Medical Physics

AS Unit 4

Option B: Medical Physics

Learners should be able to demonstrate and apply their knowledge and understanding of:
a) The nature and properties of X-rays
b) The production of X-ray spectra including methods of controlling the beam intensity and photon energy
c) The use of high energy X-rays in the treatment of patients (therapy) and low energy X-rays in diagnosis
d) The equation [math]I = I_0 exp(-μx)[/math] for the attenuation of X-rays
e) The use of X-rays in imaging soft tissue, and fluoroscopy to produce real time X-rays using image intensifiers
f) Techniques of radiography including using digital image receptors
g) The use of a rotating beam X-ray computed tomography (CT) scanner
h) The generation and detection of ultrasound using piezoelectric transducers
i) Scanning with ultrasound for diagnosis including A-scans and B-scans incorporating examples and applications
j) The significance of acoustic impedance, defined by [math]Z = cp[/math] for the reflection and transmission of sound waves at tissue boundaries, including the need for a coupling medium
k) The use of the Doppler equation [math]\frac{\Delta f}{f_0} = \frac{2v}{c}[/math] to study blood flow using an ultrasound probe
l) The principles of magnetic resonance with reference to precession nuclei, resonance and relaxation time, and to apply the equation [math]f = 42.6 \times 10^6 \, B[/math] for the Lamor frequency
m) The use of MRI in obtaining diagnostic information about internal structures
n) The advantages and disadvantages of ultrasound imaging, X-ray imaging and MRI in examining internal structures
o)

The effects of α, β, and γ radiation on living matte

the Gray (Gy) as the unit of absorbed dose and the Sievert (Sv) as the unit of equivalent dose and effective dose. Define absorbed dose as energy per kilogram
p)

The use of the equations

• equivalent dose = absorbed dose × (radiation) weighting factor [math]H = DW_R[/math]

• effective dose = equivalent dose × tissue weighting factor E HW = T
q) The uses of radionuclides as tracers to image body parts with particular reference to technetium-99m (Tc-99m)
r) The use of the gamma camera including the principles of the collimator, scintillation counter and photomultiplier / CCD
s) Positron emission tomography (PET) scanning and its use in detecting tumours

  • a)    Nature and Properties of X-Rays

  • Electromagnetic Radiation:
  • X-rays are a form of electromagnetic radiation with wavelengths typically in the range of 0.01 to 10 nanometers. They lie between ultraviolet light and gamma rays in the EM spectrum.
  • Figure 1 Electromagnetic radiation waves
  • High Energy and Penetration:
  • Because of their high frequency and energy (ranging from a few keV to several MeV), X-rays are highly penetrating.
  • They can pass through soft tissues but are absorbed more by denser materials like bone, which is why they are useful in medical imaging.
  • Figure 2 High Energy and penetration
  • Ionizing Radiation:
  • X-rays are ionizing; they have enough energy to remove tightly bound electrons from atoms, which can lead to molecular damage.
  • This property is both useful (in cancer treatment) and a concern (due to potential radiation damage).
  • Production Mechanisms:
  • X-rays are typically produced by accelerating electrons to high speeds and colliding them with a metal target, resulting in:
  • Bremsstrahlung Radiation:
  • A continuous spectrum produced as electrons decelerate.
  • Figure 3 Bremsstrahlung radiation
  • Characteristic X-Rays:
  • Discrete energy lines produced when electrons knock inner-shell electrons out of target atoms, and electrons from higher energy levels drop down to fill the vacancy.

  • b)   Production of X-Ray Spectra

  • X-Ray Tube:
  • In an X-ray tube, a heated cathode emits electrons that are accelerated toward a metal anode (often tungsten) by a high voltage.
  • When these high-energy electrons hit the anode, they decelerate rapidly, producing X-rays.


    Figure 4 Production of X-rays spectra

  • Controlling Beam Intensity:
  • – Tube Current (mA): Increasing the current raises the number of electrons hitting the target per unit time, thus increasing the X-ray intensity.
  • – Exposure Time: The longer the exposure, the more X-ray photons are generated.
  • Controlling Photon Energy:
  • – Accelerating Voltage (kVp ): Determines the maximum kinetic energy of the electrons, and hence the maximum energy of the emitted X-rays. Higher kVp results in higher-energy X-rays.
  • – Filtration: Filters (often made of aluminum) are used to absorb low-energy photons, which do not contribute to image quality but increase patient dose. This “hardens” the beam, shifting the average photon energy upward.
  • X-Ray Spectrum:
  • The spectrum comprises a continuous component (from Bremsstrahlung) and characteristic peaks (from the target material’s atomic transitions).

  • c)    Applications in Therapy and Diagnosis

  • ⇒ High-Energy X-Rays for Therapy:
  • Radiotherapy:
  • High-energy X-rays (often in the MeV range) are used to treat cancer by damaging the DNA of tumor cells. Their deep penetration allows them to target tumors within the body while sparing superficial tissues.
  • Figure 5 High energy X-ray for therapy
  • Low-Energy X-Rays for Diagnosis:
  • – Diagnostic Radiography:
  • Lower-energy X-rays are used for imaging bones and soft tissues. They provide good contrast between tissues of different densities (e.g., bone vs. muscle), which is essential in techniques such as chest radiographs, dental X-rays, and CT scans.


    Figure 6 Low Energy X-rays

  • d)   Attenuation of X-Rays

  • ⇒ Exponential Attenuation Law:
  • As X-rays pass through matter, their intensity diminishes according to:
  • [math]I = I_0 exp⁡〖(-μx)[/math]
  • Where:
  • – I is the transmitted intensity,
  • – ​[math]I_o[/math] is the incident intensity
  • – μ is the linear attenuation coefficient (dependent on the material and X-ray energy),
  • – x is the thickness of the material.
  • ⇒ Implication:
  • This equation is used to determine the required shielding (e.g., lead aprons) and to predict how different tissues will absorb X-rays in diagnostic imaging.

  • e) Imaging Soft Tissue and Fluoroscopy

  • ⇒ Imaging Soft Tissue:
  • Contrast Agents:
  • Since soft tissues have similar densities, contrast agents (like iodine or barium) are often used to enhance image contrast in procedures such as angiography or gastrointestinal studies.
  • Computed Tomography (CT):
  • Uses X-rays to create cross-sectional images of the body, offering high contrast between different soft tissues.
  • Figure 7 Imaging soft tissues
  • ⇒ Fluoroscopy:
  • Real-Time Imaging:
  • Fluoroscopy uses a continuous X-ray beam to produce real-time images, which are especially useful for guiding procedures such as catheter insertions.
  • Image Intensifiers:
  • These devices convert incoming X-rays into visible light and amplify the image, allowing for the display of moving images with enhanced brightness and contrast.
  • Applications:
  • Widely used in interventional radiology, orthopedic procedures, and diagnostic studies where dynamic imaging is needed.

  • f)     Techniques of Radiography Including Digital Image Receptors

  • Radiography is a non-invasive imaging technique that uses X-rays to create images of the internal structures of the body.
  • ⇒  Conventional Radiography
  • Uses X-ray film as a detector.
  • The film darkens in response to X-ray exposure, creating a negative image where denser materials (like bones) appear white.
  • ⇒  Digital Radiography (DR)
  • Uses digital detectors instead of film.
  • ⇒ Advantages over film radiography:
  • – Faster processing and immediate image availability.
  • – Higher contrast resolution.
  • – Images can be enhanced, stored, and shared electronically.
  • Figure 8 Digital radiography
  • ⇒  Types of Digital Image Receptors
  • 1. Computed Radiography (CR)
  • – Uses phosphor plates to store X-ray energy.
  • – Plates are scanned by a laser to produce a digital image.
  • 2. Direct Digital Radiography (DDR)
  • – Uses flat-panel detectors to directly convert X-rays into digital signals.
  • – More efficient than CR, requiring lower doses of radiation.
  • 3. Fluoroscopy
  • – Uses a continuous X-ray beam and an image intensifier or flat-panel detector.
  • – Provides real-time moving images, useful in guided procedures like catheter insertions.

  • g)   Rotating Beam X-Ray Computed Tomography (CT) Scanner

  • CT scanning is an advanced imaging technique that produces cross-sectional images of the body.
  • ⇒  Working Principle
  • A rotating X-ray beam passes through the body and is detected by an array of digital sensors.
  • The system collects multiple projection images from different angles.
  • A computer processes the data using complex algorithms (filtered back-projection or iterative reconstruction) to generate cross-sectional slices.
  • ⇒  Components of a CT Scanner
  • X-ray tube: Emits rotating X-ray beams.
  • Detectors: Measure transmitted X-rays.
  • Gantry: Houses the rotating X-ray system.
  • Computer System: Reconstructs the image.
  • Figure 9 Rotating beam X-ray CT Scanner
  • ⇒  Advantages of CT Scanning
  • Provides detailed 3D imaging of soft tissues, bones, and organs.
  • Used in emergency settings (stroke, trauma).
  • Can be enhanced with contrast agents to improve visualization of blood vessels and tumors.

  • h)   Generation and Detection of Ultrasound Using Piezoelectric Transducers

  • ⇒  Generation of Ultrasound
  • Ultrasound waves are produced using piezoelectric crystals in a transducer.
  • When an alternating current (AC) is applied to the crystal, it vibrates at high frequencies, emitting ultrasound waves.
  • ⇒  Detection of Ultrasound
  • The same piezoelectric crystals detect returning echoes.
  • The returning sound waves cause the crystal to vibrate, generating an electrical signal that is processed into an image.
  • Figure 10 Direction of Ultrasound
  • ⇒ Properties of Ultrasound
  • Frequencies used: 2 MHz – 15 MHz.
  • Higher frequency = better resolution, but lower penetration.
  • Lower frequency = deeper penetration, but lower resolution.
  • Ultrasound is reflected when it reaches a boundary between two mediums and the amount of reflection that takes place depends on the difference in acoustic impedance of the two mediums. The acoustic impedance (Z) is a measure of how difficult it is for an acoustic wave to travel through a medium.
  • [math]Z = pc[/math]
  • A coupling medium is used to reduce impedance and reflections at the boundary and as ultrasounds difficulty travelling in air, it is normally in the form of a gel.
  • The half-value thickness (X1/2) is the thickness of a material at which the intensity is reduced to half of the initial value and can be measured by using the following formula:
  • [math]X_{1/2} = \frac{\ln 2}{\mu}[/math]

  • i)   Ultrasound Scanning Techniques: A-Scan and B-Scan

  • ⇒  A-Scan (Amplitude Mode)
  • – One-dimensional ultrasound scan.
  • – Used mainly in ophthalmology to measure eye structure distances.
  • – The echoes are displayed as spikes, with their height indicating the strength of reflection.
  • ⇒  B-Scan (Brightness Mode)
  • Two-dimensional ultrasound imaging.
  • The returning echoes are converted into a grayscale image, where:
  • – Bright areas = strong echoes (e.g., bone).
  • – Dark areas = weak echoes (e.g., fluid).
  • Used in abdominal, cardiac, and obstetric imaging.
  • Figure 11 Ultrasound scanning technique, Scan A and Scan B
  • ⇒  Applications of Ultrasound
  • Obstetric Imaging: To monitor fetal development.
  • Cardiac Echocardiography: To assess heart function.
  • Abdominal Imaging: To detect liver, kidney, and gallbladder diseases.
  • Doppler Ultrasound: To measure blood flow in arteries and veins.

  • j)   Acoustic Impedance and Its Role in Ultrasound Imaging

  • ⇒  Definition of Acoustic Impedance
  • [math]z = cp[/math]
  • Where:
  • – Z = acoustic impedance (kg/m²s),
  • – c = speed of sound in the medium (m/s),
  • – ρ = density of the medium (kg/m³).
  • Reflection and Transmission at Tissue Boundaries
  • When ultrasound waves encounter a boundary between two tissues with different acoustic impedances, part of the wave is reflected, and part is transmitted.
  • The greater the impedance difference, the stronger the reflection.
  •   Need for a Coupling Medium
  • Air has a very low acoustic impedance compared to body tissues, which causes almost total reflection of ultrasound waves.
  • Gel is applied between the transducer and skin to eliminate air gaps and allow efficient transmission of sound waves.

    • k)   Doppler Equation and Its Use in Studying Blood Flow

    • ⇒ The Doppler Equation:
    • The Doppler equation used in medical ultrasound for blood flow measurements is:
    • [math]\frac{\Delta f}{f_0} = \frac{2v}{c}[/math]
    • Where:
    • – Δf is the shift in frequency of the ultrasound wave,
    • – [math]f_o[/math]​ is the original (transmitted) frequency,
    • – v is the velocity of the moving blood,
    • – c is the speed of sound in tissue (approximately 1540 m/s).
    • ⇒  Explanation:
    • Doppler Effect:
    • When ultrasound waves hit moving red blood cells, the frequency of the reflected wave is shifted. If the cells are moving toward the probe, the frequency increases; if they are moving away, it decreases.

      Figure 12 Doppler’s Principle

    • “The Doppler principle is the change in frequency of sound or light waves due to the motion of a source relative to an observer”
    • Factor of 2:
    • The factor of 2 appears because the ultrasound signal is reflected – the wave undergoes a Doppler shift twice (once on the way in and once on the way out).
    • Clinical Application:
    • This equation allows clinicians to measure blood flow velocities in vessels, which is crucial for diagnosing circulatory problems.

    • I)   Principles of Magnetic Resonance and the Larmor Frequency

    • ⇒  Basic Principles:
    • Precession of Nuclei:
    • In a strong external magnetic field B, certain nuclei (commonly hydrogen protons) behave like tiny magnets and process around the field direction at a specific frequency.
    • Resonance:
    • When a radiofrequency (RF) pulse matching this precession frequency (the Larmor frequency) is applied, the nuclei absorb energy and are “excited” to a higher energy state.
    • Relaxation:
    • After the RF pulse, the nuclei return to equilibrium through processes known as T1 (spin-lattice) and T2 (spin-spin) relaxation, releasing energy in the process.
    • Figure 13 Basic Principle of Cardiovascular
    • ⇒  Larmor Frequency Equation:
    • [math]f = 42.6 \times 10^6 \, B[/math]
    • – f is the Larmor frequency (in Hz),
    • – B is the magnetic field strength in Tesla,
    • – The constant [math]f = 42.6 \times 10^6 \, Hz/T[/math] is specific for hydrogen nuclei.
    • ⇒   Application in MRI:
    • MRI (Magnetic Resonance Imaging) uses these principles to generate detailed images based on differences in proton density and relaxation times in tissues.
    • By applying RF pulses at the Larmor frequency and measuring the emitted signals as nuclei relax, MRI systems can construct cross-sectional images with excellent soft tissue contrast.

    • m)    Use of X-Rays in Therapy and Diagnosis

    • ⇒  High-Energy X-Rays in Therapy:
    • Radiotherapy:
    • High-energy X-rays (often in the MeV range) are used to treat cancer by damaging the DNA of tumor cells. Their deep penetration allows targeting tumors deep within the body while sparing superficial tissues.
    • ⇒  Low-Energy X-Rays in Diagnosis:
    • Diagnostic Radiography:
    • Lower-energy X-rays (keV range) are used for imaging bones and soft tissues. They provide good contrast between different tissue densities (e.g., bones absorb more X-rays than soft tissues), which helps in diagnosing fractures, infections, or other conditions.
    • Attenuation of X-Rays
    • ⇒  Exponential Attenuation Equation:
    • [math]I = I_0 \exp(-\mu x)[/math]
    • Where:
    • – I is the transmitted X-ray intensity after passing through material,
    • ​- [math]I_o[/math] is the incident intensity,
    • – μ is the linear attenuation coefficient (which depends on the material and photon energy),
    • – x is the thickness of the material.
    • ⇒  Explanation:
    • As X-rays traverse a medium, they are absorbed or scattered, leading to an exponential decrease in intensity.
    • This equation is critical for determining required shielding and for image contrast in diagnostic radiography.
    • X-Ray Imaging and Fluoroscopy
    • ⇒  X-Ray Imaging:
    • Imaging Soft Tissue:
    • X-rays are commonly used to image bones due to high absorption. For soft tissues, contrast can be improved using contrast agents (e.g., iodine or barium) to enhance differences in absorption.
    • ⇒  Fluoroscopy:
    • Real-Time Imaging:
    • Fluoroscopy uses a continuous X-ray beam and image intensifiers to produce real-time images of internal structures.
    • Image Intensifiers:
    • These devices convert X-rays into visible light, amplify the image, and then display it on a monitor, which is essential for procedures like catheter insertions or gastrointestinal studies.
    • Figure 14 Fluoroscopy

    • n)   Advantages and Disadvantages of Ultrasound, X-Ray, and MRI

    • ⇒  Ultrasound Imaging:
    • Advantages:
    • – Non-invasive and does not use ionizing radiation.
    • – Real-time imaging, useful for dynamic processes (e.g., heart function, fetal monitoring).
    • – Portable and relatively low-cost.
    • Disadvantages:
    • – Limited penetration in air or bone.
    • – Operator-dependent and lower resolution for deep structures.
    • ⇒  X-Ray Imaging:
    • Advantages:
    • – Excellent for imaging bones and detecting fractures.
    • – Fast and relatively inexpensive.
    • Disadvantages:
    • – Uses ionizing radiation, which poses a risk with repeated exposure.
    • – Poor contrast resolution for soft tissues.
    • ⇒  MRI:
    • Advantages:
    • – Provides detailed images of soft tissues with excellent contrast.
    • – No ionizing radiation, making it safer for repeated use.
    • Disadvantages:
    • – Expensive and time-consuming.
    • – Sensitive to patient motion; not suitable for patients with certain metal implants.

    • o)    Effects of α, β, and γ Radiation on Living Matter

    • ⇒  Alpha (α) Radiation:
    • Properties:
    • – Consists of helium nuclei (2 protons and 2 neutrons).
    • – Highly ionizing but low penetration; stopped by paper or skin.
    • Biological Effect:
    • – Very harmful if ingested or inhaled, as they can cause significant damage to tissues.


      Figure 15 Radiation on living matter

 

    • ⇒  Beta (β) Radiation:
    • Properties:
    • – Consists of high-speed electrons (or positrons).
    • – Moderately penetrating; can be stopped by a few millimeters of aluminum.
    • Biological Effect:
    • – Can cause skin burns and damage internal tissues if ingested or if large doses are absorbed.
    • ⇒   Gamma (γ) Radiation:
    • Properties:
    • – High-energy electromagnetic radiation.
    • – Highly penetrating; requires thick shielding (e.g., lead, concrete).
    • Biological Effect:
    • – Can damage tissues and DNA deep within the body, increasing cancer risk.
    • ⇒  Units of Radiation Dose:
    • Gray (Gy):
    • The unit of absorbed dose; 1 Gy = 1 joule of energy absorbed per kilogram of tissue.
    • Sievert (Sv):
    • The unit of equivalent dose or effective dose; it factors in the biological effectiveness of the radiation type. It is calculated by multiplying the absorbed dose (Gy) by a radiation weighting factor.

    • p)     Radiation Dose Equations

    • ⇒  Equivalent Dose (H)
    • Equation:
    • [math]H = D \times W_R[/math]
    • ⇒ Explanation:
    • – D is the absorbed dose (energy deposited per unit mass, measured in Gray, Gy).
    • ​- [math]W_R[/math] is the radiation weighting factor, which accounts for the relative biological effectiveness of different types of radiation (for example, [math]W_R = 1[/math] for X-rays and gamma rays, higher for alpha particles).
    • – H (measured in Sieverts, Sv) gives a measure of the potential biological damage.
    • ⇒  Effective Dose (E)
    • Equation:
    • [math]E = H \times W_T[/math]
    • or equivalently,
    • [math]E = D \times W_R \times T_W[/math]
    • ⇒ Explanation:
    • – [math]T_W[/math]​ is the tissue weighting factor, which reflects the sensitivity of different tissues and organs to radiation.
    • – The effective dose (E), also in Sieverts, provides an overall estimate of risk by summing contributions from different tissues.

    • q)   Radionuclides as Tracers: Technetium-99m (Tc-99m)

    • ⇒  Uses and Properties:
    • Radionuclides are radioactive isotopes that emit gamma rays and can be detected externally. They are used as tracers in nuclear medicine because they mimic the behavior of physiological substances.
    • Technetium-99m (Tc-99m) is widely used due to its:
    • – Ideal half-life: Approximately 6 hours (long enough for imaging, short enough to minimize patient dose))
    • – Gamma Emission: Emits a 140 keV gamma photon, ideal for detection with gamma cameras.
    • – Versatility: It can be chemically attached to various pharmaceuticals to target specific organs (e.g., bone, heart, thyroid).
    • ⇒  Application Example:
    • Bone Scanning: Tc-99m labeled compounds accumulate in areas of high bone metabolism, helping to detect fractures, infections, or tumors.

    • h)   Gamma Camera: Principles and Components

    • ⇒  Working Principle:
    • A gamma camera is used in nuclear medicine to create images of radionuclide distribution within the body.


      Figure 16 Gamma Camera and its components

 

  • 1. Collimator:
  • Function:
  • A lead or tungsten structure with many parallel holes that allows only gamma rays traveling in specific directions to reach the detector.
  • Purpose:
  • Improves image resolution by restricting stray rays and controlling the direction of incoming photons.
  • 2. Scintillation Crystal (Scintillation Counter):
  • Function:
  • A large, flat crystal (often sodium iodide doped with thallium, NaI(Tl)) that absorbs gamma rays and converts them into flashes of light (scintillations).
  • Purpose:
  • Converts the high-energy gamma photons into visible light, which is then detected by photodetectors.
  • 3. Photomultiplier Tubes (PMTs) or CCDs:
  • Function:
  • These devices detect the light pulses from the scintillation crystal.
  • Photomultiplier Tubes:
  • Convert the light flashes into electrical signals with high gain, preserving the spatial information.
  • CCD Cameras:
  • Sometimes used in modern systems for digital image capture.
  • ⇒  Image Formation:
  • The signals from the PMTs or CCD are processed by a computer to form a two-dimensional image representing the spatial distribution of the radionuclide in the body.

  • s)      Positron Emission Tomography (PET) Scanning

  • ⇒  Principles:
  • PET scanning uses positron-emitting radionuclides (e.g., fluorine-18 in FDG, a glucose analog).
  • ⇒ Positron Emission:
  • The radionuclide decays by emitting a positron, which rapidly encounters an electron. Their annihilation produces two gamma photons traveling in nearly opposite directions (approximately 180° apart).
  • ⇒ Detection:
  • PET scanners have a ring of detectors that simultaneously record the gamma photons. By reconstructing the lines along which the photons travel, the system localizes the source of the annihilation events.
  • Figure 17 PET Scanner
  • ⇒  Applications in Tumour Detection:
  • Metabolic Imaging:
  • Tumours often have a higher metabolic rate than normal tissue. PET imaging with FDG highlights these areas of increased glucose uptake.
  • Diagnosis and Monitoring:
  • PET scans are valuable for detecting cancer, staging tumors, and monitoring the response to therapy.
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