the physics of medical imaging

7/28/2019 The Physics of Medical Imaging

http://slidepdf.com/reader/full/the-physics-of-medical-imaging 1/14

THE PHYSICS OF MEDICAL IMAGING

This report will analyse the physics principles of various medical imaging techniques, including

ultrasound, x-ray, CT, MRI and radiopharmaceuticals. It will discuss how images are produced and

how the information is useful in making a diagnosis.

Medical imaging is an invaluable diagnostic tool and it allows doctors to gather high quality

information of specific internal structures or bodily processes. Much of this information cannot be

sourced in any other way, or in some cases the only other option is surgery. Medical imaging has the

advantage of being non-invasive and it allows doctors to make an accurate diagnosis earlier.



Ultrasound

Ultrasound machines use ultrasound waves which exceed the audible frequency for humans. Humans

can detect sound up to 20 kHz and ultrasound machines generally use a frequency of 1 to 10 MHz.

The waves are produced using a piezoelectric transducer. This utilises the piezoelectric effect, which

states that the shape of a crystal such as quartz changes when placed in an electric field, and the

amount of deformation is proportional to the size of the electric field. Reversing the direction of the

electric field will make the crystal structure deform in the opposite direction.

http://www.piezomaterials.com/

By controlling the potential difference across a crystal it can be made to deform back and forth or

oscillate. These vibrations are what produce the sound waves. The piezoelectric effect also states the

inverse, which is that deforming a crystal by applying a force to it will cause charge separation and

produce an electric current.

Ultrasound can produce useful images because different materials in the body reflect different

amounts of sound. The ability of body tissues to reflect sound waves is referred to as tissue

echogenicity. A slightly different measure is called acoustic impedance, which describes how tissuesresist sound. ' Acoustic impedance is proportional to the tissue density and to the speed of sound in

that kind of material. The larger the acoustic impedance the greater the amount of ultrasound waves

that are reflected.' (Clickview video) The following table lists acoustic impedances for different

materials.

http://www.nanomedicine.com/NMI/ListTables.htm

Body fluids do not reflect much sound back to the transducer so an ultrasound will display these as

darker regions, whereas fatty masses for example reflect more sound waves and will be displayed as



lighter regions. This is why the foetus can be clearly distinguished from the surrounding fluids in the

uterus.

http://www.pregnancycheck.com/pregnancy-ultrasound.html

An ultrasound machine's probe is also able to measure the time taken for sound waves to reachinternal features and return. It is also possible to determine the direction of blood flow in arteries, for

example, by understanding the Doppler effect. The sound waves reflected from something that has a

certain velocity towards the probe take less time to return than those reflected from something moving

away from the probe.

X-rays

X-rays are a high energy (120 eV to 120 keV) type of electromagnetic radiation with wavelengths of between 10

-8and 10

-11m. This means that they are able to penetrate many different materials. The

materials that make up the body have different densities due to differences in the arrangement of atoms, and the amount of radiation blocked is proportional to the density. Once the x-rays have passed through the body they exposed on film. The density of bone > soft tissue/water > fatty tissue > air.According to Schram (2001) the intensity of the exiting x-rays ‘depends on the density of the material (the linear attenuation coefficient increases with density) and the thickness of the material.’

X-rays are most useful for obtaining clear images of bone structures because bone is much denser

than the surrounding tissues and therefore shows up clearly on the film as white, less-exposed regions.



X-rays are produced in an evacuated x-ray tube where electrons from a heated filament are

accelerated by a very large potential difference (tens to hundreds of kV) from the cathode to the

anode, where they collide with a metal target. The high energy electrons remove some electrons

occupying the inner shells of the atoms in the metal target. For each electron ejected an electron from

the next highest energy level will fall to the shell below to replace it. This releases energy in the formof radiation (x-rays in this case) equivalent to the difference in binding energies of the two energy

levels. [Nave, 2010] Because different atoms have unique energy levels the amount of energy released

is characteristic to the type of atoms used in the metal target, therefore the x-rays produced by the x-

ray tube are called characteristic x-rays. X-ray generation can be thought of as the opposite of the

photoelectric effect, where electrons are released from a metal target that is bombarded with photons.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xtube.html

The following graph is an x-ray spectrum for a rhodium target and the potential difference between

the cathode and anode was 60 kV.



X-ray spectrum for rhodium, 60 kV potential difference

Handbook of X-ray spectrometry by René Grieken, Andrzej Markowicz, page 3, Google books link

The spectrum has sharp peaks or 'k lines' at certain energies which correspond to the characteristic x-

rays. On the horizontal axis is wavelength (»), from which it is possible to calculate the frequency ( f )

with the equation:

speed of light = λ

Also the energy ( E ) of a photon is proportional to its frequency: = ℎ

where h is Planck's constant.

On the vertical axis is counts per second which is a measure of the rate of radioactive decay, that is

the number of atoms that decay per second (this can either be actual decays or only the decays that are

detected).

The following table lists the characteristic x-ray lines for rhodium. There are five listed here and note

that the first two have very similar energies and wavelengths - these probably only show up as a

single line on the spectrum. The third line has the smallest wavelength so it is most likely the leftmost

line on the spectrum. Its wavelength of 0.0546 nm, which is 54.6 pm, matches the graph. The last two

lines would be placed on the far right of the spectrum, but perhaps the chance of these energy level

transfers is very low so the counts per second isn't registered.

Line Energy Wavelength

Rh K±1 20.214 keV 0.0613 nm

Rh K±2 20.072 keV 0.0617 nm

Rh K±1 22.721 keV 0.0546 nm

Rh L±1,2 2.694 keV 0.4601 nm

Rh L±2 2.834 keV 0.4374 nm

http://www.bruker-axs.de/fileadmin/user_upload/xrfintro/sec1_4.html

http://books.google.com/books?id=i_iDRTp75AsC&pg=PA3






The rest of the spectrum is continuous, which is caused by a type of radiation called bremsstrahlung ,

meaning braking radiation. In an x-ray tube the bombarding electrons suddenly decelerate when they

encounter the target. Deceleration occurs because the electrons experience Coulomb attractions with

the nuclei of the atoms in the target, or in some cases they have a direct collision. Any kinetic energy

lost is released as a photon, or usually a number of photons. Because a range of kinetic energies can

be lost there will be a continuous spectrum of radiation.

http://imagine.gsfc.nasa.gov/docs/science/how_l2/xray_generation_el.html

On the rhodium spectrum given previously there are no X-rays with a wavelength smaller than

approximately 21 pm because the x-ray tube was operated at a voltage of 60 kV and therefore the

maximum energy of an accelerated electron is 60 keV. In the event that an electron has a direct

collision with an atomic nucleus all of its kinetic energy would be converted into at most a single 60

keV photon.

60 keV = 60 × 103 eV = 6 × 104 eV

1 = 1.6 × 10−19 J

∴ 6 × 1 04 = 6 × 1 04 × 1.6× 10−19 J

= 9.6 × 10−15 J

= ℎ and = λ so =ℎ

λ

λ =ℎ

=6.63 × 10−34 × 3 × 1 08

9.6 × 10−15

= 2.07 × 10−11 m

= 20.7 pm

The smallest wavelength is approximately 21 pm, which matches what is shown on the graph.

Although the metal target used to produce this spectrum was made of rhodium, commonly tungsten is

used. 'Tungsten is the most commonly used target material in the anode because it has a high atomic

number which increases the intensity of the x-rays, and because it has a sufficiently high melting point

that it can be allowed to become white hot. During operation, the tungsten target can get as high as

2,700 degrees centigrade.'

(http://www.orau.org/ptp/collection/xraytubescoolidge/coolidgeinformation.htm)



CT

Computed tomography (CT) scans are produced with x-rays from an x-ray tube, so most of the

physics has already been discussed. The main difference is that a CT machine uses multiple x-rays to

develop a comprehensive three dimensional model of the body. The x-ray tube rotates at high speed

around the body and there are x-ray detectors opposite the tube. As the apparatus is rotating the

patient is moved along the central axis, so the result is a series of slices through a section of the body.

http://www.worldculturepictorial.com/blog/content/ct-scan-study-shows-increased-radiation-

exposure-cancer-risks-tests-often-unnecessary

With regular x-rays a bone fracture or other injury can often only be seen from a certain angle. CT has

the advantage of scanning the body from various angles in a single procedure. The comprehensive

imaging that CT provides means that it is also effective for imaging body features other than bones.

MRI

Nuclear magnetic resonance imaging (MRI) uses a strong magnetic field and low energy, non-

ionising radiation in the form of radio waves to create detailed images of soft tissues. It relies on the

fact that hydrogen atoms are abundant in the body in the form of water and fat. The nucleus of each

hydrogen atom consists of a proton with a single positive charge that spins on an axis. When these

charged particles spin they create a very small magnetic field. MRI machines utilise very strong

electromagnets typically with a magnetic field strength of around 1.5 T. When the machine's main

magnetic field is activated (running through the centre of the electromagnet coil from the patient's

head to feet) the normally randomly arranged protons line up both with and against the magnetic field.



http://en.wikipedia.org/wiki/File:Electromagnetism.svg

http://en.wikipedia.org/wiki/File:VFPt_Solenoid_correct.svg

There is an extremely small yet measurable excess of protons which prefer to line up with the

magnetic field because this is a lower energy state.

http://www.simplyphysics.com/page2_2.html

The magnetic fields of the protons facing in opposite directions cancel each other out, but because

there is a slight excess in one direction the result is a small net magnetic field. An MRI machine is

able to produce an image by using a radio wave transmitter. This emits photons perpendicular to the

magnetic field and each photon needs to have a particular frequency such that the protons will absorb

energy and change their alignment. This is called the Larmor frequency ( f L), which depends on the

magnetic field strength (B) and the gyromagnetic ratio (³ ) of the proton:

L =

Hydrogen has a gyromagnetic ratio of 42.58 MHz/T.

The Larmor frequency is specific to each atom because the energy an atom gains by absorbing a

photon must match the energy difference between the lower energy state and the higher energy state.

The energy of a photon is given by:

= ℎ

And since L = the energy needed to excite a hydrogen proton from its ordinary spin state to a

different spin state is:

= ℎ

The radio transmitter producing the photons can then be switched off and the protons will begin

wobbling or precessing as they relax back to their original spin state. Precession releases photons with

energies equal to the difference between the spin states and the photons are detected by a radio

receiver. This return signal is what is used to produce an image.



Tissues have varying densities of protons and therefore the intensity of the returning radio signals can be used to distinguish between tissues. Also, 'Water is the major source of the MR signal in tissuesother than fat. Mineral-rich structures, such as bone and calculi, and collagenous tissues, such asligaments, tendons, fibrocartilage, and tissue fibrosis, are low in water content and lack mobile

protons to produce an MR signal. These tissues are low in signal intensity on all MR sequences.'(Reference article) The surrounding environment of a particular tissue is important in generating MRIscans.

http://www.cis.rit.edu/htbooks/nmr/chap-3/chap-3.htm

Diagram summarising the physics involved in MRI

'(a) Illustration of random direction of magnetic dipole moments in absence of external magnetic

field. (b) Alignment (parallel or antiparallel) of magnetic dipole moments in the presence of an

external magnetic field. A (small) preference for parallel alignment exists, depending on field

strength. (c) Use of a radiofrequency (RF) pulse to ‘flip’ magnetic dipole moments into the transverse

plane. The RF pulse is generated using a transmitter coil. (d) Precession of magnetic dipoles withinthe transverse plane. Measurement of the RF signal caused by the precession using a receiver coil. (e)

Schematic drawing of the main components of an magnetic resonance imaging scanner.'

http://www.heartandmetabolism.org/issues/hm34/hm34refresherc.asp

Radiopharmaceuticals

An isotope of an atom has the same number of protons but a different number of neutrons. Isotopescan be unstable if the ratio of the number of protons to neutrons falls outside a particular range – the

region of stability is graphed below.



An unstable atom can achieve stability by emitting alpha particles (alpha decay), electrons (beta

decay) or positrons (also a type of beta decay, called beta plus decay). In beta plus decay a proton isconverted to a neutron, a positron and a neutrino.

http://www.euronuclear.org/info/encyclopedia/betaplusdecay.htm

Positron emission tomography (PET) is a nuclear medicine procedure that involves beta plus decay. Aradiotracer, which is a radioisotope such as carbon-11, fluorine-18 or oxygen-15, can be injected,inhaled or ingested. The positrons emitted by the radiotracer combine with electrons to release two photons of gamma radiation, which are detected by gamma cameras. A gamma camera works by a process called scintillation, where light is released when an electron in a crystal (iodine, for example)falls back to a lower energy state after being excited by the gamma radiation from the radiotracer.This light is detected and is used to generate an image.



Principles of positron emission tomography image acquisition

http://www.heartandmetabolism.org/issues/hm34/hm34refresherc.asp

Radiotracers spread throughout the body and the intensity of the radiation emitted indicates theconcentration of radiotracer in a particular part of the body, for example an organ. The amount of radiotracer found in an organ usually depends on its metabolic activity, so abnormal radiotracer levels

can be used to make certain diagnoses. ' By making sequential images over time, it is possible to followthe uptake, retention, and washout of the tracer in tissue. This time course of the radiotracer or thedistribution of a tracer at a certain period after its administration can be used to obtain functional (or

physiological) information such as cardiac wall perfusion or glucose consumption.'[http://www.heartandmetabolism.org/issues/hm34/hm34refresherc.asp]



TASK 2

16: Positron emission tomography (PET) scan of a person on cocaine

'Cocaine has other actions in the brain in addition to activating reward. Scientists have the ability to see how cocaine actually affects brain function in people. The PET scan allows one to see how the

brain uses glucose; glucose provides energy to each neuron so it can perform work. The scans show

where the cocaine interferes with the brain's use of glucose - or its metabolic activity. The left scan is

taken from a normal, awake person. The red color shows the highest level of glucose utilization

(yellow represents less utilization and blue shows the least). The right scan is taken from a cocaine

abuser on cocaine. It shows that the brain cannot use glucose nearly as effectively - show the loss of

red compared to the left scan. There are many areas of the brain that have reduced metabolic activity.

The continued reduction in the neurons' ability to use glucose (energy) results in disruption of many

brain functions.'

http://www.nida.nih.gov/pubs/teaching/teaching4.html

'Whole-body PET scans from two patients. The left scan isnormal; the right scan is from a patient with a lung tumor that

spread from primary breast cancer. This scan shows increased

F-18 FDG uptake in the tumor (arrow) because a growing tumor has a higher rate of sugar metabolism than the

surrounding normal tissue.'

http://www.doemedicalsciences.org/pubs/sc0033/radio.shtml






Bibliography

Garner, S. (2009). The Physics of Medical Imaging . (Video Recording). Bendigo : VEA

This video covered almost all aspects of medical imaging. It gave fairly detailed explanations of how

each technique produces images and there was also discussion by an expert of what can be interpreted

from different images. The video gave a decent introduction to some of the more complicated physics

aspects and in the case of MRI there was some advanced terminology used without giving a detailed

explanation.

Piezoelectric Materials. (2007). Retrieved 2010, from http://www.piezomaterials.com/

This website provided a brief summary of the piezoelectric effect and a clear diagram was also

sourced from here.

Frietas, R. (1997). Nanomedicine. Retrieved 2010, from

http://www.nanomedicine.com/NMI/ListTables.htm

The table of acoustic impedances was retrieved from this website and this was very relevant to the

discussion of ultrasound.

Pregnancy Check . (2010). Retrieved 2010, from

http://www.pregnancycheck.com/pregnancy-ultrasound.html

The ultrasound scan of a woman’s womb was retrieved from this website and was used to

demonstrate how different acoustic impedances translate to an image.

Nave, R. (2010). Hyperphysics. Retrieved 2010, from

http://hyperphysics.phy-astr.gsu.edu/hbase/

This website was most useful for learning about x-ray radiation. There was an easy to understand

explanation of x-ray generation and x-ray tubes with an accompanying diagram. This site was helpful

in understanding what an x-ray spectrum is.

http://imagine.gsfc.nasa.gov/docs/science/how_l2/xray_generation_el.htmlThis website was searched for information about bremsstrahlung. Whilst a definition was given there

was no further explanation and I was left with more questions than answers.

http://www.simplyphysics.com/page2_2.html

This website offered an advanced explanation of the physics associated with MRI, including spin and

the relaxation stages. I liked the mathematical approach the author took in the discussion, which

included many diagrams with vectors and also some equations. Unfortunately a lot of the terminology

and some of the theory was beyond my comprehension. It would have been helpful to see some links

to background information.

National Institute of Drug Abuse.



http://www.nida.nih.gov/pubs/teaching/teaching4.html

This website provided the PET scan of the brain with and without cocaine.

Salwa Aziz & Christina Derbidge

the physics of medical imaging

Documents