Ultrasound & X-rays (CIE A Level Physics)

[1]

Data for the thickness x of the samples of bone and of muscle, together with the linear attenuation coefficients μ of the radiation in bone and in muscle, are given in Table 10.1.

Table 10.1

Calculate the ratio

.

ratio = ........................................ [2]

[3]

[2]

State the approximate value of the intensity reflection coefficient at the boundary between the two media when:

•    Z₁ is almost equal to Z₂

intensity reflection coefficient = ................................

•    Z₁ is very different from Z₂.

intensity reflection coefficient = ................................

[2]

An X-ray image is taken of the skull of a patient. Another patient has a CT scan taken of their entire head.

Describe how the image produced during CT scanning differs from the image produced by X-ray imaging.

Ultrasound is thought to be more suitable than X-rays for scanning an unborn foetus.

Some values of linear attenuation coefficient of different media are shown in Table 1.1

Table 1.1

Fig. 1.1 shows a diagram of a piezoelectric transducer.

Fig. 1.1

With reference to Fig. 1.1:

Two patients arrive at a hospital. One patient is a child with a broken arm, the other is a pregnant woman coming in for a check-up for her unborn foetus.

Over the course of the diagnosis and treatment of the child’s broken arm, several images of the arm are required.

Similarly, to check the progress of a woman’s pregnancy, several images of the foetus are required.

For each scenario, suggest the most appropriate imaging technique to use and give two reasons for the choice.

Ultrasound is incident on a boundary between two materials. Some of the ultrasound is reflected at the boundary and the rest is transmitted across the boundary.

The acoustic impedance of air is 4.29 × 10² kg m^–2 s^–1

The acoustic impedance of coupling gel is 1.48 × 10⁶ kg m^–2 s^–1  

The acoustic impedance of skin is 1.65 × 10⁶ kg m^–2 s^–1

An X-ray image showing the cross-section of the bone and muscle is shown in Fig. 1.1.

Fig. 1.1

Parallel X-ray beams of intensity are incident on the muscle and bone as shown. The emergent beam after passing through muscle alone has an intensity of and an intensity of  after passing through the bone and the muscle.

(i)

Determine, in terms of , the intensities and of the emergent X-rays.

 

The linear attenuation coefficient of bone is 2.90 cm⁻¹

The linear attenuation coefficient of muscle of 0.95 cm⁻¹.

[4]

Most modern ultrasound transducers are made from the piezoelectric material lead zirconate titanate (PZT).

Fig. 1.1 shows the effect on the structure of a crystal of PZT when an alternating potential difference is applied across it.

Fig. 1.1

An eye can be imaged using either an A-scan or a B-scan ultrasound. Fig. 1.2 shows the position of a piezoelectric transducer being used during an A-scan of an eye.

Fig. 1.2

Fig. 1.3 shows an ultrasound A-scan trace from the scan of an eye.

Fig. 1.3

The speed of ultrasound in the eye is 1520 m s^–1 and the speed of ultrasound in the lens is 1670 m s^–1.

Use Fig. 1.3 to calculate the thickness of

The graph in Fig. 1.4 shows the attenuation of the intensity of ultrasound at a frequency of 3 MHz with depth.

Fig. 1.4

Table 1.1

The data in Table 1.1 shows how the attenuation coefficient μ depends on the energy of the X-rays in bone and muscle. 

Table 1.1

maximum X-ray energy / keV	/ cm−1	/ cm−1
50	3.32	0.54
100	0.60	0.21
250	0.32	0.16
4000	0.087	0.049

Using the data in Table 1.1, state and explain which X-ray energy would produce an image of a bone next to a muscle with the best contrast.

For X-ray energies around 30 keV and below, the attenuation coefficient μ is approximately proportional to the cube of the proton number Z of the absorbing material.

The proton numbers of muscle, bone and some contract media are shown in Table 1.2

Table 1.2

substance	main elements
muscle	,  ,
bone	,  ,  ,  ,
contrast media	,

Using the information in Table 1.2

The graph in Fig. 1.1 shows how the attenuation coefficient μ of muscle varies with photon energy E.

Fig. 1.1

Using Fig. 1.1, explain why X-rays with energies less than 20 keV are usually filtered out of the beam.

An X-ray beam of energy 20 keV and intensity  is incident on a sample of muscle and bone as shown in Fig. 1.2. The emergent beam intensities from the muscle and bone are  and  respectively.

Fig. 1.2

Using the graph in Fig. 1.1, calculate the ratio of intensities to compare the attenuation produced by 1 cm of bone and 1 cm of muscle.

An ultrasound investigation was used to identify a small volume of an unknown substance in a patient. It is suspected that this substance is either a cyst or a tumour.

During the ultrasound investigation, an ultrasound pulse of frequency 5 MHz is passed through soft tissue and then into the small volume of the unknown substance.

The ratio of the reflected intensity to the incident intensity for the ultrasound pulse reflected at the boundary was found to be 7.54 × 10⁻⁵.

Table 1.1 shows some information about the density and speed of ultrasound in soft tissue, cysts and tumours.

Table 1.1

Fig. 1.1 shows a beam of X-rays of energy 20 keV incident normally on some soft tissue which contains the cyst.

The cyst is located 2.1 cm from the surface of the soft tissue.

Fig. 1.1 (not to scale)

The attenuation constant of the soft tissue is 0.85 cm^–1. The incident intensity of the beam is 4.6 × 10³ W m^–2.

The X-ray beam is switched on for a time t.

Determine the energy of the X-ray beam incident on the front surface of the cyst each second. State any assumptions you make.

The ratio of the intensities of the emergent X-ray beams X and Y is determined to be

Suggest a different imaging technique that could be used to image the cyst. Explain one advantage and one disadvantage of using this technique over ultrasound.