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2. Compare the half-value thickness and attenuation coefficients for bone and muscle.

Outline the basis of CT scanning

– X-ray image of target taken at different angles (many different directions)

- computer produces detailed image of slice (these images are combined using computers to form a two-dimensional image of section)

– images of many sections/slices can be obtained

– combined to build up a 3D image so image can be rotated for viewing from any angle

7. Discomfort is experienced by a person with normal hearing when the intensity is approximately 1.0 W/m2.

a) What is the corresponding intensity level for this intensity?

b) Compare the intensity at this intensity level to the threshold of hearing.

IL versus frequency diagram for a person with normal hearing

CT or CAT scan: Computer-Assisted Tomography or Computerized Axial Tomography

Pressure:

Computed Tomography (CT)

Factors affecting choice of diagnostic frequency:

a) Resolution: size of smallest object that can be imaged. Ultrasound is a wave so diffraction effects must be minimized. Use smallest wavelength possible.

Favors:

b) Attenuation: absorption of signal. Attenuation increases as frequency increases. High frequency ultrasound will be absorbed and not reflected back to receiver. High frequency can’t scan organs deep in body – poor depth penetration

Favors:

Compromise:

The diagram above shows an ultrasound transducer (probe) in contact with the skin in an effort to determine the depth and width of the organ shown. An A-scan of the results is shown also. The average speed of the ultrasound used in tissue and muscle is 2.0 x 103 m/s.

a) Identify the source of each reflection labeled A, B, C, and D.

b)

Types of ultrasound scans

Comparisons of Diagnostic Imaging Techniques

2. Radiation from a gamma source creates an exposure of 4.3 x 10-3 C/kg. The average energy to singly ionize an atom in human tissue is approximately 40 eV. What is the absorbed dose and dose equivalent of this exposure? How much energy is deposited in each gram of tissue?

a) Lever action of ossicles (Force multiplier effect): The mechanical advantage of the ossicles acting as a lever turns a small force at the ear drum into a larger force at oval window (1.5:1).

Formula:

Example of therapy technique using iodine-131 to treat thyroid cancer:

a) Iodine-131 decays with beta-minus and gamma particle

b) Iodine readily absorbed by thyroid so will concentrate in target area

c) Beta-particles are absorbed over small volume so dose is localized (whereas alpha-particles are absorbed over large volume – more indiscriminate and therefore dangerous)

d) Gamma will escape from body so can be monitored

e) Effective half-life is about six days so patient will receive effective dose for a reasonable period of time but not too long to cause other damage

|Quantity |Symbol |Formula |Units |

|Exposure | | | |

|Absorbed Dose | | | |

|Quality Factor (Relative Biological | | | |

|Effectiveness) | | | |

|Dose Equivalent | | | |

1. Why use the dose equivalent rather than the absorbed dose when assessing the biological effects of radiation?

The effect that radiation has on tissue depends on the amount of ionization produced by the particular type of radiation used. Alpha particles cause more ionizations per unit length of its track so that for the same absorbed dose, alpha particle do more damage (ionization) than x-rays. By using a quality factor, the dose equivalent takes into account both the amount of radiation (absorbed dose) and the type of radiation (quality factor).

Advantages:

1) Any situation where detailed tomography/slicing/imaging is required

2) Large scale investigations where dose of ionizing radiation would be too great

3. A person of mass 75 kg and body surface area 1.5 m2 is exposed to monochromatic x-rays of energy 250 keV from a source that produces x-ray photons at an average rate of 109 m-2 s-1. Determine the dose equivalent received by this person during a CT scan that lasts 2.0 minutes.

Units:

Air pressure:

Aim of radiotherapy:

To target malignant cells in preference to normal healthy cells. Malignant cells are slightly more susceptible to damage from radiation than healthy cells since cells are more easily killed when dividing.

Scale on frequency axis:

2. Why are X-rays preferred over ultrasound for bone fractures?

Nearly all ultrasound is reflected by bone (at bone/tissue boundary) but x-rays can penetrate bone therefore X-rays show up internal structures.

Type of energy used:

1)

2)

1)

Why/how are barium meals used to assist X-ray imaging of stomach or intestinal tract?

a) All tissues in the abdominal cavity have approximately the same attenuation coefficient so there is little to no contrast on photographic film.

b) The attenuation coefficient for barium is greater than for the tissues in the abdominal cavity.

c) Barium meal lines the stomach.

d) Outline of stomach becomes clearer (greater contrast).

Uses:

1) imaging blood flow and soft tissue in the body

2) Preferred for the brain and central nervous system

3) Detecting tumors, strokes, infections in brain, spine, joints

a) What is the relationship between the transmitted intensity and the thickness?

1. The power output of a speaker is 100 W.

a) Determine the intensity of the sound heard by a person 3.0 m away from the speaker.

b) Determine the energy delivered to the person’s eardrum each second. (The total area of the eardrum is approximately 60 mm2.)

4. Apart from health hazards, why are different means of diagnosis needed?

a) Different types of tissues and bone have different absorption/attenuation properties

b) Some are better at distinguishing boundaries of organs

c) Some provide two dimensional slice imaging – some provide complete three dimensional images

d) Some are better at monitoring static or dynamic conditions

e) Some are better to investigate at large or small scales

f) Some can be used to study concentrations of specific types of tissue or pharmaceuticals

g) Some are better at monitoring specific organ functions

Diagnostic radiation: radiation used for imaging

Therapeutic radiation: radiation used for treatment

Operating Principles:

a) Large constant uniform magnetic field causes hydrogen atoms to line up (align their spin axes) – act like tiny magnets

b) Small non-uniform magnetic field is superimposed on top of larger field – localized magnetic field – weak oscillating field in the form of pulses of radio waves

c) If frequency of radio waves matches that of the hydrogen atoms (resonance) then the smaller field makes some hydrogen atoms realign

d) When small non-uniform field is removed, atoms relax back to original alignment

e) As they relax they emit radio-waves

f) Time it takes to relax is measured

g) Frequency of emitted radio waves and relaxation times are processed to produce the NMR image

Ultrasound Imaging

Significance: This attempts to quantify the amount of radiation that tissue absorbs but is difficult to measure directly.

3. What are the main advantages of each of the following imaging techniques?

X-rays:

To detect broken bones because bone and tissue show different attenuation/good distinction between bones and flesh

Ultrasound:

Any soft tissue analysis – takes advantage of reflections off organ boundaries

Pre-natal scans because there is no risk from ionizing radiation

NMR:

Any situation where detailed tomography/slicing/imaging is required

Large scale investigations where dose of ionizing radiation would be too great

b) Different areas: The area of the eardrum is larger than the area of the oval window (20:1).

Medical Physics

The Ear and Hearing

1. Distinguish among the:

a) Outer ear: ear canal up to the ear drum – filled with air

b)

2. Describe the function of the:

a) Ear canal:

channels sound wave (variations in air pressure) to ear drum

b) Eardrum (tympanic membrane, tympanum):

vibrates in resonance with sound wave to drive the ossicles

c) Eustachian tube:

equalizes pressure on both sides of eardrum

d) Ossicles: consists of three small bones known as the malleus, incus, and stapes (also known as hammer, anvil, and stirrup)

vibrates the oval window causing fluid in cochlea to vibrate

e) Cochlea:

transforms vibrations of fluid into electrical impulses via vibration of hairs (cilia) -

different hairs resonate with different frequencies

f) Auditory nerves:

send electrical impulses to brain to allow sound to be interpreted

5. How are sound pressure variations in air changed to larger pressure variations in the cochlear fluid?

6. Why is the middle ear necessary? Why not have the sound waves vibrate the oval window directly?

When densities are very different on either side of a boundary, like the oval window, most of a wave that hits the boundary will be reflected, not transmitted. The middle ear acts as a mechanism for pressure transformation between media of different densities (air and fluid). This is known as impedance matching. Without it, most sound would be reflected from the cochlear fluid rather transmitted.

4. What frequency is a normal ear most sensitive to?

Result: The lever action of the ossicles increases the force which then acts on a smaller area. Sound pressure is amplified by inner ear

Intensity and Loudness

Power:

Units:

Units:

Formula:

Formula:

Intensity:

Total area of sound energy:

As distance from source doubles . . .

Area of eardrum (or oval window) where sound is received:

2. What is the difference between intensity and loudness?

Loudness:

NOTE: The response of the ear to intensity is logarithmic. Doubling the intensity does not double loudness since the relationship is logarithmic.

3. Why discuss intensity rather than loudness?

Intensity is a well-defined term whereas loudness is not well-defined.

The same intensity does not seem as loud at different frequencies. The perception of loudness varies from person to person and from frequency to frequency.

Intensity Level (IL):

8. What are the effects of short-term and long-term exposure to noise?

a) temporary and permanent deafness

b) tinnitus

c) selective frequency loss

Intensity Level

3. What is the range of audible frequencies experienced by a person with normal hearing?

Units:

3. Calculate the intensity level of a 100 W speaker at a distance of 6.50 meters.

4. A sound meter placed 0.5 meter from a circular saw measures 92 dB.

a) What is the intensity of the sound that corresponds to this intensity level?

b) How much sound power does the saw produce?

6. What is the difference in the readings on the two sound meters at right?

Change in sound intensity levels:

5. If the intensity of a sound doubles, by how much does the intensity level change?

Curve:

a)

b)

c)

1. a) Can a 100 Hz note from a piano be heard by a person sitting in the audience at such a distance that the intensity level of the sound is 20 dB? Explain.

b) What is the minimum intensity and intensity level that the listener could hear for this note?

c) What is the lowest frequency note that the listener could hear at 20dB?

2. Sketch on the graph the results of a hearing test for an elderly person.

Medical Imaging and Diagnostic Techniques

X-Rays

Various imaging techniques are used for diagnostic purposes:

1) X-rays: use high energy radiation

2) Computed Tomography (CT): 3D x-ray (also known as a CAT scan)

3) Ultrasound: uses high frequency sound waves

4) Nuclear Magnetic Resonance (NMR): uses magnetic fields (also known as MRI)

5) Lasers

Production of X-rays:

a) Electrons are boiled off a filament due to heating.

b) They are accelerated through a high potential difference.

c) They strike a metal target, often tungsten.

d) The inner shell electrons of the target (tungsten) jump to high energy level and emit x-ray photons when they relax.

Imaging technique:

a) X-rays pass through person and fall on a photographic film which darkens when x-rays hit it.

b) Bone absorbs more of x-rays than soft tissue so on the film tissue appears darker and bone appears lighter.

Contrast:

Therefore,

Attenuation:

a)

b)

Attenuation coefficient:

Half-value Thickness:

Symbol:

Units:

1. X-rays are incident on the muscle of a patient as shown at right. The intensity of the transmitted x-rays is measured and plotted as a function of the thickness of the muscle.

Intensity Equation:

where ¼ =

Relationship between Half-value thickness and attenuation coefficient

Units:

Symbol:

1. The graph at right shows the μ =

Relationship between Half-value thickness and attenuation coefficient

Units:

Symbol:

1. The graph at right shows the transmitted intensity of a parallel beam of X-rays versus the thickness of a certain type of tissue. Determine the:

a) half-value thickness of this tissue

b) attenuation coefficient of this tissue

6. Analyze the intensity graph at right by straightening it.

Compare X-ray imaging and CT scans

X-ray imaging

1) uses ionizing radiation (X-rays)

2) short duration of exposure

3) smaller dose of radiation

4) two-dimensional shadow image

CT scanning

1) uses ionizing radiation (X-rays)

2) long duration of exposure (hard for kids)

3) larger dose of radiation

4) three-dimensional image

Operating principles: High frequency sound waves are transmitted from a probe into the patient’s body and are reflected at each boundary between different types of tissue and bone. The same probe both transmits and receives the ultrasound waves. By measuring the time between transmission and reception, the distance to each boundary can be calculated using the speed of sound and thus the location and surface of each organ can be mapped.

Typical operating frequencies of ultrasound waves:

Type of energy used:

Advantage:

Reflection at a boundary:

Production and detection of ultrasound waves

Piezoelectric crystal: a quartz crystal that changes shape when a potential difference is applied across it

Production: apply an AC voltage to generate a vibration at desired frequency

Detection: received sound wave causes it to vibrate and generate an AC voltage that can be measured

Formula:

Units:

Where

Z =

ρ =

c =

Acoustic Impedance:

Ultrasound of intensity Io is traveling in a medium of impedance Z1 and is incident on a medium of impedance Z2. The intensity of the reflected ultrasound is IR and is given by the formula:

4. What is the purpose of putting gel on probe and the patient’s skin?

3. From what boundary will most of the energy of the ultrasound waves be reflected?

1. The time delay for an ultrasound pulse going through body fat to reach and be reflected from the liver is 0.133 ms. The speed of the ultrasound through fat at the chosen frequency is 1450 m/s.

a) Calculate how far from the probe the liver is.

b) What are some assumptions made in this calculation?

II. A-scan:

a)

b)

1)

I. B-scan:

a)

b)

c) Calculate the width of the organ.

NMR:

MRI:

NMR

b) Calculate the depth of the organ.

Uses:

Presentation:

Use:

Presentation: Uses the signal strength to affect the brightness of a dot on the screen which can be displayed as a real-time video. Many B-scans are combined to give an image of the internal organs or baby.

5. Calculate the fraction of ultrasound that would be reflected from a patient’s skin if gel were not applied to the tip of the ultrasound wand.

2. Complete the table with the acoustic impedance of each of the above substances.

|Material |Density |Speed of sound |Acoustic Impedance (kg m-2 s-1) |

| |(kg m-3) |(m s-1) | |

|Air (200 C) |1.21 |344 | |

|Muscle |1075 |1580 | |

|Bone |1900 |3780 | |

|Fat |900 |1480 | |

|Soft Tissue (skin) |1060 |1540 | |

What is ultrasound?

1. What are the advantages and disadvantages of using ultrasound instead of X-rays?

Advantage: not as harmful since no ionizing radiation

And so can be used for pregnant women

Disadvantages:

Small depth of penetration

Limit to size of objects that can be imaged

Blurring of images due to reflection at boundaries

Radiation dosimetry: techniques for the measurement of amounts of ionizing radiation

Therapeutic Radiation

2. Absorbed Dose –

Significance: This is an attempt to quantify the total amount of ionization produced by radiation but it has limited application since doesn’t measure ability of body tissue to absorb radiation.

1. Exposure –

What are three factors that affect the absorbed dose?

1)

2)

3)

4)

Significance: Other radiations are measured against x-rays so the QF = 1 for x-rays. Note that alpha particles are 10 - 20 times more damaging per dose than x-rays. Remember that alpha particles have a very high ionizing ability.

Significance: This is really the absorbed dose taking into account the type of radiation that is used. It attempts to measure the radiation damage that actually occurs in tissues.

3. Quality Factor (Relative Biological Effectiveness): For the same absorbed dose, this factor measures the relative effectiveness of different radiations in destroying cells.

4. Dose Equivalent (Equivalent Dose) –

Radiation Therapy

Types of treatments:

1) Internal: A radioactive source can be placed within the tumor itself, either physically (intravenous injection) or chemically (swallowing it in a pill or liquid).

2) External: Overlapping beams of radiation can be used. Where they overlap the dose will be high (at the tumor site) while elsewhere the does will be low.

Balanced risk:

If the dose is too high, too many healthy cells are killed. If the dose if too low, cancer is not destroyed. The dose needs to be as high as possible in the region of the cancer and as low as possible everywhere else.

Types of sources:

1) A radioactive element

2) High energy X-rays, gamma rays or protons from particle accelerators

c) Inner ear: cochlea (oval window to auditory nerves) - filled with fluid

Example of therapy technique using X-rays to kill cancer cells in a tumor:

a) X-rays are much higher intensity than those used to take chest X-rays

b) Cancer cells are targeted to receive a high dose by irradiating region from different angles with tumor in overlap region

c) Aim is to minimize danger to other healthy cells while killing cancerous ones since malignant cells are preferentially susceptible to x-rays.

4. A parallel beam of X-rays passes through muscle and reduces to one-eighth of its initial intensity. Determine the fraction of the intensity of this beam when it is transmitted through the same thickness of fatty tissue. The half-value thickness of muscle is 4.0 mm and the half-value thickness of fatty tissue is 6.0 mm.

3. The half-value thickness for soft tissue (muscle) is about 20 cm and for bone is 150 times less than this. Determine the attenuation coefficient for bone and for soft tissue.

5. The half-value thickness of a 30 keV X-ray photon in aluminum is 2.4 mm. The initial intensity of the X-ray beam is 4.0 x 102 kW/m2.

a) What is the beam intensity after passing through 9.6 mm of aluminum?

b) What is the beam intensity after passing through 1.5 mm of aluminum?

Effective Half-life (TE) –

Biological Half-life (TB) –

Physical Half-life (TP) (same as T1/2) –

a. the time taken for ½ the number of radioactive nuclei in sample to decay

b. the time taken for the activity of a sample to decrease to ½ its initial value

Half-Life

Half-Life Relationship

1. If the physical half-life of a radioisotope is 10 days and the biological half-life is 15 days, what fraction will remain after 30 days?

b) Middle ear: ear drum to oval window (cochlea) - filled with air

2. a) The isotope iodine-131 can be used to treat malignant growths in the thyroid gland. The isotope has a radioactive half-life of 8 days and a biological half-life of 21 days. Calculate its effective half-life and determine the time it would take for its activity to decrease to 10% of its initial activity. 5.8 days

b) The isotope technetium-99 is also readily absorbed by the thyroid but has a radioactive half-life of only six hours. Comment on which of these two isotopes is preferable to use for:

i) diagnostic purposes

ii) therapeutic (treatment) purposes.

I0 =

I =

x =

b) What is the half-value thickness of the muscle shown above?

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