Suggest the advantage in medical diagnosis of using ultrasound of frequency 1 MHz rather than 0.1 MHz.

Calculate the density of skin.

Outline how ultrasound is generated for medical imaging.

State the property of protons used in nuclear magnetic resonance (NMR) imaging.

Outline the formation of a B scan in medical ultrasound imaging.

Calculate the acoustic impedance Z of muscle.

Outline why the fracture in a broken bone can be seen in a medical X-ray image.

Describe how the measurement in (b) provides diagnostic information for the doctor.

State and explain, with reference to you answer in (a)(i), what needs to be done to produce a clear image of the leg artery using X-rays.

In nuclear magnetic resonance (NMR) protons inside a patient are made to emit a radio frequency electromagnetic radiation. Outline the mechanism by which this radiation is emitted by the protons.

The diagram shows X-rays incident on tissue and bone.

The thicknesses of bone and tissue are both 0.054 m.

The intensity of X-rays transmitted through bone is I_b and the intensity transmitted through tissue is I_t.

The following data are available.

Mass absorption coefficient for bone = mass absorption
coefficient for tissue = 1.2 × 10^–2$$m²$$kg^–1
Density of bone = 1.9 × 103 kg$$m^–3
Density of tissue = 1.1 × 103 kg$$m^–3

Calculate the ratio $\frac{I_{\text{b}}}{I_{\text{t}}}$.

the radio-frequency signal emitted towards the patient.

the non-uniform magnetic field applied to the patient.

the large uniform magnetic field applied to the patient.

State a typical frequency used in medical ultrasound imaging.

In nuclear magnetic resonance (NMR) imaging radio frequency electromagnetic radiation is detected by the imaging sensors. Discuss the origin of this radiation.

Ultrasound of intensity 50 mW m^-2 is incident on a muscle. The reflected intensity is 10 mW m^-2. Calculate the relative intensity level between the reflected and transmitted signals.

Describe one advantage and one disadvantage of using high frequencies ultrasound over low frequencies ultra sound for medical imaging.

Show that the attenuation coefficient for bone of density 1800 kg m^–3, for X-rays of 20 keV, is about 7 cm^–1.

Explain, with appropriate calculations, why a gel is used between the transducer and the skin.

Show that the ratio $\frac{I_{\mathrm{b}}}{I_{\mathrm{t}}}$ is close to 1.

Determine, in terms of I₀, the intensity of ultrasound that is reflected at the muscle–bone boundary.

Suggest one reason why doctors use ultrasound rather than X-rays to monitor the development of a fetus. 

Explain the cause of the radio-frequency emissions from a patient’s body during nuclear magnetic resonance (NMR) imaging.

The density of muscle is 1200 kg m^–3. Calculate the ratio of intensities to compare, for a beam of 20 keV, the attenuation produced by 1 cm of bone and 1 cm of muscle.

In the ultrasound scan the frequency is chosen so that the distance between the transducer and the organ is at least 200 ultrasound wavelengths. Estimate, based on your response to (b)(ii), the minimum ultrasound frequency that is used.

Outline how a gradient field allows NMR to be used in medical resonance imaging.

The acoustic impedance of soft tissue is 1.65 × 106 kg m^-2 s^-1. Show that the speed of sound in the soft tissue is approximately 1500 m s^–1.

A physician has a range of frequencies available for ultrasound. Comment on the use of higher frequency sound waves in an ultrasound imaging study.

A parallel beam of X-rays travels through 7.8 cm of tissue to reach the bowel surface. Calculate the fraction of the original intensity of the X-rays that reach the bowel surface. The linear attenuation coefficient for tissue is 0.24 cm^–1.

The fluid in the bowel has a similar linear attenuation coefficient as the bowel surface. Gases have much lower linear attenuation coefficients than fluids. Explain why doctors will fill the bowel with air before taking an X-ray image.

Describe how an ultrasound transducer produces ultrasound.

Ultrasound of intensity 0.012 W$$cm^–2 is incident on a water–muscle boundary. The acoustic impedance of water is 1.50 x 10⁶ kg$$m^–2$$s^–1.

The fraction of the incident intensity that is reflected is given by

$\frac{{\left(Z_2-Z_1\right)}^2}{{\left(Z_2+Z_1\right)}^2}$

where Z₁ and Z₂ are the acoustic impedances of medium 1 and medium 2.

Calculate the intensity of the reflected signal.

State what is meant by half-value thickness in X-ray imaging.

A monochromatic X-ray beam of energy 20 keV and intensity I₀ penetrates 5.00 cm of fat and then 4.00 cm of muscle.

Calculate, in terms of I₀, the final beam intensity that emerges from the muscle.

Compare the use of high and low energy X-rays for medical imaging.