Ultrasonic Linear Array Medical Imaging System

Transcription

1 Ultrasonic Linear Array Medical Imaging System R. K. Saha, S. Karmakar, S. Saha, M. Roy, S. Sarkar and S.K. Sen Microelectronics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata ABSTRACT Modern ultrasound scanners use large either linear or phased array of piezoelectric transducers. Design principle of electronic beamforming networks thus draws heavily from that of adaptive antenna array. However, the interaction of ultrasound with human tissue appears to be much more complicated than that of the electromagnetic wave. While with X- rays we get a shadow image of the system, with ultrasound complete imaging of different organs of different tissue composition is possible. Main criterion that differentiates the interaction is in the very nature of ultrasound. When ultrasound propagates through human tissue layers it spends longer time because of its comparatively lower velocity. The density, elasticity, sound velocity, specific acoustic impedance, absorption, scattering, and the parameters of non-linearity directly control the amount and characteristics of the back scatter component that is received by the same transmitting transducers. In this paper describing the basic ultrasound linear array imaging system briefly a design of a sixteen-element delay-sum beamformer is presented. INTRODUCTION Efficacy of an ultrasound medical imaging system depends largely on the transmit/receive probe that normally is a piezoelectric transducer. This entails that a large portion of historical development of diagnostics is captured by the history of development of the transducer technology that includes material research, understanding of the physics of wave and its propagation through fluid and solid and particularly through tissue media. The complexity of the interaction of ultrasound with human tissue is resulted because of the composition of the media. It is highly inhomogeneous, non-linear and anisotropic. It is embedded with different types of tissue types, namely, hard, soft, softer etc. some examples being, bone, muscle, blood, fat and so on. During interactions of ultrasound with such a medium the physical processes that become important are attenuation, reflection, and scattering. The tissue acoustic parameters that play major role are acoustic impedance, sound velocity, attenuation coefficient, viscosity, and various relaxation processes. Frequency-dependent attenuation and dispersion are very complex processes in tissue and need deep understanding for properly designing the diagnostic ultrasound system and of course the front-end part; design of the transducer, the foremost part being the most crucial. In a complete diagnostic system ultrasound probe is singularly the most expensive and delicate part. The basic scanning process followed in ultrasound scanning machines has a good overlap with radar techniques. Thus there has been a growing need for replacing single element transducer with an array; this is mainly for improving various resolutions like axial, lateral and elevational, and to improve image quality. At the present state of development application of single element transducer is almost confined to amplitude mode of imaging i.e. the A-mode, all other modes like B- mode, transducer-array is used. The terminologies expressed in italics are borrowed from the literatures on radar because of, as mentioned elsewhere, the very similar principle of operation followed in both the cases; difference of course lies in the modalities involved in these two cases. This difference creates ultimately a lot of typicality in each system s design criteria including the devices needed and algorithm followed for implementation. MEDICAL ULTRASOUND TRANSDUCERS Non-invasive nature of diagnostic capability of ultrasound is made possible only through proper probe; both mechanical design and beam profile have important roles to play. In single element transducers beam profile has a direct relevance to the transducer diameter which varies from 4-6mm to 19-20mm. Transducer with larger cross sectional area generates a beam that covers wider area while sweeping at the cost of lateral resolution. These transducers can be either focused or 1

2 unfocussed. In focused transducers focal length is always shorter than the near zone. For imaging axial region around the minimum cross sectional area of the beam is used. TABLE 1 TRANSDUCER TYPES Linear Array - Transducer shape determines display image format - Generally more elements than Phased Array Phased Array - Key Feature: Dynamic focusing and steering of beam - Display Image Format: Sector only Two-dimensional Array -Allows for full volume imaging Hardware complexity increases by N 2 Annular Array Two-dimensional focusing, but no beam steering By steering the transducer element a sector image of a medium can be formed. A micro motor that physically swings the crystal, executes the steering of the beam. Using oil damper in the surroundings of the crystal controls Single Pulse Length that is related with the axial resolution of the system. Major limitations in this single element transducers that were felt are (i) usual sluggishness of the mechanical system is reflected in the scanning operation (ii) no provision for controlling the transducer aperture and dynamic focusing. Primarily because of the limitation (ii) almost all present generation ultrasound imagers use array transducers. Extra benefits obtained are electronic steering and automatic identification of the targeted object by incorporating adaptive array signal processing in the beamformer. TANSDUCER ARRAYS The majority of ultrasound systems employ transducers with many individual rectangular piezoelectric elements arranged in linear or curvilinear arrays. Typically, 128 to 512 individual rectangular elements compose the transducer assembly. Each element has a width typically less than half the wavelength and a length of several millimeters. Two modes of activation are used to produce a beam. These are the linear (sequential) and phased activation/receive modes. Linear Arrays Linear array transducers typically contain 256 to 512 elements; physically these are the largest transducer assemblies. In operation, the simultaneous firing of a small group of ~20 adjacent elements produces the ultrasound beam. The simultaneous activation produces a synthetic aperture (effective transducer width) defined by the number of active elements. Echoes are detected in the receive mode by acquiring signals from most of the transducer elements. Phased Arrays A phased-array transducer is usually composed of 64 to 128 individual elements are activated nearly (but not exactly) simultaneously to produce a single ultrasound beam. By using time delays in the electrical activation of the discrete elements across the face of the transducer, the ultrasound beam can be steered and focused electronically without moving the transducer. During ultrasound reception, all of the transducer elements detect the returning echoes from the beam path, and sophisticated algorithms synthesize the image from the detected data. Table above lists some of the common variety of array transducers along with an idea of their structure. 2

3 BEAMFORMING The job of an imager is to pick up the intended object from a crowd of many and form its clear image. Beamformer performs the first part. So essentially it is spatiotemporal filter implemented either in analog or digital domain changing thereby the terminology accordingly. In an array transducer there occurs some side lobes. As in the case of radar it depends upon the number of elements, their separation, and individual dimension etc. It is often necessary to apodize the side lobes by using apodizing multiplier and incorporate interpolation filters for improving image quality. Linear Array Single element of the array Figure 1 - The beam cross section of linear and phased arrays BASIC PRINCIPLE AND FORMULA FOR BEAMFORMING A simple beam-forming algorithm by an array of sensors and related formulas, relevant to the physical situation, will be discussed in this section. Naturally, sensors are placed in an ordered way to receive the signal. The sensed and combined signal of the sensors is a function of number of sensors, their separations and orientation. Generally these sensors receive the external disturbance and accordingly convert into electrical signal. These transducers also act as transmitter as well as receiver in real case. They receive signals between two successive transmissions. Let us consider a plane wave, as shown in the figure 2, incident on the transducers. We assume that the incident wave is sinusoidal, of angular frequency ω, in nature. The unit vector u corresponds to the direction of propagation of the plane wave, which is basically the z 0 u Plane wave d 2d 3d 4d r m on x Figure 2 - Projection of a plane wave on the linear array 3

4 reflected wave. Let the signal received at any instant t by the first sensor is given by, x(t) = exp(jωt) (1) For this configuration the plane wave has to travel an extra path d m to reach the mth transducer, where d m = r m.u = r m u sinψ = r m sinψ (2) and r m is the position of the mth sensor with respect to the origin of the coordinate system and (90 0 ψ) is the angle between r m and u. Thus, the path difference d m is the projection of r m on u. This path difference will introduce a time delay of t m = d m /c, where c is the velocity of the wave within the medium, and the corresponding phase shift is, ρ m = ωt m = ωd m /c = ω r m (sinψ)/c. (3) The signal received by the mth sensor at the same instant is, x m (t) = exp j(ωt ρ m ), for m = 1,., M, (4) where M is the total number of sensors, conventionally it is taken as 2 n. Summing these signals yields, y(t) = Σ a m x m (t) = exp(jωt) Σ a m exp(-jρ m ). (5) The summation runs from 1 to M and Σ a m exp(-jρ m ) is the complex beam pattern. The scaling factor or the weighting function a m governs the shape of the beam pattern along with the other parameters. Usually the value of a m is externally controlled and depends upon the nature of the problem. SIMULATION FOR ONE DIMENSIONAL ARRAY In case of one dimensional array the equispaced point sensors of separation d are placed in a line as depicted in the figure 2. With this orientation the equation (5) becomes, The complex beam pattern reduces to, If we assume for simplicity, a m = 1 and after summation we get, y(t) = exp(jωt) Σ a m exp(-j(m-1)dω sinψ/c). (6) b(f, u) = Σ a m exp(-j(m-1)dωsinψ/c). (7) b(f, u) = sin(πdfmsinψ/c) / sin(πdfsinψ/c). (8) The beam pattern for M=16 and for a particular angles is obtained by calculating equation (8). In our simulation the velocity of the ultrasound wave is taken as c=1540 m/s, which is equal to the velocity of the ultrasound in soft tissue medium or equivalent phantom. The frequency of the ultrasound wave for diagnostic purpose is generally taken from 2 MHz to 10 MHz. For calculations, we take 5 MHz as the frequency of the incident wave. The separation d between two consecutive sensors is taken as 0.4λ where λ is the wavelength of the incident wave in that medium. The figure 3 describes that for a given frequency the output is maximum when the wave front of the incident wave is parallel to the transducer array. In this case the output of each sensor is summed coherently with the other as because all the sensors receive the input at the same phase. Due to the phase difference the output gradually decreases and then oscillates for other angles. The selection nature of the direction of the input wave front is also clear from the figure. The beam pattern vanishes when the numerator of the equation (8) becomes zero. Zero crossings occur at, sin(πdfmsinψ/c) = 0. (9) 4

5 This is possible when, πdfmsinψ/c = nπ, for n = ±1, ±2 (10) ψ = sin -1 (nc/dfm). for n = ±1, ±2 (11) The region of the beam pattern between the first zero crossings is called the main lobe. The remaining regions are called side lobe regions. The width of the main lobe is inversely proportional to the number of transducers M, frequency of the incident wave and the spacing d. For greater spatial selectivity (closer zero crossings) it is desirable to use closely spaced large array of sensors. Another relevant point is that the beam pattern also has same nature when each transducer emits the pressure wave coherently with others in the transmitting mode. Figure 3 - Normalized patterns of a linear array of 16 sensors spaced at 0.12 mm and the frequency of the incident wave is 5 MHz. Wave front of the incident wave is parallel to the transducer array. In reality the reflected wave can come from any direction between 90 0 to with respect to the normal of the array. But for diagnostics purpose the interesting regions fall between 60 0 to With the above array arrangement the maximum response can be obtained only for parallel input wave front. For other angles the maximum output can be achieved by introducing additional phase differences. To add the sensor signals coherently for an arbitrary direction vector u 0 we calculate the projection of the sensor position vectors r m on the vector (u u 0 ). For the equally spaced linear array the summation becomes, y(t) = exp(jωt) Σ a m exp(-j(m-1)dω (sinψ sinψ 0 ) /c, (12) where ( ψ 0 ) is the angle between r m and u 0. This equation is simply a set of sinusoids act as the input to the sensors and the phase depends upon the position of the sensor as well as the delay added to get a maximum response from a particular direction. Assuming a m = 1, beam pattern can be calculated as previously done, resulting in: b(f, u) = sin(πdfm(sinψ sinψ 0 ) /c) / sin(πdf(sinψ sinψ 0 )/c). (13) 5

6 A typical example of response of the output is plotted in the figure 4. It is clear from the figure 4 that the beam has a peak at This is obtained by putting ψ 0 =15 0. By adjusting the phases the highest response for other than zero degree can be achieved and is known as electronic beam steering. The coherent sum of the outputs of sensors is possible for any angle in analog steering as it is 15 0 in this case. In digital steering process the steering directions are fixed and it depends upon the separation between the sensors, sampling frequency, and velocity of the wave in the medium. Keeping the same configuration, interpolation filters can be added before or after the beamformer to improve image quality. Figure 4 - Normalized patterns of a linear array of 16 sensors spaced at 0.12 mm and the frequency of the incident wave is 5 MHz. Wave front of the incident wave makes an angle 15 0 with the transducer array. CONCLUSION In this paper a brief but in-depth study of ultrasonic linear array medical imaging system is described. Authors have performed simulation of a 16-element phased array beamformer. This gives an excellent guidance to the design of such a sophisticated array transducer system with larger number of elements. The simulation has been targeted to a digital beamforming circuit. Future work will include simulation and design of interpolation and decimation circuits as well as the design of apodizing multipliers needed for better image formation. REFERENCES 1. G. Hampson, and A.P. Paplin ski, Beamforming by Interpolation, Technical Report 93/12, Monash University. 2. R.E. Crochiere, and L.R. Rabiner Interpolation and Decimation of Digital Signals- A Tutorial Review, Proc. IEEE, Vol. 69, No. 3, March MATLAB Version 6. 6