SON4000 Physics of Medical Ultrasound and Instrumentation

Introduction

The purpose of this assignment is to assess your understanding of spectral Doppler imaging. In particular, two important aspects of it will be considered, namely,

1. The measurement of blood flow velocity in spectral Doppler imaging and the way in which the blood flow direction is specified and handled. The definition of the Doppler angle and the reasons for limitations to its value are considered.
2. Electronic beam focusing and steering and the magnitude of time delays between the firing of successive elements are required to achieve this.

To provide you with as much information as possible about our expectations in the writing of formal submissions, instructions and guidance are given below about content, structure and layout and referencing. This will help you in the preparation of your submissions.

CONTENT

1. The Spectral Doppler Display

Give an account of the spectral Doppler imaging mode as follows:

The overall spectral Doppler display incorporates two main components, a B-mode image and a Doppler spectrum. Obtain an image of a typical spectral Doppler display including the B-mode image and the Doppler spectrum (properly citing your source reference) and include it as a figure and then answer the following questions about it. Number your answers to correspond with the following question numbers.

1. Describe the main purpose of the spectral Doppler imaging mode.
2. Explain the purpose of the B-mode image in the display and how it is used
3. The vertical scale on the Doppler spectrum represents two parameters even though only one is shown. What are they and what are their usual units?
4. In your image of the display, draw and label the scan line on the B-mode image.
5. Label the sample volume on the B-mode image and explain clearly what it represents.
6. Define the range gate and explain the relationship between the sample volume, as indicated on the B-mode image, and the range gate, clearly distinguishing between the two.
7. Label the Doppler angle cursor and explain how it is used.
8. Explain the shape of the Doppler spectrum, the meaning of its peaks and troughs, and its variation with time.
9. Find and include as a separate figure another image showing spectral broadening on the Doppler spectrum. Explain what spectral broadening is and give two possible causes of spectral broadening.

2. Blood Flow Velocity Measurement

Doppler Angle

Draw a labelled diagram showing the patient's surface, a linear transducer, a scan line approximately perpendicular to the patient's surface and a blood vessel at an angle to the surface. On this diagram, show the Doppler angle. Give a written definition of the Doppler angle based on this diagram.

The Doppler angle is normally chosen so that it lies between about 30? and 60?. Consider a scenario in which the sonographer has set a Doppler angle of 63? (that is, above the normal permissible range). In this case the system measures the Doppler shift to be 1553.0 Hz and the blood flow velocity is determined to be 43.9 cm/s with a transducer frequency of 6 MHz. However, the sonographer has, unknowingly, set the Doppler angle cursor 3? too low.

Calculate (i) the true blood flow velocity at the true Doppler angle of 66? for this case and (ii) the percentage by which the velocity value determined is in error relative to the true velocity value?

Aliasing

Given a blood flow velocity of 55 cm/s, a Doppler angle of 52?, and a transducer frequency of 7 MHz, calculate the Doppler shift frequency that would be found under the given conditions. If the pulse repetition frequency is 5.9 kHz, state the Nyquist limit frequency. Can spectral Doppler imaging be carried out without aliasing in the present case? Explain why or why not.

If aliasing did occur, draw a diagram describing its appearance in spectral Doppler imaging. Give three possible methods for alleviating aliasing artefacts (excluding base-line shifting).

3. Beam Focusing and Steering

The ultrasound beam may be focused to a point electronically and also steered to provide a beam angle which is not perpendicular to the patient's surface. Both focusing and steering of the beam is achieved by setting appropriate time delays between the emission of pulses from the various transducer elements.

The purpose of this part of the assignment is to assess your understanding of the mechanism of the electronic steering and focusing of the beam and also your knowledge of the magnitudes of the time delays involved in firing the transducer elements.

1. Give a brief written description of the main principle behind electronic beam focusing and steering mentioning, in your description, (i) transducer elements, (ii) time delays between pulse emissions from individual elements and (iii) the effect on beam shape and lateral resolution. Use a carefully labelled diagram to support your description.
2. Demonstrate the magnitudes of typical time delays between pulse emissions from different transducer elements when focusing and steering the ultrasound beam by performing the following calculation.

1. a. Consider a 300-element, linear transducer, which is 50 mm between the centre lines of the first and the three-hundredth elements. Determine the pitch of the elements, that is to say, the distance between the centre lines of successive elements.
2. At a given time, a single beam is generated by an active group of 19 elements. This beam is steered 11.5 degrees off-axis to the right as measured at the centre of the group to a focal point at a depth of 6.5 cm. Figure 1 (below) is a schematic diagram of this single group showing elements 1 to 19 (not all elements are shown) and the focal point.(Note that this diagram is not to scale. Diagrams that are not to scale are often used in diagrammatic representations. In this case, the group of elements appears to be much larger than its actual size relative to the 6.5 cm depth dimension which appears much shorter than the actual depth, and the 11.5-degree angle appears much larger than 11.5 degrees.)
3. State the order in which elements 1, 10 and 19 have to be fired. Then, calling the time at which the first element is fired, time zero, calculate the time at which the other two elements are subsequently fired. The two successive times will be given in ms, or ns as appropriate. Calculate, finally, the time delay between the firing of successive elements in the array.

Hint: You can use knowledge of the element pitch, elementary trigonometry, and the theorem of Pythagoras, to determine the three path lengths from elements 1, 10 and 19 to the focal point and hence, determine the time delays between the firing times of the three elements.

Note: Units (such as mm, cm, ms etc) must be included. A figure without units is meaningless.