Chapter 13 Medical Physics Flashcards
The piezoelectric effect is defined as:
The ability of particular materials to generate a potential difference (p.d.) by transferring mechanical energy to electrical energy
A transducer is any device that
- converts energy from one form to another
Piezoelectric Crystals
- At the heart of a piezoelectric transducer is a piezoelectric crystal
- Piezoelectric crystals are materials which produce a p.d. when they are deformed
- This deformation can be by compression or stretching
If a p.d. is applied to a piezoelectric crystal, then it
deforms, and if the p.d. is reversed, then it expands
- If this is an alternating p.d. then the crystal will vibrate at the same frequency as the alternating voltage
- Crystals must be cut to a certain size in order to induce resonance
One of the most common piezoelectric crystals is
quartz, which is made from a lattice of silicon dioxide atoms
- When the lattice is distorted, the structure becomes charged creating an electric field and, as a result, an electric current
- If an electric current is applied to the crystal, then this causes the shape of the lattice to alternate which produces a sound wave
- Due to the conventional direction of electric current, it will flow from the positive to the negative region of the crystal
A molecule in a quartz crystal. When the compression and stretching alternates, an alternating e.m.f. is induced
Applications of the Piezoelectric Transducer
- Microphone
- A piezoelectric microphone detects pressure variations in sound waves
- These can then be converted to an electrical signal for processing
Applications of the Piezoelectric Transducer
- Ultrasound
- In a piezoelectric transducer, an alternating p.d. is applied to produce ultrasound waves and sent into the patient’s body
- The returning ultrasound waves induce a p.d. in the transducer for analysis by a healthcare professional
- An ultrasound is defined as:
A high frequency sound above the range of human hearing
- This is above 20 kHz, although in medical applications the frequencies can be up to the MHz range
An ultrasound transducer is made up of a
- piezoelectric crystal and electrodes which produce an alternating p.d.
- The crystal is heavily damped, usually with epoxy resin, to stop the crystal from vibrating too much
- This produces short pulses and increases the resolution of the ultrasound device
The structure of an ultrasound transducer
A piezoelectric crystal can act as both a receiver or transmitter of
ultrasound
- When it is receiving ultrasound, it converts the sound waves into an alternating p.d.
- When it is transmitting ultrasound, it converts an alternating p.d. into sound waves
Generation:
An alternating p.d. is applied across a piezo-electric crystal, causing it to
- change shape
- The alternating p.d. causes the crystal to vibrate and produce ultrasound waves
- The crystal vibrates at the frequency of the alternating p.d., so, the crystal must be cut to a specific size in order to produce resonance
Detection:
When the ultrasound wave returns
- the crystal vibrates which produces an alternating p.d. across the crystal
- This received signal can then be processed and used for medical diagnosis
The frequency of the ultrasound is important because
- The higher the frequency of the ultrasound, the higher the resolution and the smaller structures that can be distinguished
The ultrasound gives two main pieces of information about the boundary:
- Depth: the time between transmission and receipt of the pulse (the time delay)
- Nature: amount of transmitted intensity received (will vary depending on the type of tissue)
- In an ultrasound scanner, the transducer sends out a beam of sound waves into the body
- The sound waves are
- reflected back to the transducer by boundaries between tissues in the path of the beam
- For example, the boundary between fluid and soft tissue or tissue and bone
- When these echoes hit the transducer, they generate electrical signals that are sent to the ultrasound scanner
- Using the speed of sound and the time of each echo’s return, the scanner calculates the distance from the transducer to the tissue boundary
- These distances can be used to generate two-dimensional images of tissues and organs
- The acoustic impedance, Z, of a medium is defined as:
The product of the speed of the ultrasound in the medium and the density of the medium
- This quantity describes how much resistance an ultrasound beam encounters as it passes through a tissue
- Acoustic impedance can be calculated using the equation:
Z = ρc
- Where:
- Z = acoustic impedance (kg m-2 s-1)
- ρ = the density of the material (kg m-3)
- c = the speed of sound in the material (m s-1)
- Acoustic impedance can be calculated using the equation:
Z = ρc
- Where:
- Z = acoustic impedance (kg m-2 s-1)
- ρ = the density of the material (kg m-3)
- c = the speed of sound in the material (m s-1)
Z = ρc
This equation tells us
- The higher the density of a tissue, the greater the acoustic impedance
- The faster the ultrasound travels through the material, the greater the acoustic impedance also
- This is because sound travels faster in denser materials
- Sound is fastest in solids and slowest in gases
- The closer the particles in the material, the faster the vibrations can move through the material
At the boundary between media of different acoustic impedances, some of the wave energy is
- reflected and some is transmitted
The greater the difference in acoustic impedance between the two media, the greater the
reflection and the smaller the transmission
- Two materials with the same acoustic impedance would give no reflection
- Two materials with a large difference in values would give much larger reflections
- Air has an acoustic impedance of Zair = 400 kg m-2 s-1
- Skin has an acoustic impedance of Zskin = 1.7 × 106 kg m-2 s-1
- The large difference means ultrasound would be significantly
- reflected, hence a coupling gel is necessary
- The coupling gel used has a similar Z value to skin, meaning that very little ultrasound is reflected
- The intensity reflection coefficient α is defined as:
The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave
intensity reflection coefficient α equation is
- Where:
- α = intensity reflection coefficient
- IR = intensity of the reflected wave (W m-2)
- I0 = intensity of the incident wave (W m-2)
- Z1 = acoustic impedance of one material (kg m-2 s-1)
- Z2 = acoustic impedance of a second material (kg m-2 s-1)
- This equation will be provided on the datasheet for your exam
- This ratio shows:
- If there is a large difference between the impedance of the two materials, then most of the energy will be reflected
- If the impedance is the same, then there will be no reflection
Coupling Medium
- When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body
- The soft tissues of the body are much denser than air
- If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected
- The coupling gel is placed between the transducer and the body, as skin and the coupling gel have a similar density, so little ultrasound is reflected
- This is an example of impedance matching
- Attenuation of ultrasound is defined as:
The reduction of energy due to the absorption of ultrasound as it travels through a material
The attenuation coefficient of the ultrasound is expressed in
decibels per centimetre lost for every incremental increase in megahertz frequency
- Generally, 0.5 dB/cm is lost for every 1MHz
- The intensity I of the ultrasound decreases with distance x, according to the equation:
I = I0 e−μx
- Where:
- I0 = the intensity of the incident beam (W m-2)
- I = the intensity of the reflected beam (W m-2)
- μ = the absorption coefficient (m-1)
- x = distance travelled through the material (m)
The absorption coefficient μ, will vary from
- material to material
- Attenuation is not a major problem in ultrasound scanning as the scan relies on the reflection of the ultrasounds at boundaries of materials
X-rays are
- short wavelength, high-frequency part of the electromagnetic spectrum
- They have wavelengths in the range 10−8 to 10−13 m
- X-rays are produced when fast-moving electrons rapidly decelerate and transfer their kinetic energy into photons of EM radiation
Producing X-rays
- At the cathode (negative terminal), the electrons are released by thermionic emission
- The electrons are accelerated towards the anode (positive terminal) at high speed
- When the electrons bombard the metal target, they lose some of their kinetic energy by transferring it to photons
- The electrons in the outer shells of the atoms (in the metal target) move into the spaces in the lower energy levels
- As they move to lower energy levels, the electrons release energy in the form of X-ray photons
When an electron is accelerated, it gains energy equal to the
- electronvolt; this energy can be calculated using:
Emax = eV
- This is the maximum energy that an X-ray photon can have
the maximum X-ray frequency fmax, or the minimum wavelength λmin, that can be produced is calculated using the equation:
- Where:
- e = charge of an electron (C)
- V = voltage across the anode (V)
- h = Planck’s constant (J s)
- c = speed of light (m s-1)
Using X-rays in Medical Imaging
- X-rays have been highly developed to provide detailed images of soft tissue and even blood vessels
- When treating patients, the aims are to:
- Reduce the exposure to radiation as much as possible
- Improve the contrast of the image
Reducing Exposure
- X-rays are ionising, meaning they can cause damage to living tissue and can potentially lead to cancerous mutations
- Therefore, healthcare professionals must ensure patients receive the minimum dosage possible
In order to reduce exposure, what are used
aluminium filters are used
- This is because many wavelengths of X-ray are emitted
- Longer wavelengths of X-ray are more penetrating, therefore, they are more likely to be absorbed by the body
- This means they do not contribute to the image and pose more of a health hazard
- The aluminium sheet absorbs these long wavelength X-rays making them safer
- Contrast is defined as:
The difference in degree of blackening between structures
- Contrast allows a clear difference between tissues to be seen
Image contrast can be improved by:
- Using the correct level of X-ray hardness: hard X-rays for bones, soft X-rays for tissue
- Using a contrast media
- Sharpness is defined as:
How well defined the edges of structures are
Image sharpness can be improved by:
- Using a narrower X-ray beam
- Reducing X-ray scattering by using a collimator or lead grid
- Smaller pixel size
Bones absorb
- X-ray radiation
- This is why they appear white on the X-ray photograph
- When the collimated beam of X-rays passes through the patient’s body, they are absorbed and scattered
- The attenuation of X-rays can be calculated using the equation:
I = I0 e−μx
- Where:
- I0 = the intensity of the incident beam (W m-2)
- I = the intensity of the reflected beam (W m-2)
- μ = the linear absorption coefficient (m-1)
- x = distance travelled through the material (m)
- The attenuation coefficient also depends on the energy of the X-ray photons
The intensity of the X-ray decays
- exponentially
- The thickness of the material that will reduce the X-ray beam or a particular frequency to half its original value is known as the half thickness
A good contrast is when:
- There is a large difference between the intensities
- The ratio is much less than 1.0
Computed Tomography Scanning
- A simple X-ray image can provide useful, but limited, information about internal structures in a 2D image
- When a more comprehensive image is needed, a computerised axial tomography (CAT or CT) scan is used
The main features of the operation of a CT scan are as follows:
- An X-ray tube rotates around the stationary patient
- A CT scanner takes X-ray images of the same slice, at many different angles
- This process is repeated, then images of successive slices are combined together
- A computer pieces the images together to build a 3D image
- This 3D image can be rotated and viewed from different angles
Advantages of CAT Scans
- Produces much more detailed images
- Can distinguish between tissues with similar attenuation coefficients
- Produces a 3D image of the body by combining the images at each direction
Disadvantages of CAT Scans
- The patient receives a much higher dose than a normal X-ray
- Possible side effects from the contrast media
- A radioactive tracer is defined as:
A radioactive substance that can be absorbed by tissue in order to study the structure and function of organs in the body
Radioactive isotopes, such as technetium-99m or fluorine-18, are suitable for
radioactive tracers
- They both bind to organic molecules, such as glucose or water, which are readily available in the body
- They both emit gamma (γ) radiation and decay into stable isotopes
- Technetium-99m has a short half-life of 6 hours (it is a short-lived form of Technetium-99)
- Fluorine-18 has an even shorter half-life of 110 minutes, so the patient is exposed to radiation for a shorter time
- Positron Emission Tomography (PET) is:
A type of nuclear medical procedure that images tissues and organs by measuring the metabolic activity of the cells of body tissues
A common tracer used in PET scanning is a
glucose molecule with radioactive fluorine attached called fluorodeoxyglucose
- The fluorine nuclei undergoes β+ decay – emitting a positron (β+ particle)
The radioactive tracer is
- injected or swallowed into the patient and flows around the body
- Once the tissues and organs have absorbed the tracer, then they appear on the screen as a bright area for a diagnosis
- This allows doctors to determine the progress of a disease and how effective any treatments have been
- Tracers are used not only for the diagnosis of cancer but also for the heart and detecting areas of decreased blood flow and brain injuries, including Alzheimer’s and dementia
The Process of Annihilation
- When a positron is emitted from a tracer in the body, it travels less than a millimetre before it collides with an electron
- The positron and the electron will annihilate, and their mass becomes pure energy in the form of two gamma rays which move apart in opposite directions
- Annihilation doesn’t just happen with electrons and positrons, annihilation is defined as:
When a particle meets its equivalent antiparticle they are both destroyed and their mass is converted into energy
- As with all collisions, the mass, energy and momentum are conserved
Once the tracer is introduced to the body it has a short
half-life, so, it begins emitting positrons (β+) immediately
- This allows for a short exposure time to the radiation
- A short half-life does mean the patient needs to be scanned quickly and not all hospitals have access to expensive PET scanners
In PET scanning:
- Positrons are emitted by the decay of the tracer
- They travel a small distance and annihilate when they interact with electrons in the tissue
- This annihilation produces a pair of gamma-ray photons which travel in opposite directions
Detecting Gamma-Rays from PET Scanning
- The patient lays stationary in a tube surrounded by a ring of detectors
- Images of slices of the body can be taken to show the position of the radioactive tracers
- The detector (for pet scanning) consists of two parts:
-
Crystal Scintillator – when the gamma-ray (γ-ray) photon is incident on a crystal, an electron in the crystal is excited to a higher energy state
- As the excited electron travels through the crystal, it excites more electrons
- When the excited electrons move back down to their original state, the lost energy is transmitted as visible light photons
- Photomultiplier -The photons produced by the scintillator are very faint, so they need to be amplified and converted to an electrical signal by a photomultiplier tube
Detecting gamma rays with a PET scanner
Creating an Image from PET Scanning
- The γ rays travel in straight lines in opposite directions when formed from a positron-electron annihilation
- This happens in order to conserve momentum
- They hit the detectors in a line – known as the line of response
- The tracers will emit lots of γ rays simultaneously, and the computers will use this information to create an image
- The more photons from a particular point, the more tracer that is present in the tissue being studied, and this will appear as a bright point on the image
- An image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons
Calculating Energy of Gamma-Ray Photons
- In the annihilation process, both mass-energy and momentum are conserved
- The gamma-ray photons produced have an energy and frequency that is determined solely by the mass-energy of the positron-electron pair
- The energy E of the photon is given by
E = hf = mec2
- Where:
- me = mass of the electron or positron (kg)
- h = Planck’s constant (J s)
- f = frequency of the photon (Hz)
- c = the speed of light in a vacuum (m s–1)
- The momentum p of the photon is given by
- Where:
- me = mass of the electron or positron (kg)
- h = Planck’s constant (J s)
- f = frequency of the photon (Hz)
- c = the speed of light in a vacuum (m s–1)
