linear
	DAS	DAS + APD	DAS + CF	DAS + APD + CF
(a)
SNR dB	26.21	32.88	52.83	53.66	47.85
FWHM mm	1.19	1.08	0.98	0.88	0.73
CNR ($xz$-plane) dB	6.24	6.95	12.64	16.96	19.36
CNR ($yz$-plane) dB	9.32	14.38	18.93	24.46	26.29
CNR (needle) dB	7.69	7.98	16.39	17.26	10.36
(b)
	$R_h$
	10	7.5	5	2.5
SNR dB	49.69	50.55	51.33	53.66
FWHM mm	0.92	0.87	0.85	0.88
CNR ($xz$-plane) dB	14.08	14.34	15.11	14.96
CNR ($yz$-plane) dB	23.06	23.25	24.37	24.46
CNR (needle) dB	15.21	16.69	16.92	17.26
(c)
	$M_e$
	4	8	16	32
SNR dB	29.38	42.41	47.67	53.66
FWHM mm	2.92	1.97	1.11	0.92
CNR ($xz$-plane) dB	4.99	8.8	12.22	14.66
CNR ($yz$-plane) dB	17.99	19.65	19.91	23.25
CNR (needle) dB	7.99	12.53	14.45	16.26
(d)
	$N_e$
	18	36	72
SNR dB	53.66	54.01	55.24
FWHM mm	0.87	0.92	0.9
CNR ($xz$-plane) dB	14.74	14.23	14.66
CNR ($yz$-plane) dB	21.14	22.63	23.25
CNR (needle) dB	16.01	16.26	17.33

3.3. Effect of Design Parameters

The performance of the ring array with varying design parameters was evaluated with the simulated phantom. The utilized parameters for the ring array configuration are listed in Table 1. In this simulation, we evaluated the image metrics by changing one parameter from the inner radius $R_h$, the number of the ring layer $N_e$, and the number of the transducer element in each ring layer $M_e$ while fixing the other parameters.

Table 1.

Ring array configuration in simulation and experiment.

Parameters	Simulation/experiment
Transducer center frequency $f_0$	6 MHz
Transducer fractional bandwidth	0.6
Sampling frequency $f_s$	40 MHz/20 MHz
Height of element	5 mm/0.25 in.
Focusing depth	10 mm/0.5 in.
Number of lines in the reconstruction image	500
Pitch of each of the ring layers $d_r$	0.2 mm
Hole radius $R_h$	2.5, 5, 7.5, 10 mm/1.5, 3, 4.5, 6 mm
Number of layers $N_e$	4, 8, 16, 32
Number of elements in each layer $M_e$	18, 36, 72

The reconstructed images with the different inner radiuses $R_h$ are shown in Fig. 7. $N_e$ and $M_e$ were fixed at 32 and 72 in those images, respectively. Figure 8 represents the reconstructed images with varying the number of the ring layer $N_e$. $R_h$ and $M_e$ were fixed at 2.5 and 72 in those images, respectively. Figure 9 represents the reconstructed images with varying the number of the transducer element in each ring layer $M_e$. $R_h$ and $N_e$ were fixed at 2.5 and 32 in those images, respectively. The SNR, FWHM, and CNR in each of those conditions are listed in Table 2 (b)–(d). The performance of the beamformer across the point target is shown in Figs. 5(c)–5(f).

Fig. 7.

Reconstructed images showing (top) $\mathrm{x}\mathrm{z}$-plane and (bottom) $\mathrm{y}\mathrm{z}$-plane under varying the hole radius $R_h$ [(a) 10 mm, (b) 7.5 mm, (c) 5 mm, and (d) 2.5 mm]. $N_e$ and $M_e$ were fixed at 32 and 72, respectively.

Fig. 8.

Reconstructed images showing (top) $\mathrm{x}\mathrm{z}$-plane and (bottom) $\mathrm{y}\mathrm{z}$-plane under varying the number of the ring layers $M_h$ [(a) 4, (b) 8, (c) 16, and (d) 32]. $R_h$ and $M_e$ were fixed at 2.5 and 72, respectively.

Fig. 9.

Reconstructed images showing (top) $\mathrm{x}\mathrm{z}$-plane and (bottom) $\mathrm{y}\mathrm{z}$-plane under varying the number of the transducer elements in each ring layer $N_h$ [(a) 18, (b) 36, and (c) 72]. $R_h$ and $N_e$ were fixed at 2.5 and 32, respectively.

From the observation of the results, reducing the hole radius $R_h$ improved the SNR of the point target and CNR of the needle appearance, although the FWHM of the point target and CNR of the anechoic cylinder were not affected. Increasing the number of the ring layer $M_e$ was able to improve all metrics significantly. As shown in Fig. 8, the visibility of the boundary of the anechoic cylinder and needle was clearly improved. This was because the number of transducer elements above the reconstructed plane, which contributed significantly to the beamforming, was increased. Increasing the number of transducer elements in each ring layer $N_e$ improved the SNR and CNR of the needle appearance slightly, but other metrics were not affected. This may have been because the applied apodization weight almost reduced the out-of-plane signals received by the increased transducer elements. Comparing the CNR between the coronal and sagittal planes of the anechoic cylinder, the trends for different design parameters were almost the same. Therefore, the simulation results indicated that the number of the ring layer $M_e$ was the most critical factor for the reconstruction, and the hole radius $R_h$ should be small in terms of SNR and CNR.

4. Experiments

4.1. Experimental Setup

In this section, we evaluated the image contrast and resolution of the ring array configuration with different design parameters using a wire phantom and cyst-mimicked phantom. Using the customized 3D printer with the single-element transducer, prebeamforming RF data were collected. The single-element transducer was moved above the target in the $\mathrm{x}\mathrm{y}$ plane, and the RF data were collected by scanning the area from $-50$ to 50 mm along the $x$-axis and from –50 to 50 mm along the $y$-axis at a pitch of 0.1 mm. The reconstruction images were produced with the RF data received in the utilization elements corresponding to the intended pattern in Table 1, which were selectively extracted from all RF data collected. The combination of DAS and CF while applying the apodization weight was used as beamforming in all conditions. Regarding the wire phantom, three wires were located along the depth axis, beginning almost 40 mm from the transducer surface, as shown in Fig. 10(a). The distance of each wire was $\sim 15\mathrm{mm}$. The reconstruction plane was generated perpendicularly to the wires, so it provided the cross-section of the wire. Similar to the simulation evaluation, we quantified image quality by calculating the SNR and FWHM of the second wire when varying the array configuration. Skinless and seedless grapes were embedded in gelatin, which appeared to be hyperechoic sphere targets as cyst-simulating phantoms. The gelatin to embed the grapes was formed by dissolving gelatin powder (G-2500, Sigma Chemicals, USA) in water at a concentration of 15% by weight and adding silica (S-56 31, Sigma Chemicals, USA) at 2% by weight to generate the speckle texture. A seedless grape is often used as a tumor-like target in medical training phantoms.³⁵ The reconstruction plane was generated at the center of the grape, so it provided the cross-section of the grape, as shown in Fig. 10(b). We quantified the image quality by calculating the CNR with the cyst-mimicked phantom when varying the array configuration.

Fig. 10.

Reconstructed images showing (a) wire phantom and (b) cyst-mimic phantom, and lateral resolution under varying (c) the hole radius $R_h$, (d) the number of ring layers $M_e$, and € the number of the elements in each ring layer $N_e$. The red dashed frame shows the region of interest for the CNR of the cross-section of the cyst-mimic phantom. The yellow dashed line marks the cross-section to assess the lateral resolution.

4.2. Results

The reconstructed images with the different inner radiuses $R_h$ are shown in Fig. 11. $N_e$ and $M_e$ were fixed at 32 and 72 in those images, respectively. Figure 12 represents the reconstructed images with varying the number of the ring layer $N_e$. $R_h$ and $M_e$ were fixed at 1.5 and 36 in those images, respectively. Figure 13 represents the reconstructed images with varying the number of the transducer element in each ring layer $M_e$. $R_h$ and $N_e$ were fixed at 1.5 and 32 in those images, respectively. The SNR, FWHM, and CNR in each of those conditions are listed in Table 3. The performance of the beamformer across the middle wire is shown in Figs. 10(c)–10(e).

Fig. 11.

Reconstructed images showing (top) wire phantom and (low) cyst phantom under varying the hole radius $R_h$ [(a) 6 mm, (b) 4.5 mm, (c) 3 mm, and (d) 1.5 mm].

Fig. 12.

Reconstructed images showing (top) wire phantom and (low) cyst phantom under varying the number of the ring layers $M_h$ [(a) 4, (b) 8, (c) 16, and (d) 32].

Fig. 13.

Reconstructed images showing (top) wire phantom and (low) cyst phantom under varying the number of the transducer elements in each ring layer $N_h$ [(a) 18, (b) 36, and (c) 72].

Table 3.

Image metric varying (a) radius of hole, (b) number of ring layers, and (c) number of transducer elements in each ring layer in the experiment.

	$R_h$
	6	4.5	3	1.5
(a)
SNR dB	45.16	48.68	51.01	55.15
FWHM mm	1.32	0.88	0.8	0.76
CNR dB	6.58	8.14	10.91	11.85
(b)
	$M_e$
	4	8	16	32
SNR dB	53.37	54.69	54.87	55.15
FWHM mm	1.47	1.5	0.83	0.76
CNR dB	10.53	11.73	11.89	11.85
(c)
	$N_e$
	18	36	72
SNR dB	54.04	54.10	55.15
FWHM mm	0.82	0.73	0.76
CNR dB	9.44	10.95	11.85

Focusing on Fig. 11, the result of a large hole radius did not visualize the wire at a shallow depth, but decreasing the hole radius enabled all of the wire phantom to be shown and focused well, and it improved the SNR, FWHM, and CNR. By increasing the number of ring layers, both the wire and cyst phantoms were focused, and then FWHM was improved. By increasing the number of transducer elements in each ring layer, all image metrics were slightly improved.

5. Discussion

5.1. Design Parameters

The results showed the feasibility of RAF imaging for visualizing a target located at a deep location through simulations and experimental studies. The design parameters directly influencing the image quality through the simulations and experiments were the hole radius $R_h$ and the number of ring layers $M_h$. The large hole degraded the shallow depth region of the reconstruction image. Because the US beam transmitted from each element had directivity, the intensity of the signals in the shallow depth region may have been weakened compared with the deep region. Furthermore, the number of ring layers was related to the number of transducer elements above the reconstruction plane, which could simply increase the produced scan lines along the reconstruction plane. Although the number of elements in each ring layer $N_h$ was not the critical factor in terms of the visualization of the coronal and sagittal planes, the parameter will affect image quality when reconstructing the plane with arbitrary slice angles between the coronal and sagittal planes because there are regions of coarseness and fineness of the elements above the reconstruction plane depending on the selected slice angle. Given that $N_h$ was set at 72 in this study, it is possible to reconstruct images of equal quality at 5 deg intervals in the slice angle, but how the image quality deteriorates when selecting a slicing angle with a resolution $<5\mathrm{deg}$ is questionable.

Although increasing the number of transducer elements enabled the side lobe effect to be lower and tended to improve the image metrics, the drawbacks of increasing the number of transducer elements are a high computational cost for reconstruction and an expensive fabrication cost. The maximum number of transducer elements used in this study was 2304. The number was reasonable for 2D matrix array probes because the number of this element ranges from the thousands to the ten-thousands. A high-end 2D matrix array probe (XL14-3, Philips, Netherlands) has 56,000 elements.

In cases in which the number of applicable transducer elements is limited to a few hundred, it is necessary to consider how the applicable elements are assigned to the number of the ring layer $M_h$ and the number of the transducer element in each ring layer $N_h$. Although increasing $M_h$ effectively improved image quality compared with $N_h$ in the simulation results because the number of elements that received the in-plane signals was increased, $N_h$ to be allocated must be reduced in the case that $M_h$ is increased with limited applicable elements. Reducing $N_h$ creates a blank space between each transducer element along the radial direction in which there is no transducer element to receive the signal, which may lead to degrading image quality when the reconstruction plane is rotated within the blank space. Thus, it is necessary to investigate balanced $M_h$ and $N_h$ to further satisfy the required step angle of a reconstruction slice and the diagnosable image quality in a procedure utilizing this system. Alternative ways for improving the image quality with limited elements are to reduce the size of the hole as much as possible and to apply advanced beamforming techniques, such as effective aperture reconstruction, to suppress the artifact.³⁶

5.2. Beamforming

Applying the apodization weight reduced the side lobe effect and significantly enhanced target visibility compared with the case without applying the apodization weight. This ring array configuration receives signals two dimensionally and reconstructs a slice image with those signals. When the apodization weight is not applied, out-of-plane signals for the reconstruction slice are included in the acquired dataset, and then the target may not be focused well. The proposed apodization weight is used to reduce the signal received by the transducer element located far from the pixel location to be reconstructed in the elevational and lateral directions, which can contribute to improving the image quality under the ring array configuration. However, combining the CF and apodization weight may be largely suppressed in the background. Although the simulation results showed that the CNR was improved by applying the CF and apodization weight, the speckles may have been removed too much so that the shape of the cyst was not fully visible in the experiment. Excessive speckle removal may not be desired in applications in which speckles may provide helpful features for diagnosis. Reference 27 also reported that the use of CF in combination with beamforming has some issues in terms of robustness against low-SNR cases. Thus, combining the CF and apodization weight would be a proper option for contrast-enhanced US imaging with some contrast agent, but for conventional US imaging to display anatomical structures in the B-mode image, we may need to consider applying other beamforming techniques, such as a synthetic aperture³⁷ or delay multiply and sum.³⁸

5.3. Limitations

There were several uncovered limitations in this study. Although we showed the feasibility of RAF US imaging through the simulations and experiments with the customized 3D printer, the actual implementation of the ring array configuration was not performed. The current setup can only carry out repeating transmitting/receiving of a signal with a single transducer element and moving the transducer element to another position inside the defined ring array configuration. Because synthetic aperture beamforming based on simultaneous transmission and receiving of multiple elements could not be applied due to the physical limitation of the current setup, the reconstructed image’s quality can be further improved if concentric ring array transducers enabling transmitting and receiving signals with multiple elements are developed. Although we chose the concentric ring array configuration to explore the feasibility of RAF US imaging for deep targets first, there may be several other configurations of the ring array, such as spiral arrays, vernier arrays, and optimized arrays calculated with an energy function.^39,40 Reference 40 also suggested exploiting different arrays in transmission and reception, but the US probe fabrication may become complex.

Another limitation was the lack of the needle’s appearance in the RAF US image in the phantom study due to the limitation of the current setup, although we inserted the needle through the hole in the simulation. In our previous work, we examined forward viewing along the direction of needle insertion with a mirror-integrated US scanner and found that the needle appearance at the center of the view may not affect reconstruction significantly;⁴¹ therefore, the effect is not expected to be significant in RAF US imaging. Furthermore, the proposed system was validated with a cyst-mimicked phantom; however, ex vivo and in vivo experiments were not performed in this paper. The next step in developing a clinically deployable needle guidance device is to validate the observation of needle trajectories in biomaterial targets with RAF US imaging. Additionally, as mentioned in the introduction, the reconstructed slice will be changed in real time corresponding to the needle posture manually adjusted by the clinician in the final system. The current setup cannot perform real-time imaging because the reconstruction is performed by moving one transducer element along with concentric ring layers. Selectively limiting the received signals used for reconstruction may reduce the computational load. As discussed above, the signals received from the transducer elements located far from the reconstruction slice may cause degrading of the image contrast. Thus, the computational time can be reduced while maintaining image quality by calculating the beamforming only with the transducer elements near the reconstruction slice. Additionally, a plane wave can be applied to improve the frame rate of the RAF imaging if concentric ring array transducers are developed. We are also supposed to implement the algorithm on an FPGA device or parallel computing with GPU for real-time computations. We assume that the targeted frame rate for RAF imaging in the final system should be over 10 Hz, equivalent to the frame rate of 3D US imaging.⁴²

6. Conclusion

We presented an RAF US imaging system that enables synchronizing an intended needle trajectory with the direction of a visualized US image without any registration process and provides simple and intuitive guidance for needle interventions. This paper focused on the feasibility of RAF US imaging by demonstrating a simulation and phantom study. We investigated the design parameters of the ring array configuration, including the radius of the center hole, the number of ring layers, and the number of transducer elements in each ring layer, in terms of reconstruction image quality. Additionally, we implemented the CF and apodization weight to DAS beamforming to produce low side-lobe and poor resolution due to the ring array configuration. Our preliminary results demonstrated that the proposed RAF US imaging enables successful visualization even with the hole at the center of the transducer through simulations and experiments. In terms of the evaluated image metrics, the number of ring layers $M_h$ and the number of elements in each ring layer $N_h$ should be 32 and 72, respectively. The total number of elements is 2304, which is reasonable for a 2D matrix array probe. In addition, decreasing the hole radius $R_h$ improved the image quality of the region at a shallow depth. Although the reconstruction image with RAF US imaging still contained side lobes and had poor resolution compared with that with a conventional linear array transducer, the image quality can be enhanced by introducing additional beamforming, such as with a synthetic aperture.

Future work will address the implementation of the ring array configuration as an integrated platform and real-time visualization with an FPGA and parallel computing to translate the system from the proof-of-concept model to a clinical application model.

Biographies

Ryosuke Tsumura is a researcher in the Health and Medical Research Institute at the National Institute of Advanced Industrial Science and Technology (AIST) and an affiliated postdoctoral fellow in Department of Biomedical Engineering at the Worcester Polytechnic Institute, MA, USA. He received his BS, MS, and PhD degrees in mechanical engineering from Waseda University, Tokyo, Japan, in 2014, 2016, and 2019, respectively. His current research interests include robotic intervention and ultrasound imaging.

Shang Gao is a PhD student in the Department of Robotics Engineering in at Worcester Polytechnic Institute. He earned his MS degree from the same institution in robotics engineering in 2020, dual BEng degrees from Univ. of Detroit Mercy in robotics and mechatronics system engineering and Beijing Univ. of Chemical Technology in mechanical engineering, respectively in 2018. His current research interests include medical robotics, medical photoacoustic imaging, and robot teleoperation.

Yichuan Tang is a PhD student in the Department of Robotics Engineering in Worcester Polytechnic Institute, Worcester, MA, USA, since 2019. He received his BEng degree with honors in mechanical engineering from the University of Nottingham (China campus), Ningbo, 2016. He received his MS degree in robotics engineering from Johns Hopkins University in 2018. His research focuses on ultrasound and photoacoustic imaging instrumentation.

Haichong K. Zhang is an assistant professor in biomedical engineering and robotics engineering with an appointment in computer science at Worcester Polytechnic Institute (WPI). He is the director of the Medical Frontier Ultrasound Imaging and Robotic Instrumentation (Medical FUSION) Laboratory. He received his BS and MS degrees in human health sciences from Kyoto University, Japan, and subsequently earned his MS and PhD degrees in computer science from Johns Hopkins University.

Disclosures

No conflicts of interest, financial or otherwise, are declared by the authors.