medical diagnostic imaging ece16511/411 - spring 2007

Medical Diagnostic Imaging

ECE16511/411 - Spring 2007

Physics of Radiology

Prof Mufeed MahDUMASS Lowell

IONIZATION

DefinitionIt is the ejection of an electron from an atom, creating a free electron and positive ion.

Ionizing Radiation: Radiation that carries enough energy to ionize an atom.

ATOMIC STRUCTURE

Atomic Number:The number of protons in the nucleus and defines the element.

Mass Number:The number of nucleons in the nucleus

Electron Binding Energy

Definition: The difference between the total energy of an atom and the sum of the energy of the ionized atom plus the energy of the freed electron.

• Electron binding energy decreases with the increasing shell number.

• Metals have much larger average electron binding energies.

• Electrons orbiting the nucleus are organized into shells.

• The K-shell is the closet to nucleolus and has

the largest electron binging energy.

Ionization and Excitation

Ionization: radiation, with energy equal to or higher than the electron binding energy, knocks out an orbiting electron and forms a positive ion.

Excitation: radiation, with energy less than the electron binding energy, transfers an orbiting electron to a higher energy level.

Ionization radiation in medical imaging has energies 25 KeV-500 KeV.

A single ionizing particle/ray in medical imaging applications is capable of ionizing between 10-40,000 atoms before its energy is exhausted.

eV: The kinetic energy of an electron when accelerated across one volt potential.

1KeV =1.6 X 10-16 J

Forms of Ionizing Radiation

I. Particulate Radiation:

Any subatomic particle (proton, electron, neutron) can cause ionization when it possess kinetic energy.

The energy of these particles equal the KV potential that generated them.80 KV potential used to generate a beam of electrons with energy 80KeV.

Example:

Calculate the speed of the electron that is accelerated between the cathode and the anode at 120 KV potential difference.

Forms of Ionizing Radiation

II. Electromagnetic (EM) Radiation

Composed of electric and magnetic wave traveling together at right angles to each other.

Photons: conceptualization of EMR is as packets of energy.

The energy of a photon is governed by Plank’s Equation

C = 3.0X1018 m/sec and h= 6.626X10-34 j.secλhc

E =

Nature and Properties of Ionizing Radiation:


Particulate Radiation:

Energetic Electrons interact with the medium by:

I. Collision

The most common interaction.

Part of electron energy is transferred to the other electron.

Atom release infrared radiation upon returning to original state.

II. Radioactive Transfer

• Characteristic Radiation

• Bremsstrahlung


Primary Energetic Electron Interactions: Characteristic Radiation

An incident electron collides a K-Shell orbital electron.

A temporarily hole is created, promptly filled by an electron from lower energy level.

The difference in the two electron binding energy levels is emitted as a photon characteristic x-ray.

Emitted x-ray energies are characteristic of particular atoms.


Primary Energetic Electron Interactions: Bremsstrahlung

An electron approaches the nucleus.

The electron bends because of the attraction forces with the nucleus.

Energy is released from the decelerated electron in from of photons.

(if the electron collide the nucleus, it will be annihilated and photons are emitted).


Primary Energetic Electron Interactions

• Bremsstrahlung is called the continuous spectrum.

• The highest Bremsstrahlung energy equal the anode-cathode potential.

• Characteristic radiations appear as spectral lines (spikes).

• The length of a spike is proportional to the likelihood of occurrence for such a transition.


Primary Electromagnetic Radiation Interaction:


Primary Electromagnetic Radiation Interaction: I. Photoelectric• An incident photon with energy hv collides a K-Shell orbital electron.• The photon is completely absorbed by the atom• The ejected electron (photoelectric) has energy Ee- = hv –EBinding

• The hole is promptly filled by an electron from lower energy level, which produces characteristic x-ray.

• If the characteristic radiation has enough energy it will knock out an electron form an outer shell (Auger Electron).


Primary Electromagnetic Radiation Interaction: II. Compton Scattering

• A photon with energy hv ejects an outer shell electron (Compton Electron).• The Incident electron loses energy and divert its direction.

• A Compton photon is emitted with energy

• The kinetic energy of the Compton electron is Ee=hv-hv’


Primary Electromagnetic Radiation Interaction: Probability• The probability for the photoelectric is proportional to the atomic

number and the inverse cube of the incident photon energy.

Zeff = average atomic number for a tissue/object.

• The probability of Compton scattering is proportional to the Electron Density (number of electrons per unit kilogram of material)

wm : molecular weight

Attenuation of Electromagnetic Radiation:

Measures of X-Ray Beam Strength

Measurement of x-ray is needed to:1. Characterize the inherent noise in the system.2. Estimate the biological effects of ionizing radiation.

Photon Fluence Φ: Number of Photons per unit area A.

Photon Fluence Rate φ:



Measurement of x-ray is needed to:1. Characterize the inherent noise in the system.2. Estimate the biological effects of ionizing radiation.

Energy Fluence Ψ:

Energy Fluence Rate ψ :

Intensity of an x-ray beam I:



X-ray photon is polyenergetic.

The number of photons per unit energy is constant for a given source.

Photon Fluence Rate for polyenergetic source:

Intensity of polyenergetic source


Narrow Beam , Monoenergetic Photons

Narrow Beam: the width for the x-ray photon beam is less or equal to the width of the detector used to count the number of photons.

Photons are either completely absorbed or scattered away from the detector

Number of photons lost (n) starting with N photons is



The Linear attenuation coefficient is

The rate of change in the number of lost photons is

Solving for N

For monoenergetic x-ray beam



Half Value Layer (HVL):

The thickness of the material that will attenuate half of the incident photons

For non homogenous slab, the number of photons at position x is

X-ray intensity is


Narrow Beam , Polyenergetic Photons

Homogenous Slab

The linear attenuation coefficient is a function of the energy

Heterogeneous SlabThe linear attenuation coefficient is a function of both the energy and the position


Broad Beam , Polyenergetic Photons

• More photons are detected than narrow beam case.

• Photons from outside the line-of-sight geometry might get scattered toward the detector by Compton interactions.

• The burst of detected Photons is not monoenergetic

• Compton scattering reduce photon energy.

• Beam Softening: Reduction in the effective energy of the x-ray beam due to Compton scattering.

Radiation Dosimetry:

ExposureDefinition: number of ion pairs produced in a specific volume of air by EM radiation.UNITS: SI Columbus/Kg Medical Clinic Roentgen (R)

1R =2.58X10-4 C/Kg

DoseDefinition: the amount of energy an ionizing radiation deposits in a material by Compton and photoelectric interactions.Units: SI Gray (Gy) Medical Clinic rad

1Gy = 100 rad


KermaDefinition: the amount of energy per unit mass imparted to the electrons in a given material.UNITS: Gray (Gy)

Linear Energy Transfer (LET)Definition: a measure of the energy transferred by radiation to the materialthrough which it is passing per unit lengthLET has adverse biological consequences.

Specific Ionization (SI)Average number of ion pairs formed by unit length.


The F-factor:

The dose to a material other than air is

The F-factor is

µ: linear attenuation coefficient

ρ: mass density of the material/air

µ/ρ: mass attenuation coefficient (It is independent of the physical and chemical state of the absorber).


Dose Equivalent (DE):

Different types of radiations (with same dose) have different effects on the body.

D is measured in rads and H in rems

Q: a property of the radiation used known as quality factor.

X-ray, gamma ray, electrons, β particles Q=1

Neutron and Protons Q=10

α-particles Q=20


Effective Dose:

The weighted sum of dose equivalents to different organs or body tissues.

The weights are selected such that to provide a value proportional to the radiation-induced somatic and generic risk even when the body is not uniformly irradiated.

Example:

Solution:

Assume total number of x-ray photons is N0.

Since the bars are 4 times larger than the HVL, then only (1/2)4

=(1/16) of the original x ray photons will make it through the bars.

The contrast = [N0 –N0/16] / [N0+N0/16] = 15/17

Example:

Solution:

Projection Radiography

Conventional radiographs is a projection of a 3D volume of the body onto a 2D imaging surface.

Advantages:

• Short exposure time (0.1 sec)

• Production of a large area image (14X17 in)

• Low cost

• Low radiation exposure (30 mR for chest radiology)

• High Contrast and Spatial Resolution

Clinical Usage:

• Pneumonia

• Hear Diseases

• Lung Diseases Bone Fractures

• Cancer

• Vascular Diseases

Instrumentation

The X-ray tube generates a short pulse of x-rays as a beam that travels through the patient. X-ray photons that are not absorbed within the patient body or scattered outside the region of the detector impinge upon the large area detector creating an image on a sheet of film.

X-ray Tubes:

• 3-5 A (at 6-12V) current is passed through the filament.

• A cloud of free electrons is created at the filament.

• Anode voltage is applied which force the electrons to flow creating the tube current (mA)

• A high tube voltage (30-150 kVp) is applied which produces the x-ray beam.

X-ray Tubes:

• The anode is made from molybdenum and is coated with rhenium-alloyed tungsten.

• The overall exposure is determined by the duration of the applied kVp.

• Exposure in milliampere-second (mAs) is the product for the tube current and the exposure time.

Filtration and Restriction:

Filtration is the process of absorbing low-energy x-ray photons before they enter the body.

Restriction is the process of absorbing x-rays outside a certain filed of view.

Filtration

The maximum energy of emitted x-ray photons is determined by the tube voltage kVp.

X-ray beam has a spectrum of lower energy x-ray beam (Bremstrahlung) giving a polyenergetic x-ray sources (medical imaging systems).

Low-energy photons are absorbed entirely by the body contributing to the radiation dose but not the formation of the image.

Two levels of filtration: Inherent Filtration and Added Filtration

Filtration, cont.

Inherent Filtration: tungsten anode and the glass housing of the x-ray tube both absorb low-energy x ray protons before they leave the x-ray tube assembly.

Added Filtration:

a metal (usually aluminum) assembly used to absorb low-energy x-ray photons

High energy systems, copper is used that produce attenuation higher than an equivalent aluminum with the same thickness (it should be followed by a thin 1mm aluminum layer) .

Filtration, cont.

Example:

If a minimum of 2.5 mm AL/Eq is needed for a radiograph system operating at 70 kVp, what should be the minimum added filtrationfor a system that operates at 80 kVp.

SolutionAl linear attenuation coefficient = mass attenuation X density

= .02015X2699 = 54.38 m-1Cu linear attenuation coefficient = mass attenuation X density

= .07519 X 8960 = 673.7 m-1

Set e{-µAl ∆xAl} = e{-µCu ∆xCu}

Then ∆xCu = [ µAl ∆xAl / µCu ] = 0.2 mm (Note it should be followed by 1 mm AL layer)

Restriction Beam:

X-ray beam must be restricted to avoid exposing parts of the patient that need NOT be imaged and to help reduce the deleterious effects ofCompton scatter.

Diaphragms

Flat pieces of lead with holes, centered on the x-ray beam, placed closed to the tube window.

Simple and Inexpensive

Has fixed geometry that can be used only in

dedicated systems for one purpose

(such as chest radiography).

Restriction Beam:

Cones Cylinders:Fixed geometry with better performance

CollimatorsMore expensive More flexible and better performanceHas variable diaphragms with movable pieces of leadTwo collimators are used (close and further way from the tube)

Compensation Filters and Contrast Agents:

The different attenuation constants within an image yield different contrasts which give better differentiation for tissues.

Compensation Filters:

Motivation:Thick/Dense body parts attenuates more x-rays than thin/soft parts.

For the same organ one region would overexposed while the other is underexposed giving unstable diagnostic image.

Remedy:Specially shaped aluminum or leaded-plastic objects are placed between the x-ray beam and the patient to secure a more uniform x-ray distribution over the whole organ being scanned.


Compensation Filters, cont.:


Contrast Agents:

Motivation:

Different soft tissue structures are difficult to visualize due to insufficient intrinsic contrast.

Remedy:

Chemical compounds (Contrast agents) are introduced into the body to increase x-ray absorption within the anatomical regions.

Iodine has atomic number Z =53, K-shell binding energy = 33.2 KeV, used with blood vessels, heart chambers, tumors, etc.

Barium has atomic number Z=56 and K-shell binding energy =37.4 KeV, used with gastrointestinal tract, stomach, etc.

(both within the range of the medical diagnostic x-ray energy levels)


Contrast Agents, cont.:

Grids, Air gaps, Scanning Slits:

Scatter is a random process that cause random fog in the image if was not corrected.

Grids:

Thin stripes of lead alternating with highly transmassive interspaced material (aluminum and plastic).

Has different structures:

linear–focused, crosshatch, and parallel.


Grids, cont:


Grids, cont. :

The effectiveness of the grid for reducing scatter is a function of the grid ratio

Grid Ratio = h/b

Grid ratios are 6:1 to 16:1 (2:1 for mammographs).

Higher ratios implies taller lead strips and finer spacing.

Grid Spacing is referred to by the Grid frequency.

Grid frequency is 60 cm-1 for conventional and 80 cm-1 for mammography


Grids, cont. :

The grid conversion factor is a ratio that characterizes the amount of additional exposure required for a particular grid.

Typical GCF is in the range 3-8

Rule of thumbs to use a grid:

when the tube voltage is above 60KVp

When the body part to be imaged is thicker than 10 cm.


Air gaps:

Used to reduce the scatter at the cost of increased geometric magnification and blurring or unsharpness.

Scanning Slits:

Mechanical lead slits that are placed at the front and/or back of the patient.

The slits move together during the x-ray exposure.

It reduce scatter by 95%

It is expensive and yield a more complicated imaging system.

Film-Screen Detectors

To improve the efficiency of the photographic film intensifying screens on both sides of the radiographic film. The screens stop most of the x-ray photons and convert them into visible light, which expose the film.


Intensifying Screens:

PhosphorsUsed to transform x-ray photons into light photons.The light photons travel into the film causing it to be exposed and to form a latent image.

BaseUsed to provide mechanical stabilityMade of polyester plastic

Reflective layerUsed to reflect back light from the phosphor back to the film instead of losing in to the base.

25µm thick and made of magnesium oxide or titanium dioxide.


Intensifying Screens, cont:

Luminescent (conversion of one form of energy to another)

It has two forms:

Fluorescence: emission of light happens within 10-8 second of excitation

Phosphorescence: Light emission can be delayed and extended over a longer period of time.

Characteristics of Good Intensify Screens:

1. It has more phosphorescence than fluorescence

2. High x-ray attenuation

3. Emit many light photons for every x-ray photon stopped


Intensifying Screens, cont:

Conversion Efficiency

A measure of the number of light photons emitted per incident x-ray photon

In the range 5%-20% depends on the phosphorous material and its thickness

A 50 KeV x-ray photon produces 103 light photons.

Speed of the Screen:

A measure of its conversion efficiency

Higher conversion efficiency the faster is the screen


Radiographic Film:

An optical film made to capture the optical image created within the screens that sandwich the film.

Common Sizes include: 8X10, 10X12, 11X14, 14X14, 7X17, and 14X17

Radiographic Cassette

A Holder for two intensifying

screens and the film.

One side is radiolucent,

the other side includes a sheet of lead foil.


X-Ray Image Intensifiers:

• used in Fluoroscopy: low-dose, real-time projection is required.

• X-rays absorbed by the input phosphor generate flashes of light channeled toward the photocathode.

• Photocathode generates free electrons within the vacuum tube

• Electrons are accelerated because of the dynodes voltage of 25-35 Kevcompared to the photocathode.

• Electrons are absorbed by the anode or the output phosphor screen

• Electrons are converted back to light photons and focused using a lens to be used for real time imaging using TV camera, or Off line Snapshots using Film Camera


X-Ray Image Intensifiers:

Image Formation

Basic Image Equation:

• Consider a line segment of length r = r(x,y) through the object starting at the x-ray origin and ending on the detector plane at point (x,y).

• The intensity of the x-rays incident on the detector at (x,y) is

• For different lines, we have

different tissue structures with

different attenuation coefficients

( µ is a function of x and y).

Image Formation

Geometric Effect:

X-ray beam is diverging in nature which lead to reduction of net flux flow of photons and obliquity

Inverse Square Law:

The net flux of photons decreases as inverse square of the distance from the x-ray origin.

Assume: No Object and X-ray Source IsThe intensity at the origin of the detector

(x=y=0) is

Image Formation

Geometric Effect: Inverse Square Law, cont:

The intensity at an arbitrary point (x,y) is SMALLER than the intensity at the origin of the detector and it is calculated as:

Since cosθ =d/r, then

Image Formation

Geometric Effect:

Obliquity:

Reduces x-ray beam intensity away from the detector origin.

Caused by the surface of the detector is NOT perfectly orthogonal to the direction of the x-ray propagation.

For an orthogonal area A, the projected area

is

The measure intensity due to obliquity is

Image Formation

Beam Divergence and Flat Detector:

A flat detector suffers from reduced beam intensity due to both the inverse square law and due to obliquity.

The overall intensity relative to the intensity Io of the detector at the origin is given by:

The flat detector effect can be reduced if:

• the tube was at a farther distant from the detector (large d) and/or

• the detector size is small (small θ)

Image Formation

Anode Heel Effect:

X-rays traveling out of the anode in the cathode-to-anode direction have more anode material through which to propagate before leaving the anode as compared to those leaving the anode in the backward direction

The beam intensity is higher in the cathode direction than the opposite direction.

Anode heel effects overweighs the inverse square law and obliquity

Anode heel effect will be much less noticeable if

• the focal-film distance is large.

• A small film is being exposed.

Image Formation

Path Length:

If a slab of material with uniform linear attenuation coefficient and thickness L is placed between the x-ray source and the detector.

The x-ray intensity at the origin of the detector is

Io the intensity of the beam in absence of the slab.

The path length through the slab along the line between the x-ray source and (x,y) is given by

More x-rays will be attenuated along this line than along the central path

Image Formation

Path Length, cont:

The x-ray intensity (due to path length) ignoring Inverse square law, Obliquity and Anode heel effect is

The intensity INCLUDING the Inverse square

law, Obliquity and Anode heel effect is

Image Formation

Depth Dependent Magnetization:

Observations:

The object always appear larger on the detector than the true reality.

The height of the object on the detector is different depending on the position of the object n the field of view.

The height of the object located at position z is

The magnification M(z) is given by

Image Formation

Imaging Equation with Geometric Effects:Consider a thin object tz(x,y) that is:infinitesimally thinlocated in a single plane given by the coordinate z is capable of differentially attenuates x-rays as a function of x and y.

The recorded intensity, if the object is at the detector plane, is

The recorded intensity of the object at a distant z (0 = z = d ) is

Image Formation

Blurring Effects:

Three major sources of blurring: z extent of the object (thick objects), extended x-ray source, intensifying screens.

Extended Sources:

It refers to spot size of the emitted x-ray beam.

It causes fuzziness at the edge of the filed of view and fuzziness of the object boundary.

It has convolutional nature and is account for by convolving the source shape with the object shape.

The source magnification m(z) is

Image Formation

Blurring Effects: Extended Sources, cont:

Image Formation

Extended Sources, cont:

For a source with intensity distribution s(x,y), the recorded intensity at arbitrary location (x,y) in the detector plane is

Film Screen Blurring:

For a film-screen impulse response h(x,y), the recorded intensity at arbitrary location (x,y) in the detector plane is

Image Formation

Film Screen Blurring, cont:

Detector Efficiency: The fraction of photons captured by the detector on average.

The thicker the screen the higher the efficiency and the lower the resolution.

Thinner screens are used for good resolution application (mammographs) and thicker screen are used for good efficiency (conventional radiography).

Image Formation

Film Characteristics:

Observations

1. The intrinsic spatial resolution of film is high, it is not considered.

2. Film is a very poor direct detector of x-ray photons, image formed from the x-rays is ignored.

Optical Density: a ratio that characterizes the transformation between exposure to light and the degree of blackening of the film.

Optical Transmissivity: the fraction of light transmitted through the exposed film

(dark areas may have T= 0.1 and transparent areas may have T 0.9)

Image Formation

Film Characteristics, cont:

Optical Opacity: The reciprocal of the transmissivity.

Optical Density (D): The common logarithm of optical opacity.

H&D curve: Without intensifying screens, optical density has an S-nonlinear relationship with the x-ray exposure (R).

Image Formation

Film Characteristics: H&D curve, cont:

Image Formation

Film Characteristics: H&D curve, cont:

D Never reaches zero (fog and base)

In the linear region, the optical density is related to the x-ray exposure as:

Γ: is the slope of the H&D curve in the linear region, called film gamma,

it is a characteristic for the film.

Xo: is the interpolated exposure intercept.

Latitude: the range of exposure for which the H&D curve is linear.

Speed: the inverse of the exposure at which D= 1+fog and base.

Image Formation

Noise and Scattering: Signal to Noise Ratio

Quantum Mottle: the discrete quantum nature of the x-ray photons, there will random fluctuations in the number of arrived photons which introduces noise.

If the noise caused by quantum fluctuations in the background is characterized by a standard deviation (σb), then

For monoenergetic x-ray photons, the average background intensity is

The background variance is

Image Formation

Noise and Scattering: Signal to Noise Ratio

To change the SNR either is to be changed • the contrast of the structure

• Contrast agent • Changing the energy of the x-ray

• and/or the number of photons• Changing the filament current• The duration of the x-ray burst• More efficient detector• Larger area elements (pixels)• The energy of the x-ray

Image Formation

Noise and Scattering: Quantum Efficiency

It is the probability that a single photon incident upon the detector will be detected.

A high QE is not enough to judge detectors but its reproductively is more important.

Detective Quantum Efficiency:

A measure for the transformation of SNR from detector’s input to its output.

It provide a measure of deterioration in the SNR due to detection.

Image Formation

Noise and Scattering: Compton Scattering

Effect on Image Contrast:

Local contrast without scattering

Local contrast with scattering

Scattering reduce contrast by a factor of (1+Is/Ib).

(Is/Ib) is the scatter-to-primary factor

Image Formation

Noise and Scattering: Compton Scattering

Effect on SNR:

SNR without scattering

SNR with scattering

Hence

Scattering reduce SNR by a factor of √[1+Is/Ib].

Thank You

medical diagnostic imaging ece16511/411 - spring 2007

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