Minggu, 05 Desember 2010

Physics: Diagnostic Imaging

Diagnostic Imaging

In the exam, you are expected to know about:
  • Ultrasound imaging;
  • Reflection and transmission characteristics of sound waves at tissue boundaries, acoustic impedance;
  • Advantages and disadvantages of ultrasound imaging in comparison with alternatives including safety issues and resolution;
  • Piezoelectric devices;
  • Principles of generation and detection of ultrasound pulses;
  • A-scan and B-scan; 
  • Examples of applications.
Ultrasound is any sound that is higher than the upper limit of human hearing. 

Question 1  What is the upper limit of human hearing?  ANSWER
The upper limit of human hearing is 20 000 Hz

Bats and dolphins use frequencies in the range of 30 - 100 kHz for echo location and in the Second World War experiments in ultrasound were tried out to detect submarines.  Ultrasound imaging is a proven method of investigating objects internally without causing damage.  It is widely used in medicine because it is non-invasive.

Generation and Detection of Ultrasound
The ultrasound probe or transducer is used to generate and detect the ultrasound waves.  The most common method is by use of a piezoelectric transducer.  If you squeeze or stretch a crystal of quartz (easier than might be thought) a voltage is induced.  It can be high enough for a spark to jump.  Gas lighters use the effect.  Conversely, if you apply a voltage to a piezoelectric material, you can make it change shape.  If the voltage is alternating, the crystal will vibrate.  Maximum energy transfer occurs when the crystal is in resonance.

Question 2  What are the conditions needed for resonance?  ANSWER
The forcing frequency is the same as the natural frequency.

The material, usually lead zirconate titanante (PZT), an artificial ceramic, has a thickness of half a wavelength of the ultrasound wave.

The lens protects the PVT slice and acts to converge the beam slightly.  The beam consists of short pulses of frequencies of several megahertz.  The vibrations are damped by the backing block which is made of epoxy resin.  The whole is contained in a metal case which protects the probe mechanically and electrically.

Question 3  A sound wave has a frequency of 5 MHz and travels at 1500 m/s.  What is the wavelength? ANSWER
 Use c = fl
l = c/f = 1500 m/s ÷ 5 × 106 = 3 ×10-4 m/s = 0.3 mm

Ultrasound in the Body
When ultrasound passes into the body:
  • it is a longitudinal wave travelling in a material
  • it is reflected at boundaries between different tissues;
  • it is absorbed by tissues.
The extent to which the ultrasound is absorbed or reflected gives information about the structures below.

The table below gives some ultrasound properties of some body tissues:

Material
Density (kg m-3)
Velocity (m/s)
Acoustic Impedance (=rc)  (kg m-2 s-1)
Air
1.3
330
429
Water
1000
1500
1.50 × 106
Blood
1060
1570
1.59 × 106
Brain102515401.58 × 106
Fat92514501.38 × 106
Muscle107515901.70 × 106
Bones (varies)190840807.78 × 106
PZT Transducer7650379129.0 × 106
Quartz Transducer2650573615.2 × 106


The acoustic impedance is the product of the density and speed of sound in the material.

Question 4 What is the thickness of a slice of PZT material if its fundamental resonant frequency is 1.5 MHz? ANSWER

Find the wavelength of the resonant frequency: l = c/f = 3791 ÷ 1.5 × 106
= 2.53 x 10-3 m = 2.53 mm
Therefore the wavelength will be half this, 1.27 mm



Question 5  The time delay for a pulse going through fat is 0.133 ms.  How deep is the fat?
ANSWER
 The time taken to reach the boundary is 0.5 x 1.33 x 10-4 = 0.665 x 10-4s
Distance = speed x time = 1450 m/s x 0.665 x 10-4s = 0.096 m (= 9.6 cm)

If the probe is placed straight on to the skin, almost all the energy will be reflected.  So the probe has to have a coupling medium between it and the skin.  This is a gel or an oil.  If there is gas anywhere, it can cause big problems for imaging.

When the waves reach a boundary, a small amount, about 1% gets reflected.  However if the difference in acoustic impedance between two tissues is large, a high proportion of the ultrasound waves are reflected.  For example the boundary between lung tissue and the air in the lungs leads to a 99.9% reflection, making it impossible to view structure behind the lungs.


Imaging in the Body
The ultrasound passes through the tissue and is reflected at various boundaries as shown:


The resolution of the beam means the smallest distance that can be discriminated in the image.  The higher the frequency, the better the resolution.  However as the beam passes through, the sound waves get scattered and absorbed by the molecules.  This attenuation is more marked with higher frequency.  Therefore a compromise has to be made.  The optimum frequency for imaging the brain and abdomen is roughly 1 - 3 MHz.  
  • Axial resolution is the resolution in the direction of the beam.  It can be improved by making the pulses short.  While the transducer is producing pulses, it cannot detect echoes. Therefore it makes sense to make the pulses as short as possible.
  • Lateral resolution is determined by the beam width.  If two structures are within one beam, they cannot be discriminated.
  • Resolution is limited by diffraction effects.  Just like in light, objects less than 1 wavelength apart cannot be resolved, the same is true of sound.  1 MHz waves can discriminate structures that are 1.5 mm apart.
 When the return pulses are received, the transducer turns them into electrical signals to be stored:
  • using video tape;
  • on a storage CRO;
  • as digital data for analysis by a computer.
There are a number of ways in which ultrasound can be used.  We will consider:
  • A-scan, which is the amplitude modulated display
  • B-scan, which is a brightness modulated display.
The two are compared in the diagram below:


A-scans are used where the anatomy of a section is well know and a precise depth measurement is needed.  One example is where the position of the midline of the brain is needed.  Any delay could indicate the presence of a tumour or a fluid filled space.

The B-scan is the basis of two-dimensional scanning.  The transducer is moved about to view the body from a variety of angles.  The probe can be moved in a line (linear scan), or rotated from a particular position (sector scan).



The two movements can be combined to give a compound scan.  It requires considerable skill and a good knowledge of anatomy for the sonographer to get a decent image and to interpret it.  However it is a widely used technique for assessing the growth of the prenatal foetus.  It can give early indications of any problems that may arise.  

Ultrasound is used in other investigations such as detections of cysts, abscesses, and tumours.

Real time B-scans  use a linear array of up to 100 transducers to get a cross section of the body.  Moving images are possible.

Ultrasound can be used with the Doppler effect to watch the movement of blood through the blood vessels.

Advantages and Disadvantages of Ultrasound Scanning
Ultrasound is generally a very safe diagnostic technique:
  • There are no known hazards with low frequency (low energy) beams.
  • It is non-invasive.
  • There is no discomfort apart from a cold probe!
  • More effective than X-ray techniques in producing images of soft tissue;
  • The equipment is relatively inexpensive, can be moved about very easily, and does not need a specialist room.
  • There are no hazards for the operator.
However:
  • The sonographer has to be skilled at operating the probe and its associated equipment to get a decent image.
  • The image needs skilful interpretation.
  • Attenuation can reduce the resolution of the image.
  • Bone absorbs ultrasound so that brain images are hard to get;
  • Gas-soft tissue interfaces reflect 99.9% of the incident energy.  Images of tissues on the far side of lungs are impossible to get.
High energy ultrasound waves can be used for therapeutic purposes.  Low intensity ultrasound can be used in healing wounds and relieving discomfort and pain in conditions like arthritis.  High intensity beams can shatter kidney stones.  Ultrasound treatment has to be done with care because:
  • the temperature in the tissues can rise;
  • the pressure changes can rupture cells;
  • bone is a strong absorber of ultrasound.
While this would not cause many problems for an adult, it must be avoided where there is a growing foetus.

Question 6  Write down two advantages of using ultrasound as a diagnostic tool and two disadvantages.  ANSWER
Advantages
  • There are no known hazards with low frequency (low energy) beams.
  • It is non-invasive.
  • There is no discomfort apart from a cold probe!
  • More effective than X-ray techniques in producing images of soft tissue;
  • The equipment is relatively inexpensive, can be moved about very easily, and does not need a specialist room.
  • There are no hazards for the operator.
Disadvantages:
  • The sonographer has to be skilled at operating the probe and its associated equipment to get a decent image.
  • The image needs skilful interpretation.
  • Attenuation can reduce the resolution of the image.
  • Bone absorbs ultrasound so that brain images are hard to get;
  • Gas-soft tissue interfaces reflect 99.9% of the incident energy.  Images of tissues on the far side of lungs are impossible to get.


SummaryUltrasonic waves are above 20 kHz
Medical ultrasound has frequencies from 1 to 15 MHz.
Piezoelectric effects are used in the probes.
The greater the difference in acoustic impedance, the more the sound is reflected.
Coupling gels are used between the probe and the skin.
Resolution is improved with higher frequency.
Attenuation is increased with higher frequency.
A-scan is used to measure the depth of an organ.
B-scans produce a two dimensional picture of the body.
Axial resolution is improved by using shorter pulses.
Lateral resolution is improved by using narrower beams.
Ultrasound offers many advantages over X-rays

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