X-Ray Production

• X-rays are a form of electromagnetic radiation
• They are produced when high-speed electrons hit metal targets
  
• Production of X-rays:
  • Heated filament undergoes thermionic emission, releasing high-speed electrons
  • P.d. between cathode and anode causes electrons to accelerate
  • Electrons bombard metal target, emitting x-rays which leave through the window
  • Some kinetic energy of electrons transferred into the metal target as thermal energy
  • The metal target is cooled by water or spun around to increase target area
• Tube Current: is the rate of arrival of electrons at metal target
  
• Some ‘soft’ x-rays are always produced which cannot fully pass through the patient and contribute to the total radiation dose of the patient
• to reduce the radiation dose, hence cut off ‘soft’ x-rays, an aluminum filter should be used to absorb them

X-ray Spectrum

• X-rays emerge from the tube with a range of energies as represented in the spectra below
  
• The spectra is made up of two components:
  • Braking Radiation: X-ray photons released when electrons decelerate as it strikes the anode, they are attracted by the nucleus of an atom in the anode and loses energy
  • Characteristic Radiation: Rearrangement of electrons in the anode when a high speed electron strikes, excites orbital electrons which then de-excite, emitting photons and giving rise to spectrum lines; specific to the material of the anode

X-ray Imaging

• X-ray radiation blackens photographic plates in the same way as visible light
• Degree of blackening depends on total x-ray exposure
• It is mostly used to distinguish bones from tissue because bones have a higher density than the surrounding tissue
• It can be used to identify organs if the densities of the surrounding tissues are sufficiently different

X-ray Quality

• Sharpness is the ease with which the edge of a structure can be determined
  • Improving sharpness of x-ray:
    • Reduce the area of target anode
    • Reduce aperture size (window): This reduces the beam width
    • Place lead grid in front of photographic film: This absorbs scattered x-rays and reduces partial images
• Contrast is the visual difference between the areas of blackening and light
  • Improving contrast of x-ray:
    • Increase the exposure time
    • Use harder x-rays: This increases penetration power
    • Reduce scattering of x-ray beam
    • Use fluorescent ‘contrast medium’

X-ray Intensity

• In the medium where x-rays are absorbed, intensity of a parallel x-ray bean decreases by a constant fraction in passing through equal small thickness of the medium
• This gives rise to an exponential decrease in the intensity of the transmitted beam:
  • I = I₀e^-μx
  • I is the instantaneous intensity of the x-ray beam
  • I₀ is the initial intensity of the x-ray beam
  • x is the thickness of the medium passed by x-ray
  • μ is the linear absorption coefficient unique to medium, dependent on photon energy and in
    mm^-1
• This can be represented graphically:
  
• Half-value Thickness (x_½): is the thickness of the medium required to reduce the transmitted intensity to one half of its initial value
• It can be related to the linear absorption coefficient by:
  • x_½ × μ = ln 2

Computed Tomography (CAT/CT Scan)

• X-ray imaging only produces a 2-dimensional image with no impression of depth, it cannot tell if a tissue is near to the surface or deep within the body
• Tomography is a procedure which forms a 3-dimensional plane of the object
• The diagram below shows the procedure
  
• Putting together several planes produces a whole 3-dimensional image which can be rotated

Voxel Development in CT Scans

• Voxel is a small cube in a three-dimensional image
• The number in each square is the density that the computer will register for that section of the object
• As the scanner goes around each part, it has a different density which the computer can model
• The computer then puts these together to form a 3-dimensional shape
• Building the image
  
• For a well-defined image in a CT scan, we need voxels to be small and to do so:
  • X-ray beams must be well collimated so that it consists of parallel ray — rays must not spread
  • The detector must consist of a regular array of tiny detecting elements — the smaller, the detector the better the image
• Advantages of a CT Scan:
  • It produces images that show 3-dimensional relationships between different tissues
  • It can distinguish tissues with quite similar densities

Ultrasonic Waves

• Ultrasound is any sound wave that has a frequency above the upper limit of human hearing, 20 kHz
• Piezo-electric transducers can be used to record and produce ultrasonic waves
• A diagram of a Piezo-electric transducer:
  
• Quartz crystal is the macromolecule formed by SiO₂
• Generating Ultrasonic Waves:
  • Charged atoms of a transducer in an electric field move closer to oppositely charged plates and the overall crystal either compresses or extends:
    
  • When an alternating voltage with frequency f is applied to the crystal, it causes it to contract and expand at the same frequency of f
  • This acts as the vibrating source of ultrasound waves
• Receiving Ultrasonic Waves:
  • Ultrasonic waves change pressure in a medium
  • Charged atoms in the crystal shift position closer to the plates
  • Opposite charges are induced in the silver plates
  • Induced potential difference across the plates
  • Potential difference fluctuates which can be processed

Reflection of Ultrasonic Waves

• Ultrasound requires ultrasonic waves to pass from one medium to another
• When a beam of ultrasound wave reaches a boundary between two different media, the beam is partially refracted and partially reflected
  
• From the law of conservation of energy:
  • I = I_R + I_T
• Specific Acoustic Impedance (Z): is the product of the density of the medium and the speed of sound in the medium
  • Z = ρc
• Between two media, the difference in acoustic impedance determines the fraction of incident intensity that is reflected
• Intensity Reflection Coefficient (α): is the ratio of the intensity of the reflected wave and the intensity of the incident wave
  • α = ^I_R/_I = ^{(Z₂ – Z₁)²}/_{(Z2 + Z1)²}
• Comparing acoustic impedances (^I_R/_I):
  • A very large fraction is reflected at the air-tissue boundary
  • A large fraction is reflected at the tissue-bone boundary
  • A very little fraction is reflected at the boundary between soft tissues
• A gel is applied before carrying out scan because when the wave travels in or out of the body, there is:
  • very little transmission at an air-skin boundary
  • almost complete transmission at a gel-skin boundary because acoustic impedance of gel and skin are very similar

Attenuation of Ultrasonic Waves

• Similar to x-rays, ultrasonic waves are also absorbed by the medium in which they are passing through
• They also follow the same decay equation as x-rays:
  • I = I₀e^-kx
  • Note: The constant is different
  • k is called the absorption coefficient

Ultrasound Imaging Procedure

• A transducer is placed in contact with the skin and a gel acting as a coupling medium
• Pulses of ultrasound are directed into the body
• The wave is reflected at the boundary between tissues
• The reflected pulse is detected and processed
• The time for return of echo gives information on the depth
• The amount of reflection gives information on the structures
• Two techniques for display:
  
  • A-scan: Measures the distance of different boundaries from the transducer, held in one position graphically
  • B-scan: Repeats A-scan from multiple angles to form a 2-dimensional image

Nuclear Magnetism

• Atomic nuclei with an odd number of protons behave as tiny magnets when introduce to a magnetic field
• Hydrogen nucleus (proton) is used most because it is abundant in all organic tissues
• When there is no magnetic field;
  • All protons are aligned randomly
• When a magnetic field is introduced:
  • Most protons align themselves with ‘north’ facing ‘south’ — stable low energy state
  • Some protons align themselves in the opposite way with ‘south’ facing ‘south’ — unstable high energy state

Nuclear Magnetic Resonance

• Aligned protons are not stationary; the spin on their axis of rotation
  
• Atomic Spin: is a fundamental property (like charge or mass) of a subatomic particle that defines how the particle rotates on its axis
• Precession: The movement of the axis of rotation of a spinning object (proton) around another external axis
• Larmor Frequency (ω₀): The angular frequency of the circular path of precession of the object (proton)
  
• MRI Scanners use a very strong external magnetic field causing ω₀ to be in the radio frequency range

Relaxation Times

• The protons in high energy state are unstable so they must ‘relax’ and come back to their lower energy state
• The excess energy is transmitted back as radio waves which can be detected
• The time taken for these radio waves to be detected determines the relaxation time
• Relaxation Time: is the time taken for a nucleus to fall back to a lower energy state
• Relaxation times depend on the environment of the protons:
  • Water and watery tissues: Several seconds — high
  • Fatty tissues: Hundreds of milliseconds — low
  • Cancerous tissues: intermediate

MRI Scanning

• A large uniform magnetic field causes all protons in the body to have the same Larmor frequency
• A non-uniform magnetic field is applied to locate a particular position of a proton within a person
• Procedure of an MRI:
  • A strong, constant magnetic field is applied along the body
  • Hydrogen nuclei precess about the direction of the field
  • A radio frequency (r.f.) pulse is applied
  • The pulse is at the Larmor frequency which causes resonance in the hydrogen nuclei
  • On relaxation, the nuclei de-excite and emit a pulse of r.f.
  • R.f. pulses are detected, processed and displayed
  • A calibrated non-uniform field enables position of nuclei to be located and for location of detection to be changed

Comparing Medical Imaging Methods