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detect the wide range of re ected signals, which are typically 1 to 2 volts at interfaces near the surface and microvolts at deeper structures In addition the receiver must introduce little noise and have a wide ampli cation bandwidth The time gain compensator circuit allows the ultrasound user to interactively amplify the echoed signal according to its depth of origin This feature compensate for the higher attenuation of the signal seen in the echoes originating from deeper interfaces and results in a more uniform image (ie, interfaces are not darker closer to the body surface on the image display solely on the basis of being closer to the transducer) The operator is able to obtain the best possible image by controlling the amount of gain at a particular depth.

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Table 10-2 (continued)

The output of the receiver is fed into the digital scan converter (DSC) and used to determine the depth (z direction) at which the echo occurred The depth at which the echo originated is calculated by determining the time that the echo takes to return to the transducer The depth of the re ector can be obtained because time and depth are related, and the depth is half the time interval from the transmission of the signal pulse to signal return times the velocity of sound in the traversal medium The encoding of the x and y positions of the face of the transducer and angular orientation of the transducer with respect to the normal of the scanning surface is determined by the scanning arm position encoder circuit In 2-D US, the scanning arm is restricted to the movement in one linear direction at a time.

The arm contains four potentiometers whose resistance will correspond to the x and y positions and cosine and sine directions (with angle with respect to the normal of the body surface) of the transducer For example, if the transducer is moved in the y direction while keeping x and the angle of rotation xed, then only the Y potentiometer will change its resistance Position encoders on the arm will generate signals proportional to the position of the transducer and the direction of the ultrasound beam The x, y, and z data are fed into the digital scan converter to generate the x, y position, and the z depth that will permit the echo strength signals to be stored in the appropriate memory locations The digital scan converter performs A/D conversions of data, data preprocessing, pixel generation, image storage, data post processing, and image display.

g2( X , t )

The analog echo signals from the receiver circuit are digitized by an analog-to-digital converter in the DSC, typically to 8 to 12 bits (256 4096 gray levels) Fast A/D converters are normally used because most ultrasound echo signals have a wide bandwidth, and the sampling frequency should be at least twice the highest frequency of interest in the image Typical A/D sampling rates range from 10 to 20 MHz The DSC image memory is normally 512 512 8 bits, for a color Doppler US image, it can be 512 512 24 bits (see Section 384) The data may be preprocessed to enhance the visual display of the data and to match the dynamic range of the subsequent hardware components Echo signals are typically rescaled, and often nonlinear (eg, logarithmic) circuits are used to emphasize and de-emphasize certain echo amplitudes 38.

It is now high time for analyzing why parallel computing is necessary and how it can be applied to the most frequently encountered computations of subsurface imaging, as mentioned in Section 325 For simplicity, we will only consider using nite elements in spatial discretizations, the reader is reminded that other common discretization strategies (such as nite difference and nite volume) can be parallelized using the same principles The transient partial differential equations (32), (34), and (39) are clearly the most computationally demanding, especially when high resolution is desired Let N denote the number of elements in a spatial solution domain The associated computational cost for (32), (34), and (39) is of order O(N ), where > 1 This is because rst an increase in N will normally require more timesteps in the temporal integration when solving (32), (34), and (3.