Low-Cost, High-Speed Back-End Processing System for High-Frequency Ultrasound B-Mode Imaging

Abstract

For real-time visualization of the mouse heart (6 to 13 beats per second), a back-end processing system involving high-speed signal processing functions to form and display images has been developed. This back-end system was designed with new signal processing algorithms to achieve a frame rate of more than 400 images per second. These algorithms were implemented in a simple and cost-effective manner with a single field-programmable gate array (FPGA) and software programs written in C++. The operating speed of the back-end system was investigated by recording the time required for transferring an image to a personal computer. Experimental results showed that the back-end system is capable of producing 433 images per second. To evaluate the imaging performance of the back-end system, a complete imaging system was built. This imaging system, which consisted of a recently reported high-speed mechanical sector scanner assembled with the back-end system, was tested by imaging a wire phantom, a pig eye (in vitro), and a mouse heart (in vivo). It was shown that this system is capable of providing high spatial resolution images with fast temporal resolution.

I. INTRODUCTION

High-frequency ultrasound is capable of providing a spatial resolution on the order of several tens of micrometers and a temporal resolution of more than 200 images per second. These characteristics have opened up applications to high frequency ultrasound: ophthalmic, dermatologic, intravascular, small animal, and molecular imaging [1]–[4]. The high temporal and spatial resolutions, in particular, are perfectly suited for real-time imaging of the mouse heart in vivo, which is often needed for the evaluation of gene and drug therapy and monitoring the progression of diseases. Because the mouse heart rate is approximately 6 to 13 beats per second [5], an imaging system is required to provide a frame rate of more than 200 images per second to adequately capture the cardiac activity. This requirement can only be satisfied with both a high-speed scanning capability for the acquisition of echo signals (front-end system [3], [6]–[9]) and for real-time display (back-end system).

The back end of a real-time ultrasound imaging system usually includes an envelope detector, a logarithmic compressor, and a digital scan converter (DSC). To reach a higher signal processing speed, the implementation of such functions requires a more sophisticated electronic design integrating more expensive components, and is consequently relatively costly. This is particularly true when the operating speed of these functions is pushed higher and higher because more expensive electronic components and a more sophisticated design are required to meet timing constraints of electronic signals.

This paper describes a high-speed back-end system suitable for cardiac imaging in mice. The back-end system employed a recently reported high-speed envelope detector [10] and a linear interpolation algorithm for digital scan conversion. A combination of these functions and efficient look-up table (LUT) strategy enabled us to implement the high-speed back-end system in a simple and cost-effective manner by using a single field-programmable gate array (FPGA). The electronics and signal processing involved in the back-end system will be described and their overall performance will be reported. To evaluate the imaging performance of the back-end system, a complete imaging system equipped with a high-speed mechanical sector scanner [6] as a front-end system was built. With this imaging system, in vivo experiments in a mouse were performed, and the test results will be shown.

II. BACK-END SYSTEM IMPLEMENTATION

A functional diagram of the overall back-end system designed to meet the requirements imposed by mouse cardiac imaging is shown in Fig. 1. In this design, echo signals from a front-end system were digitized with an analog to digital converter (ADC; AD9430, Analog Devices Inc., Norwood, MA, 12 bits, maximum sampling frequency of 210 MHz). Digitized echo signals (or RF samples) were transmitted to the main board (Fig. 1, dashed box) via a low voltage differential (LVDS) bus. Envelope detection and image formation functions were implemented in a single FPGA (Stratix EP1S60F1020C6, Altera Corporation, San Jose, CA). There were 4 steps of data preconditioning before digital scan conversion (DSC), which were, in order of execution: dc cancellation, digital time gain compensation (TGC), quadrature demodulation (QDM), and logarithmically-compressed envelope calculation. All these operations, which were performed at a 200 MHz clock rate, will be detailed later. Envelope samples were stored temporarily in one of 3 line buffers, which could each store one scanline consisting of 2048 samples. Two sets of the 3 line buffers were used for efficient storing and simple control logic. From these envelope samples, image pixel values were produced by the DSC operating at a 100 MHz clock and stored in one of 2 on-chip display memory banks. Each memory bank was capable of storing 65,536 pixel values, corresponding to an image size of 256 × 256. To improve data transfer efficiency, one memory bank stored pixel data while data stored in the other bank were being transferred to a personal computer (PC) via a 64-bit, 33-MHz PCI bus.

Fig. 1.

Functional block diagram of the back-end processing system used for high-speed, high-frequency ultrasound B-mode imaging systems. QDM stands for quadrature demodulation, and the high-speed envelope detector produces logarithmically compressed envelope samples. The block arrows indicate signal processing paths.

A graphical user interface (GUI) written in C++ controlled the transfer of images to the PC memory and the storage of these images in a hard disk, along with the time stamps indicating when these images have been stored in the memory. The software also handled a high-performance video card (RADEON 9800 PRO, ATL corporation, Frederick, MD) using the OpenGL application programming interface (API). This standard graphic API allowed the enlargement of small-sized images with a texture mapping method which required minimal computational power when they were displayed on a monitor.

A. DC Cancellation

Digitized echo signals collected may contain time-variant noise such as thermal noise from the transducer and acoustic loads as well as flicker (or 1/f) or burst noises from electronic components. These noises have large spectral components in the dc and low frequency range, which distort the echo signals and prevent an accurate calculation of their envelopes. In the back-end system, dc and low frequency noise cancellation was performed by implementing a digital 33-tap high-pass filter with a cutoff frequency of 20 MHz.

B. Digital Time Gain Compensation

Because of the attenuation due to both absorption and scattering, the amplitude of ultrasound waves propagating in biological tissues decreases exponentially as a function of depth [11]. For example, the attenuation coefficient in bovine heart muscle has a value of 8.2 dB/mm measured at 70 MHz [12] and a value of 3.4 dB/mm extrapolated to 40 MHz [13]. Note that diffraction also affects the amplitude of the beam as a function of depth. To compensate for the changes in amplitude of the propagating sound wave in tissue, it was necessary to implement a gain compensator which was a function of depth, and consequently of time; a TGC was implemented digitally. In the design, the imaging depth was divided into 8 partial zones, and the selection of an individual linear gain increment and an overall linear gain for the entire imaging depth were provided. The total linear gain was calculated by software for each sample along the scanline and saved into a 2048 15-bit word random access memory in the FPGA. In addition, the TGC allowed for selecting bits for final signals out of 17 bits of input signals to the R-shifter block. For this, a bit position, indicating several least significant bits from the 17 bits to be discarded, was set in the cutting bits block so as to secure the maximum viable amplitude of the resulted signals without saturation. Fig. 2 illustrates the functional block diagram of the implemented digital time gain compensator.

Fig. 2.

Functional block diagram of the implemented digital time gain compensator. The bold line box represents a look-up table. The u and s denote unsigned and signed integer numbers, respectively. The R-shifter represents an arithmetic right shift register. The dashed lines indicate control signals and the solid lines represent data flow paths.

C. High-Speed Envelope Detection and Logarithmic Compression

The envelope of RF signals is calculated from the inphase (I) and quadrature-phase (Q) signals obtained by quadrature demodulation. In the back-end system, demodulation was performed digitally by multiplying the digitized RF samples, r(n), by sine and cosine waveforms (Fig. 3), which were initially calculated and stored as 16-bit fixed-point vectors in 2 separate LUT. Traditionally, after low-pass filtering, the resultant digital in-phase, I(n), and quadrature-phase, Q(n), signals are used for the calculation of the envelope by $\sqrt{I{(n)}^2+Q{(n)}^2}$ . In addition, the envelope is logarithmically compressed before scan conversion.

Fig. 3.

Functional block diagram of the implemented quadrature demodulator and envelope detector. The bold line boxes represent look-up tables. The u and s denote unsigned and signed integer numbers, respectively.

The calculation of the square root involves complicated and time-consuming signal processing, which can hamper the frame rate. In the system presented in this paper, a previously developed envelope detector was used to surpass the barrier. This envelope detector employed an efficient LUT strategy which was based on the use of a binary logarithmic number system (BLNS) instead of a fixed-point number system (see [10] for details).

The efficiency of the calculation of envelope in this algorithm relied on the use of 3 LUTs containing the base-2 logarithms of I(n), Q(n), and of the square root term as shown in Fig. 3. The sizes of these LUTs were 2^m × k bits for I(n) and Q(n), and 2^k+1 × k bits for the square root term, where m is the number of bits over which I(n) and Q(n) are coded and k is the number of bits in the BLNS. The envelope detector presented here used 12-bit fixed-point numbers for I(n) and for Q(n) and 10-bit binary logarithmic numbers, so that the total size of these LUTs was 102,400 bits, dramatically reducing the size compared with approximately 160 Mbits (2¹² × 2¹² × 10) in the case of the direct use of LUT.

This BLNS LUT strategy was a relatively easy to implement and allowed the production of logarithmically compressed envelope samples at every clock cycle. Because this envelope detector operated at 200 MHz, its computation of a 2048-sample envelope corresponding to a scanline was performed in 10.4 µs (including a 32-clock-cycle latency arising from low-pass filtering and fetching date from LUTs). This allowed a maximum pulse repetition frequency (PRF) of 96 kHz for data acquisition, which was sufficient for mouse cardiac imaging. Because of this fast processing speed, no decimation was required. For the DSC, this allowed the adoption of a linear interpolation algorithm requiring over-sampled envelope data for accuracy [14], instead of a more complex bilinear interpolation algorithm [15], [16].

D. High-Speed Digital Scan Conversion

The linear interpolation performs only angular interpolation, thus calculating a pixel value V_p by

$$V_P=\frac{S1\times \alpha +S2\times \beta }{\alpha +\beta },$$ (1)

where S1 and S2 are 2 nearest samples to an object pixel along the radius direction, and α and β are angular differences between the object pixel and the 2 samples. Fig. 4 shows a functional block diagram of the high-speed DSC adopting the linear interpolation algorithm expressed as (1). In this implementation, 4 LUTs were used; these contained the pixel addresses (LUT₁), the line buffer read addresses (LUT₂), the angles of pixels (LUT₃), and the angles of left-side (SL_i, Fig. 5) of the sector scan slices delimited by 2 successive scanlines SL_i and SL_i+1 (LUT₄), respectively.

Fig. 4.

Functional block diagram of the high-speed digital scan converter with linear interpolation. The bold line boxes represent look-up tables. The u and s denote unsigned and signed integer numbers, respectively. In this design, a sector scan slice was quantized to 8-bit resolution, i.e., 256 levels so that α could be obtained by subtracting a given β value from 256.

Fig. 5.

Pixel addressing configuration for a 256 × 256 image. The multiplication signs (×) represent the location of the image pixels. SL_i and SL_i+1 represent the directions of 2 successive acquired sector scanlines. The black dots on these scanlines represent acquired samples. P is the pixel of which the value will be calculated by interpolation from the values of the 2 acquired samples S1 and S2. α and β are angles of SL_i and SL_i+1, respectively, relative to the virtual scanline intercepting P.

To reduce the size of LUT₁, the pixel addresses were encoded. Therefore, for each pixel P, a decoder was used to decode the pixel address first. Using this address, the addresses at which the data points S1 (from SL_i) and S2 (from SL_i+1) were located in the line buffers were extracted from LUT₂, and the angle of P was extracted from LUT₃. Using the index i of the scanline SL_i, in addition, the angle of SL_i was extracted from LUT₄. Note that SL_i+1 could be obtained by adding SL_i to 255 because a sector scan slice was quantized to 8-bit resolution. Then, S1 and S2 were read in the line buffers, and the angles α and β were calculated from the angles of pixel P and scanlines SL_i and SL_i+1. Finally, the value of pixel P, V_p, was calculated by linear interpolation using (1). By using the symmetry property of a sector scan image, the size of the LUTs also was reduced by approximately a factor of 2. The decoder represented the bottleneck of the back-end system because it required 3 clock cycles to decode a pixel address. However, it was shown that, for a 256 × 256 image size and a 100 MHz clock, it limited the frame rate to a value of 500 Hz, which met the requirement for mouse cardiac imaging.

With these new signal processing algorithms and the efficient use of LUTs, the high-speed back-end processing system could be implemented in a simple and cost-effective manner. As seen in Table I, only about 3 Mbits of memory was used for LUTs in performing these functions, enabling us to use only a single middle-range FPGA without any external memory for the implementation.

TABLE I.

The Usage of Internal Memory of the Field-programmable Gate Array FPGA (Stratix EP1S60F1020C6, Altera Corporation, San Jose, CA) Used for Look-up Tables (LUT) in Each Function.¹

Functions	DTGC	QDM	Envelope detector	DSC	Line buffers	Display memory
LUT size (bits)	30 720	65 536	102 400	1 646 834	98 304	1 048 576
Usage rate	57.3% (2 990 370/5 215 104 bits)2

¹DTGC = digital time gain compensation; QDM = quadrature demodulation; and DSC = digital scan conversion.

²The total amount of the memory used in the system is 2 990 370 bits of the 5 215 104 bits available in the FPGA.

III. METHODS

The signal processing performance of the back-end system was assessed in terms of accuracy and speed. In addition, its imaging performance for a beating mouse heart was tested by assembling a complete imaging device equipped with a recently reported high-speed mechanical sector scanner (see [6] and [17] for details).

The accuracy of the back-end system employing new signal processing algorithms was quantitatively evaluated by computing the normalized root mean square error (RMSE) between images from the new algorithms, the conventional counterparts, and ideal images. The evaluation was undertaken by Field II simulation [18] in which a 40-MHz single-element transducer model was used; its focal depth was 6.2 mm, F-number was 2.1, and its fractional bandwidth was 83%. Five targets, 1 mm apart along the lateral direction at a depth of 6.2 mm, were scanned by means of the mechanical sector scanning in which a viewing angle was 12.8°. Because the envelope sampling rate of the back-end system was fixed at 200 MHz, the same value as the RF sampling rate, the number of scanlines and pixel spacing would mainly affect the accuracy of the system. Therefore, this test was performed for the number of scanlines of 256, 128, 108, and 56 under the various pixel spacing values, i.e., 30.9, 15.45, and 7.725 µm.

As a standard image used for the comparison, an ideal image was created using RF signals simulated at a sampling rate of 3.2 GHz with the transducer orientated at successive angles such that its axis intercepts, one after the other, all the pixels of the image. The value of the pixel was computed by Hilbert transformation and logarithmically compressed to a 72 dB dynamic range.

To produce images by the conventional algorithms, RF signals were generated at a sampling rate of 1.6 GHz and their envelope information was extracted by QDM with numerical calculation of (1). The envelope samples were decimated by a factor of 8 to obtain a 200 MHz envelope sample rate. The decimated samples were logarithmically compressed to a 72 dB dynamic range and then the bilinear interpolation was performed.

In addition, the accuracy of the back-end system was evaluated by comparing a 20 µm-diameter tungsten wire (California Fine Wire Co., Grover Beach, CA) image from the system with that created from acquired RF data with the conventional signal processing algorithms, i.e., QDM with numerical calculation of (1) and the bilinear interpolation algorithm. Note that the characteristics of the single-element transducer were the same as those of the transducer used in the simulation. To compare −6 dB lateral and axial resolutions, a pixel with the maximum value was found and then point spread functions including the pixel along the axial and lateral directions were interpolated by a factor of 32.

The maximum processing speed of the back-end system was evaluated by using 4-cycle 25 MHz sinusoidal burst signals; they were generated by a function generator (33250A, Agilent Technologies Inc., Palo Alto, CA) and fed into the input port of the back-end system. In this experiment, the burst signals were regarded as echo signals acquired by a front-end subsystem. Back-end signal processing with the signals was performed under the condition where the number of scanlines was 210 and total view angle was 21°. Scan converted images were sent to the host processing block and stored in the hard disk of a PC with a time stamp indicating when an image had been completely transferred to the PC. To measure the maximum image rate, the pulse repetition period of the function generator was decreased by 1 µs from 15 µs until its minimum value supported by the back-end system was found.

In vivo imaging of the mouse heart was performed under a protocol approved by the Institutional Animal Care and Use Committee (IACUC ) at the University of Southern California. For the experiment, a 2-week old mouse was anesthetized with pentobarbital sodium diluted in saline to 4 mg/ml via the intraperitoneal injection of a dose of 10 µL/g body weight, and it was cleaned with a chemical hair remover. The bottom of a de-ionized-water-filled container was in contact with the mouse with ultrasound gel as a coupling medium.

IV. RESULTS

The simulation results for the evaluation of accuracies of each algorithm were summarized in Table II, and they show that the conventional algorithms perform better than new ones. This inferior accuracy of the back-end system to the conventional counterpart was mainly due to the linear interpolation algorithm because the high-speed envelope detection algorithm imposed only quantization error on the final results [10]. However, the mean value of differences in accuracy between the new and conventional algorithms was 0.56%, which we considered to be acceptable and capable of providing similar image quality as the conventional counterparts.

TABLE II.

Comparison of Accuracy of New and Conventional Signal Processing at Varying Pixel Spacings.¹

	30.9 µm		15.45 µm		7.725 µm
Number of scanlines	Conventional	New	Conventional	New	Conventional	New
256	6.19%	7.16%	5.68%	6.36%	6.00%	6.70%
128	7.26%	8.14%	7.17%	7.74%	7.55%	8.15%
108	8.63%	9.25%	8.53%	9.03%	8.96%	9.48%
56	23.95%	24.26%	24.14%	24.28%	24.21%	24.38%

¹Accuracy of algorithms was compared by computer simulation using the Field II program; the accuracy of both algorithms was evaluated as a function of the number of scanlines and pixel spacing under the condition of 200 MHz envelope sampling rate. The accuracy was quantitatively examined by computing the normalized root mean square error (RMSE) between pixel values from each algorithm and the ideal pixel values. The mean value of difference in accuracy between the new and conventional algorithms was 0.56%.

Fig. 6 shows images of the wire phantom. The total scanlines were 108, the scanning angle was 12.8°, logarithmic compression with a 72 dB dynamic range was performed, and the pixel spacing was 7.725 µm. As a result, the −6dB axial and lateral resolutions of Fig. 6(b) acquired by the system were 42.0 µm and 75.8 µm, respectively. This spatial resolution was comparable to that computed from RF data in Fig. 6(a) of which the −6 dB axial and lateral resolutions were 42.5 µm and 71.7 µm, respectively. Furthermore, the correlation coefficient of these images was 94.25%. This means that the back-end system presented here is capable of providing accurate results because of its negligible signal processing error.

Fig. 6.

Images of a 20 µm diameter tungsten wire phantom; (a) was created from acquired RF data by using the conventional signal processing algorithms, and (b) was acquired by the back-end system developed. These images were acquired by using a 40-MHz, single-element transducer and logarithmically compressed with a 72 dB dynamic range.

The number used in this experiment was 108 scanlines because it was the maximum value that the subsystem in the front end could provide when the sweep rate was about 34 Hz and PRF 20 kHz; the PRF was the maximum value that could be supplied by the pulse generator (5900PR ultrasonic analyzer, Panametrics Inc., Waltham, MA) used in the experiment. With this sweep rate, the subsystem could collect RF data at 34 frames per second (fps) during one-way swings or at 68 fps during 2-way swings. Under this situation, the PRF should be theoretically 7.344 kHz for 108 scanlines (68 × 108). Practically, however, the PRF should be around 20 kHz because the sector motor frequently decelerates and accelerates. Therefore, the time duration during which the motor maintained a constant speed, was a relatively short. To avoid irregular spacing of scanlines, the PRF should be generated within the period, thus being faster than the theoretical value. With the number of scanlines, the back-end system could provide good quality images as shown in Fig. 7, which was an excised pig eye image illustrating the sclera, commonly known as the white of the eye; the iris and cornea join forming anterior chamber angle; zonular fibers located behind the iris; and the ciliary body.

Fig. 7.

Pig eye image illustrating the sclera, commonly known as the white of the eye; the iris and cornea join forming anterior chamber angle; zonular fibers located behind the iris; and the ciliary body. The image was acquired by using a 40-MHz, single-element transducer and logarithmically compressed with a 60 dB dynamic range.

The maximum processing speed of the back-end system was estimated to be 433 images per second according to the time stamp recorded in a file. This value was determined because the minimum value of the pulse repetition period of the function generator was 11 µs. In fact, this image rate was not an obtainable maximum value of the back-end system with 100 MHz operation clock and a 256 × 256 image size, which is theoretically 457 images per second computed by 1/(T_ED × N_SL) where T_ED is the minimum computation time for envelope detection of 10.4 µs in the case of 2048 RF samples per scanline and N_SL is 210 scanlines. This difference arose from the limitation of the function generator’s capability to provide the minimum step of pulse repetition period, 1 µs. Note that it was not necessary to take into account the computational time for DSC when computing the theoretical image rate. This was so because the envelope detection was performed in parallel with DSC and its computational time was longer than that for DSC, i.e., 2 ms (500 images per second) computed in the previous section.

In vivo imaging of the mouse heart was carried out under the same condition as the previous experiments for the wire phantom test and the in vitro experiment, except using 56 scanlines. This was the maximum usable value to retain the PRF of 20 kHz for the pulse generator when the sweep rate was increased to 67 Hz, so that the frame rate became 67 fps for one-way swing. This frame rate was the maximum obtainable scanning rate of the front-end subsystem for one-way swing. Fig. 8 shows still images of a mouse beating heart acquired at a rate of 67 fps. In addition, a cineloop of a beating mouse heart was obtained from the in vivo experiments (). In the first image, acquired at t = 0 ms, we can see the left ventricle (LV), the left atrium (LA), and the coronary sinus (CS). Because the mitral valve (MV) closes, however, it is not shown in the first image. The MV starts opening from the second image acquired at t = 15 ms and is fully opened at t = 45 ms as shown in the third image. This experimental result indicates that the imaging system developed in the work is capable of adequately providing real-time visualization of important events occurring in the mouse heart, although the image quality is still lacking due to the sparse line density, i.e., 51 scanlines provided by the front-end subsystem used in the experiment.

Fig. 8.

Still images of a mouse beating heart acquired at 67 frames per second. LA: left atrium, LV: left ventricle, MV: mitral valve, CS: coronary sinus. These images were acquired by using a 40-MHz, single-element transducer and logarithmically compressed with a 60 dB dynamic range.

V. CONCLUSIONS

This paper has described a recently developed high-speed back-end processing system for high-frequency ultrasound B-mode imaging, and demonstrated from several experiments that the system might be used in a high-frequency imaging device suitable for cardiac imaging in mice to produce images with small signal processing error in real time. The new signal processing algorithms and the efficient use of LUTs allowed the back-end processing system to be implemented in a simple and cost-effective manner.

The back-end processing system presented in this paper may be equally useful for other types of front-end sub-systems equipped with high-frequency ultrasound phased arrays and convex arrays; these are capable of scanning at much faster rate than mechanical scanners if these arrays become available for cardiac imaging in mice. This is so because array imaging systems provide a segment of RF data per scanline after beam-formation which has the same configuration of input data to the back-end system as does the mechanical sector scanner.