Design and Simulation of a Ring-Shaped Linear Array for Microultrasound Capsule Endoscopy

Video capsule endoscopy (VCE) has significantly advanced visualization of the gastrointestinal tract since its introduction in the last 20 years. Work is now under way to combine VCE with microultrasound imaging. However, small maximum capsule dimensions, coupled with the electronics required to integrate ultrasound imaging capabilities, pose significant design challenges. This paper describes a simulation process for testing transducer geometries and imaging methodologies to achieve satisfactory imaging performance within the physical limitations of the capsule size and outlines many of the tradeoffs needed in the design of this new class of ultrasound capsule endoscopy (USCE) device. A hybrid MATLAB model is described, incorporating Krimholtz-Leedom-Matthaei circuit elements and digitizing and beamforming elements to render a gray-scale B-mode. This model is combined with a model of acoustic propagation to generate images of point scatterers. The models are used to demonstrate the performance of a USCE transducer configuration comprising a single, unfocused transmit ring of radius 5 mm separated into eight segments for electrical impedance control and a 512-element receive linear array, also formed into a ring. The MATLAB model includes an ultrasonic pulser circuit connected to a piezocrystal composite transmit transducer with a center frequency of 25 MHz. B-scan images are simulated for wire target phantoms, multilayered phantoms, and a gut wall model. To demonstrate the USCE system’s ability to image tissue, a digital phantom was created from single-element ultrasonic transducer scans of porcine small bowel ex vivo obtained at a frequency of 45 MHz.


I. INTRODUCTION
I. NDOSCOPIC visualization of the gastrointestinal (GI) tract has been practiced for over 200 years, with recent developments including fibre-optic light sources and high-definition cameras [1]. Video capsule endoscopy (VCE) was introduced into clinical practice in the past 20 years and has established itself particularly in diagnosis of small bowel disorders [2]. The small dimensions and minimallyinvasive nature of VCE make it safe, convenient for the patient, and able to image the remote, elongated and convoluted small bowel without the need for an insertion tube or tether.
II. Despite VCE's proven utility, it has a number of deficiencies that prevent it finding more use by gastroenterologists. A particularly important issue is that conventional optical imaging allows viewing only of the surface of the GI tract. Optical coherence tomography allows penetration beneath the tissue surface, but it is depth-limited and still at an early stage of development [3]. Fluorescence imaging is another optical technique that may expand the range of medical indications that can be addressed and it has also been proposed that imaging with microultrasound (µUS) could provide enhanced information on optically obscure diseases [4].
III. The topic considered in this paper is µUS imaging of the GI tract itself. Whilst endoscopic ultrasound (EUS) imaging is now common, clinical ultrasound capsule endoscopy (USCE) has not yet been implemented successfully [2]. There are two possibilities for USCE, one to replicate the use of EUS imaging beyond the GI tract and the other to image the wall of the GI tract. The second possibility complements VCE in diagnosis of GI tract disorders and is likely to be used in devices combining VCE and USCE to meet clinicians demands. For this application, it is important to be able to distinguish the multiple layers of tissue within the wall of the GI tract and to determine their characteristics [5]. Since the layers are relatively thin (1 -2 mm maximum), subsurface but still only superficial imaging is required. Although µUS signal attenuation with depth is often assumed to be prohibitive, the limited tissue penetration required makes capsule-based µUS imaging of the wall of the GI tract a viable technique [6].
Despite its potential, work to date on implementation of USCE has been limited e.g. [7]- [10]. However, the choice between mechanically-scanned (rotating) and array-based solutions has already arisen. Array-based systems now dominate use in diagnostic ultrasound, with mechanicallyscanned systems used only in niche applications. Mechanical scanning simplifies electronics and is therefore particularly attractive for USCE in its initial development [8], [9], [11]. USCE also has parallels with intravascular ultrasound (IVUS) in which side-looking circular transducer arrays generating radial images are now relatively common [12]- [15] and it is this configuration that is considered here and in previous work [16].
Because of the complexity of manufacturing the highly miniaturized arrays needed for µUS, detailed modelling is needed to study designs that offer the best possibility of viable images upon physical prototyping and it is this that is considered here. While finite element analysis (FEA) can well replicate the full physical characteristics of a transducer design, it suffers from long simulation times and high computational expense when applied to USCE because of the need for high array element counts and geometric features with microscopic length scales in mesoscale devices. Previous work has shown good agreement between simpler, one-dimensional (1D) models [17] such as KLM and prototype devices [18]- [20], allowing a much larger design space to be explored in a reasonable time and it is this approach we describe here.
In Section II, the development of a specification for an array-based USCE system is described. The ultrasound system model is detailed in Section III then two sections describe system design, Section IV relating to the array design and Section V to the digital beamformer. Section VI presents the results of the full system simulation and Section VII includes discussion and conclusions.

II. USCE IMAGING SYSTEM CONTEXT
As well as ultrasound, the proposed USCE device is designed to incorporate a suite of complementary sensors with diagnostic capabilities to enhance its potential use in clinical practice. The resulting complexity requires careful system-level design to allow all subsystems to operate without mutual interference. Fig. 1 shows key components of the capsule concept. For tissue assessment and disease diagnosis, both optical and microultrasound imaging systems are included, as optical systems represent the current clinical standard to be enhanced by the addition of ultrasound. A localization system is needed to record the position in the GI tract of diseased tissue identified by the imaging systems so that it can be located later for monitoring or treatment. Communications systems are required on both the capsule and the base unit to coordinate the image and localization data as well as power systems to monitor and control power usage. Finally, a user interface and image display software will need to be tailored to present the data in a clinically appropriate manner.
The clinical requirements for the capsule impose restrictions on its total size. For both wireless and tethered capsules, the limiting parameter is the need for the patient to swallow the capsule. While there is an absence of literature on patient preferences during swallowing, the system proposed here is designed with an outer diameter (o.d.) of 10 mm and a length of 30 mm, matching the largest available conventional pharmaceutical pills and within the envelope established by VCE [21]. Because of the limited space for electronics in such a small volume, an application-specific integrated circuit (ASIC) is needed to handle the analog data preprocessing along with master data flow control and data transmission and reception capabilities. This must be matched with complementary hardware on the main display platform. Here, only the ultrasound components are considered in detail but it is important to recognize that they cannot be used in isolation.
The physical dimensions of the capsule also affect the choice of ultrasonic array configuration. Previous work on USCE investigated the use of a rotating single-element transducer [7] [8], and this approach remains under investigation. However, as noted earlier, an array-based approach is reported here as it is expected to provide increased reliability and higher image quality through capabilities such as variable focal depth. For USCE, it is assumed that the array will be constructed to match the outside surface of the capsule geometrically. For the current system design, a side-looking circumferential array is proposed since this can provide complete coverage into the thickness of the wall of the gut without requiring rotation during natural passage of the capsule.
As the proposed capsule is significantly more complex than those currently in use, a corresponding increase in power consumption is expected. Current clinical capsules are designed with a 20 mW power budget based on battery supply limits [2]. To expand this power limit, work is under way on wireless power delivery. However, this leads to concerns about thermal behaviour. To address these, trial capsules were designed and manufactured to determine a viable power budget [22]. These capsules used a set of external thermistors and internal temperature sensors to determine the heating caused by various currents flowing through a power resistor. Based on the results of in vivo porcine trials, a maximum power budget of 100 mW was established for the proposed design. Numerous techniques to reduce the power consumed below this level are possible, including reduced image frame rate during periods when the capsule is moving only slowly.

III. ULTRASONIC SYSTEM MODELLING
Since USCE involves highly complex prototype fabrication, it is necessary to explore possible designs with full ultrasound system simulation. Crucially, this allows assessment of imaging resolution, particularly at small f-numbers. A simulation program was desired which would allow assessment of the system's ability to distinguish thin tissue layers, a key Subsystems are colour-coded by function: red represents power; light blue represents integrated electronics; dark blue represents the system interface and communications; green represents key functional subsystems; and beige represents physical integration components.
This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. capability for diagnostic use. Simulation is also needed to provide sufficiently accurate electrical characteristics to inform the electronic design, not just of the test circuitry but also of the ASIC at the heart of the entire capsule system. For calculation of electrical characteristics and full tissue phantom simulation, a decision was made to use a 1D model rather than FEA, saving computation and reducing the feedback time between engineer and clinician. Care was also taken to select a model compatible with future ASIC development, to minimize changes in modelling properties. By selecting a transducer/system model which can be fully converted into the electrical domain, it can be realized in pSPICE (Cadence Design Systems, Inc, San Jose, USA) for detailed electronics simulation and used when determining the system response of the silicon design and comparing it with the mathematical model. To simulate the electrical and acoustic properties of the piezoelectric transducer and its accompanying electrical circuitry, a KLM model was used [23], in conjunction with 2port electrical system modelling in MATLAB (The Mathworks, Cambridge, UK). Pre-existing modelling solutions such as Field II [24] or PiezoCAD (Sonic Concepts, Bothell, USA) were considered, but because of the unusual geometry, separate transmitter and receiver, and the desire to incorporate the full electronic pathway, an in-house solution was ultimately selected. Terminology and ABCD 2-port parameter derivations  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TUFFC.2018.2794220, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control from the literature [25] were used in the simulation of the transducer and the supporting electronics. To properly reflect the different physical dimensions and element properties of the transmission (tx) and recepetion (rx) arrays, the system was modelled as two electro-acoustic models, as shown in Fig. 2.
Using an ABCD 2-port network implementation [26], the system in Fig. 2 was simulated with the values in Table I. The capsule diameter was assumed to be 10 mm at the radial centre of the piezoelectric. Of particular note in this system, a multiplexer is integrated with each rx channel to allow synthetic aperture acquisition, and this has noticeable parasitic effects [27]. Multiplexing is handled in the digital circuitry on the tx end, but must be placed before the analog front-end in the rx circuit, so these effects should be modelled. The ADG706 (Analog Devices, Norwood, MA, USA) is a 16:1 multiplexer which was selected for the purposes of simulation and the specified input capacitance, path resistance and parasitic inactive channel capacitance can be incorporated as seen in Fig. 2.
To verify that the KLM modelling code developed is an accurate model of the expected system behavior, a singleelement, physically focused lithium niobate US transducer designed to operate at 45 MHz [28] was modelled using the same methodology, and the resultant electrical impedance spectroscopy data were compared with measurements. We used a single-element transducer for validation because this configuration closely mimics the tx device that emerged from the simulation as appropriate. As shown in Fig. 3, the modeled results have an anti-resonance peak at 44.0 MHz at an impedance of 18.4 Ω, while the experimental data shows an anti-resonance at 43.1 MHz at an impedance of 18.2 Ω, in good correspondence, thus supporting the model's ability to predict the electrical resonance behavior of the proposed system at microultrasound frequencies.
IV. ULTRASOUND ARRAY GEOMETRY AND BEAMFORMER DESIGN The number and size of the elements in an array are key determinants of ultrasound system capability and complexity. In the circumferential array considered here, the trade-off between system complexity and potential imaging performance caused by limiting the numbers of elements can be evaluated by calculating the active aperture that can be used for beamforming each radial image line, taking into account element directivity and array curvature. Increasing the total number of elements in the array, Ne, and correspondingly decreasing the element width, w, increases the active aperture size, which affects lateral resolution by improving the element directivity. The corresponding increase in the number of elements in the active aperture, NA, also improves beamforming capability.
Large numbers of elements in the array will provide better image resolution than small numbers, but even moderate element counts (e.g. Ne = 128 elements) raise concerns about the realisation of physical interconnects between the array and electronic circuitry. Intravascular ultrasound (IVUS) research has focused on arrays with ≤ 64 elements for this reason and due to space concerns [29]- [31]. Arrays with Ne = 512 elements are available commercially [32], but the relatively large number of elements raises additional concerns because of the volume of electronics required. To reduce this problem, the system defined here separates the tx and rx arrays (Fig. 4a) and requires only one tx and one rx channel to be active for each tx pulse. As full synthetic aperture approaches can have frame rate concerns, only eight tx elements are used, in a zone transmission configuration with synthetic aperture reception. Unfocused, plane wave transmission is used to fully insonate the area for each receive sequence. Each tx element comprised one eighth of the ring circumference, with the two transmitters adjacent to the active receiver used in each transmission. 512 elements are used in the rx array, in linearly stepped apertures dependent on the focal directivity. This arrangement necessitates additional multiplexing and adds a small amount of complexity to the interconnect scheme but the electronic circuitry is very much simplified overall and power consumption is also reduced. The unfocused tx scheme allows a single tx circuit to be used, and the synthetic aperture rx scheme allows only one rx front-end to be active at a time, reducing the rx power requirement by a factor equal to the aperture size.
Single element transmission and reception can have a significant impact on the maximum scan rate of the system because of the need for multiple tx pulses to completely sample the aperture. The effect can be considered by taking into account the expected maximum rate of motion of the capsule during its passage. In a healthy human GI tract, the average rate of motion through the small bowel is approximately vavg = 0.17 mm s -1 [33]. However, the motion can be highly pulsatile and variable, especially in patients with abnormalities, so much higher peak rates, vpk = 2 -5 mm s -1 [34], must be used for system design. Assuming an average sound propagation speed, v = 1540 ms -1 , a complete pulse-echo transit to a maximum radial depth of 10 mm outside the capsule is tpulse = 2 * 10 mm / 1540 m/s = 13 µs. Allowing time for additional scattering, tscan = 50 µs, and taking Ne = 512 scan lines, a full Bscan image would take ttotal = Ne * tscan = 25.6 ms, corresponding to a maximum frame rate 1 / ttotal = 39 frames per second (fps).
Even at the highest rate of motion through the bowel, vmax = 5 mm s -1 , the capsule motion during a single frame is only d = vmax * ttotal = 128 µm. This corresponds to 2.08, where the wavelength in tissue, λ = 1540 ms -1 / 25 MHz = 61.6 µm, and thus represents a minor error in the B-scan field of view.
If a full synthetic aperture approach is used, the theoretical frame rate of 39 fps is further reduced by a factor equal to the number of elements in the imaging aperture, giving ~1 fps if a 32 element aperture is implemented. Instead, our simulated results here are based on an important compromise in which, as noted, a large, de-focused tx element is used in conjunction with individually sampled rx elements, allowing the frame rate of traditional imaging to be maintained while exploiting the reduction in electronic complexity offered by a synthetic aperture.
Because of the fixed o.d. of the capsule, the maximum number of elements in the active aperture can be calculated for a given focal distance based on the directivity function. The directivity function for a rectangular element can be expressed as [35]: where w is the element width, θ is the angle between the array normal and the acoustic propagation vector in the plane of the image, and λ is the wavelength. Due to the curvature of the array, θ must be derived from the arc angle φ between the normal to the focus point and the active element normal (Fig. 4b).
For an acoustic target a distance d from the surface of an array of radius r, the distance, R, from the array element to the target can be found using the cosine law: The angle, ϕ, between segment R and d, can then be obtained using the sine law: Finally, the directivity angle is the sum of the two other angles as the outside angle of the third angle of the triangle, Fig. 4: The results of the calculations from Eqns. 2, 3 and 4 are utilised by substituting them into Eqn. 1 for each element. To avoid a contribution from noise at large angles for focal points close to the array, elements with directivity < 0.8 are removed from the active aperture. A similar calculation is performed during simulation for each acoustic scatterer and the resultant directivity applied as a weighting function to the summation. Using Eqns. 1 -4 and an estimated element width, w = 0.8 p, where p is the array element pitch, the maximum aperture can be calculated for a focal distance from the array, df = 5 mm, which is the lowest value of the imaging window and the most difficult case for the directivity calculation. Given an array with N = 512 elements, an aperture size of 31 elements is obtained, which achieves a satisfactory compromise between minimum aperture size and electronic complexity.   Fig. 5. Program flow for the ultrasound system simulation. The simulation is broken into three main components: the software beamforming, which performs the calculations which would be handled by the digital ASIC or base station in the full system; the KLM / 2-port model, which models the effects of the analog electronic and mechanical elements of the system; and the acoustic model, which propagates the simulated pressure waves and models the reflectivity of the programmed targets. physically possible with mechanical dicing of an array during fabrication [36], [37]. The tx elements are based on array of the same size, but with only 8 elements of 3.93 mm in arc length. Initial values for the thickness of the active and matching layers were calculated at this point, however they were adjusted through the simulation process and will be reported in Section V.
A MATLAB-based beamformer was created to interface with the KLM model, simulating the digital components of the proposed system, to allow virtual phantoms to be imaged. The beamformer is based on a classic delay-and-sum configuration with unfocused tx and dynamic rx beamforming [38], [39]. The full system data flow is broken into several discrete steps to allow simulation of different system specifications. As shown in Fig. 5, an initial tx pulse is defined as a single cycle, monopolar excitation at the target center frequency. The KLM / 2-port model matrices are then applied to the input pulse to obtain the transmitted acoustic wave output at the water interface. This is then propagated using ray-tracing to calculate the amplitude and delay of the echoes from the programmed acoustic scatterers as seen at the rx array elements.
The resulting received echoes are multiplied through the KLM / 2-port matrix model of the receiver, after which the amplitude and time quantization effects of a 12-bit, 100 MS/s analog to digital converter (ADC) are applied. Simulating these digitization effects is particularly important as they can affect the accuracy of the beamforming delays and the resultant focal quality. Once the rx pulses have been processed through the KLM simulation and analog electronics models, they are passed through a digital rx beamformer to process the pulse-echo data and generate B-scan images (Fig. 6). The full set of synthetic aperture rx pulses is stored in a matrix and beamformed in sets determined by the selected aperture size and aperture increment. A set of rx focal points is determined, based on the minimum and maximum depths of the desired final image as well as the image resolution. The array configuration under test is then used to calculate the appropriate directivity from the elements in the active aperture to each of the rx foci. A Hanning apodisation window is applied across the aperture before dynamic rx delays are applied to the received pulses within the active aperture. The delayed pulses are then summed and the resulting scan line is envelope-detected using a Hilbert transform and added to the image buffer.
In addition to the steps listed in Fig. 6, optional interpolation and filtering can be applied between the apodisation and dynamic rx beamforming operations. The active aperture is then incremented until all scan angles have been calculated, and the resulting B-scan is log-compressed and displayed with adjustable grey-scale resolution. A Cartesian-to-polar coordinate transformation is used to display the images in an annulus which mimics the GI tract anatomy for ease of interpretation by clinicians. The simulated beamformer is designed to allow the aperture size, windowing, directivity cut-off and other imaging parameters to be adjusted to assess the imaging abilities of the system. Initial imaging phantoms were created by defining point reflectors with individual reflection coefficients to assess axial and lateral resolution. Later, experimental data were used to allow more realistic image assessment.

V.SIMULATED SYSTEM PERFORMANCE
The response of a transducer was simulated using the KLM model with an applied single-cycle tx sinusoid centred at 25 MHz. As the intended final source for the tx excitation is an ASIC with limited slew rate, initial simulations of the digital drive suggested that the digital signal will more closely resemble a sinusoid than a square wave under capacitive drive conditions. Hence our approach mimics practical electrical excitation to a first approximation. The input impedances of individual tx and rx elements were then calculated for a frequency sweep from 0 -50 MHz. These calculations were performed only on the piezoelectric components of the transducers and neglect the influence of the electrical components, showing the unloaded resonance behaviour and electrical impedance of the transducers. Based on high performance piezocrystal commonly used in medical ultrasound imaging devices, a 40% by volume PMN-PT 2-2 composite [40] was selected as the material of choice for simulation, and the geometric mean of the acoustic impedances was used to calculate the desired matching layer impedance. The thicknesses of the piezoelectric and matching layers were then adjusted to obtain a smooth resonance curve. After adjustment, a PMN-PT composite thickness of 85 µm and a matching layer 26 µm thick with an acoustic impedance of 4.08 MRayl produced the simulated impedance curves in Figs. 7a and 7b. Of particular note is the significant difference in input impedance due to the difference in individual element size between the tx and rx arrays, which must be taken into account in the design of the corresponding electronics. The higher impedance seen in the receiver mirrors impedances which have been reported elsewhere [41].
The higher receive impedance can be handled in two ways in the receive system. For an electronic solution that is adaptable, such as an application specific integrated circuit (ASIC) which is the most likely way to deal with the very small, high frequency elements and the one we are developing, the input impedance can be designed to match the transducer impedance for maximised power transfer. However, in the circumstance that the electronics cannot be adapted to match the transducer to avoid power-loss, adjustments may also be possible in the transducer design, including increasing the elevation dimension of the transducer to reduce the impedance proportionately without otherwise impacting the acoustic stack. If this is necessary for this design, the appropriate compromise between the elevation dimension and the overall device dimensions will be determined during experimental acoustic testing.
Once an acceptable pulse-echo response had been simulated, the 0.1 m transmission line specified in Table 1 was added to the tx and rx paths, as well as the rx multiplexer modelling. The two-way pulse-echo response between individual tx and rx elements was then calculated from an ideal point-scatterer target and the pulse bandwidth and time-domain pulse were plotted, as shown in Figs. 7c and 7d. A bandwidth of 44.0% was calculated for tx-rx operation, with a centre frequency of 24.9 MHz. The slightly lower bandwidth is due to increased difficulty in matching at higher frequencies with a large mismatch in transmit and receive transducer areas. A virtual phantom was generated to assess the imaging resolution of the system and the effects of the defocused tx pulse. This had three ideal point reflectors located at (15 mm, 0), (20 mm, π/10) and in polar coordinates relative to the center of the array, the distances corresponding to the f/2, f/3 and f/4 positions as a function of the active aperture. These ideal point reflectors were used to assess the impact of zone transmission on sidelobe levels. A virtual linear array scan was then performed with an aperture comprising 36 elements and a focal distance of 15 mm. The resulting B-scan was displayed with a dynamic range of 60 dB and standard log-compression, This is wider than the theoretical ideal [38], but is expected given that the zone transmission configuration removes half of the normal focusing of delay and sum beamforming [42] and electronic parasitic effects further impact this. The axial resolutions were 160, 140 and 160 µm respectively. As the intended application of the array is to image tissue featuring well defined wall structures with relatively thin layers, a second virtual phantom was created to simulate two layers of material surrounding the array. The interfaces each consisted of 360 ideal reflectors positioned circumferentially and were separated radially by 1 mm. A sinusoidal variation in the distance from the array, between 13 and 18 mm, was added to mimic the irregularity of normal tissue layers. The resulting Bscan, Fig. 9, was produced in 22 min 24 s and shows clear resolution of the two walls.
To allow the generation of a virtual phantom with tissue layers and reflectivity similar to those in the human GI tract, a US image of porcine bowel tissue was acquired [43]; the porcine model was chosen as it closely resembles human tissue in scale and nature [44] and mechanical scanning with a singleelement, US transducer was used to generate the data. Based on ex vivo tissue scans, this novel phantom was used instead of a standard simulation [24] due to the identified need to assess the system's sensitivity to specific target tissue.
Fresh-frozen porcine small bowel sourced from an abbatoir was separated from the bowel wall along the long axis and perfused with 60 mL of degassed phosphate-buffered saline (PBS). The tissue was then pinned, mucosa uppermost (Fig.  10), on a platform comprising ~30 mm of 1% agar (w/w) on top of ultrasound absorbing material (Aptflex F28, Precision Acoustics, Dorchester, UK), submerged in degassed PBS and scanned across the short axis of the bowel. A 45 MHz singleelement transducer with a geometric focal distance of 6 mm (AFM Ltd, Birmingham, UK) was mechanically scanned using a custom motor-control and acquisition system programmed in LabVIEW (National Instruments, Austin, USA) and the resulting A-scans were imported into MATLAB. These scans were then envelope-detected, log-compressed and displayed in This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TUFFC.2018.2794220, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control grey-scale with the same beamformer architecture as the simulation code, as shown in Fig. 10a. An example stained cross-section of the relevant tissue layers, representing standard anatomy, can be seen in Fig. 10b for comparison. While there is limited literature on the acoustic impedance of the layers at this frequency, higher frequency measurements [45] show that there is minimal difference in the mechanical properties of the mucosa and submucosa in comparison to the other layers, supporting our finding of reduced contrast. The choice of US transducer frequency, 45 MHz, was made to ensure that all features expected to be visible with the 25 MHz array were represented in the simulation phantom.
Once an ex vivo image of sufficient quality had been obtained, the original annular section of the bowel was recreated by mapping the A-scan data into cylindrical coordinates. To reduce the effect of speckle in the phantom, a thresholding algorithm was applied to the data to produce four reflectivity levels at 10 dB intervals. A randomly generated set of 25,000 point scatters was then mapped onto the pre-logcompressed data and assigned reflectivity values based on the echo strength of the underlying data. The resulting virtual phantom was then used as an input into the MATLAB beamformer and imaged using the simulated transducer array operating at 25 MHz. The B-scan image output from each of the three major steps in this process is shown in Fig. 11.
Comparing the layer structure seen in Fig. 11 with that of Fig. 10, the mucosa/submucosa, muscularis and serosa layers have retained their distinction. However, some loss of granularity is observed, as expected from the reduction in centre frequency and tx defocusing. Clinical assessment indicated that the qualitative features had been successfully retained and that the image was of diagnostic quality.

VI. DISCUSSION AND CONCLUSIONS
With its very specific geometrical constraints and the need for microultrasound frequencies, USCE represents a new application of ultrasound imaging and therefore requires design procedures adapted from those used for other applications. This paper explains this adaptation. By integrating 1D KLM modelling with a full digital beamformer implemented in MATLAB, a virtual system has been created to allow assessment of the electronic and acoustic performance of proposed USCE systems and the effect of design variations on its output. For an example USCE tx-rx design, the calculation time of less than 2 min for resolution phantoms indicates that multiple design configurations may be tested and compared in a reasonable amount of time for effective virtual prototyping.
As the ultimate output of the virtual prototyping system, Fig. 11, representing results from a virtual porcine tissue phantom simulation, demonstrates a satisfactory correlation with the scan from ex vivo porcine tissue shown in Fig. 10. The broadening of the point-target side-lobes is expected because of the use of a defocused tx pulse. Similarly, the loss of resolution of the tissue phantom compared to the original scan, especially at the mucosal level, is also expected because of the reduced frequency of the USCE simulation. Nevertheless, sufficient resolution is achieved at 25 MHz to suggest a strong basis for USCE GI tract investigations and the other ultrasonic array and system parameters that were chosen have been demonstrated to be viable. The ability to distinguish layers is comparable to clinical work at 20 MHz [5], results are also comparable to previous work with mechanically scanned systems operating at 30 MHz [9].
The simulation method that has been described also holds considerable potential for exploration of other aspects of system design for USCE, such as potential operating frequencies, electrical parasitics, and system partitioning. Early modelling will provide a convenient means of evaluating a range of frequencies that are diagnostically appropriate and suitable for implementation in the USCE device. A commonly-realised added benefit is the reduction in the time and engineering effort required to determine USCE parameters. This is especially attractive given the complex nature of future physical prototype USCE devices.