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3 Informed Consent
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3.3.1 Informed Consent inTerms
oftheUse ofArticial
Intelligence
The loss of human control by assigning decisionmaking to AI-guided technologies could affect
various aspects of clinical care and the healthcare
system, including the communication in the clinician–patient relationship [10]. With the increasing use of algorithmic decision-making seen in
AI in healthcare, patients have an ethical right to
expect an explanation about how decisions
regarding their diagnosis was reached [8, 9].
However, hospitals and healthcare providers are
unlikely to inform patients that AI was used as a
part of decision-making to guide or validate a
diagnosis; there is currently no precedent for
seeking the consent of patients to use technologies for diagnosis or treatment [10].
The use of AI in medicine and failure to disclose its use could challenge the core of informed
consent and wider public trust in healthcare [10].
It is therefore unsurprising that a current area of
debate in the profession lies in what extent a
patient needs to be aware of the use of AI technologies in their procedure, treatment, and/or
decisions, and whether the decisions informed
by AI systems have been adhered to or overruled
by the doctor [11]. According to Amann et al.
[11], the underlying process and algorithms
associated with AI decision-making have to be
explained to patients. They need not to know
about every technical detail, but certainly about
how their data are to be used, how their nal
diagnosis was revealed and the risks associated
with the decision-making.
If using AI recommended diagnosis, the medicolegal question that arises is who is responsible
for the diagnosis, especially if it is a wrong diagnosis? Basically, if radiologists are no longer the
interpreters of radiological studies such as CTC
examinations, who will be accountable for the
decision made? Would it still be a radiologist
even though they will not have been able to fully
understand nor interrogate the precision within
the decision-making process? [12]. The use of AI
in the decision-making process to conrm a diagnosis following a CTC examination therefore
needs to be explained to a patient [13, 14].
The World Health Organisation (WHO) states
that transparency is crucial to promoting trust
among all stakeholders, particularly patients; the
WHO encourages practitioners to be frank with
patients from the onset about the use of AI rather
than hiding the technology [10]. This can have a
signicant impact on their right to exercise their
autonomy: the explanation must, therefore, form
part of the ‘informed’ aspect of ‘informed consent’. Practitioners should try their best to explain
to their patients the purpose of using AI, how it
functions, and what value it adds to their treatment and management. They should also be
transparent about any weaknesses of the AI technology, such as any biases, data breaches, or privacy concerns [10]. Only with transparency can
the deployment of AI for healthcare and health
science, including hospital practice, become a
long-term success. Trust is key to facilitating the
adoption of AI in medicine [10]. The principles
of AI are discussed in Chap. 25.
3.4 The Legal Aspects ofConsent
There are two distinct aspects to the legalities of
consent in medicine, both of which normally
reside in tort law, that is, the wrong committed by
one person on another being considered a civil
wrong rather than a legal matter.
The rst aspect to consider is that of patients
actually giving their consent to the examination
or procedure. Should any examination or procedure go ahead without them giving their consent,
they then may sue for trespass to the person.
Trespass to the person occurs when a patient has
not given their consent and is subject to either the
act of assault (whereby a patient apprehends a
touching of their person) or battery (whereby a
patient was actually touched). A patient who has
suffered trespass to their person is able to sue for
compensation in the civil courts. In order to do
this, they must be able to prove the touching or
the apprehension of the touching of their person,
and that it was a direct intentional interference or
had the potential to be a direct intentional
interference with them. There is no legal obligation for a patient to prove that harm has occurred
[15, 16].
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A. Ramlaul and T. Gregory
The second key element is that of negligence.
All healthcare practitioners have a duty of care to
their patients. As part of this duty of care, practitioners are required to give sufcient information
about all aspects of a procedure, including the
risks involved. Failure on the part of the practitioner to give sufcient information could result in
the bringing of an action for negligence. In order
to establish that a practitioner has been negligent,
a patient has to prove a number of key elements:
that they were owed a duty of care by the healthcare practitioner, that this duty of care was
breached by way of failure to give sufcient
information; that this breach of duty of care
resulted in them agreeing to the examination or
procedure, and that in doing so, they suffered
harm as a result.
3.5 Patient Information
Adequate information must be provided to all
patients. The information must be written in a
comprehensive manner to include all the important benets and risks of an examination and
whether the examination is being carried out as a
diagnostic test or a screening test. If current
information leaets given to CTC patients at the
preparatory stage do not include the information,
then those leaets need to be reassessed and
information on benet and harm added in [17].
Best practice in information giving should
consist of the following information as a minimum requirement [18].
Pre-procedure
• Purpose of the procedure to primarily investi-
gate the presence of bowel cancer or precan-
cerous polyps
• Full description of the procedure in detail
from start to nish with assurance that dignity
will be maintained at all times
• Contra-indications to bowel preparation
• Names and reliable contact details of appro-
priate persons who can be approached to
answer questions or provide advice and
guidance
• Bowel preparation instructions and effects on
bowel habit
Aftercare advice
• Process for being informed of results
• Possible complications and when to seek
medical advice
• Post procedure advice: eating, bowel habit,
etc.
In addition, the National Patient Safety
Guidelines (NPSA) must be followed during the
prescribing of laxatives for bowel preparation.
The consent provided by a patient must be
recorded in writing, including the date and designation of the person to whom consent was given.
This should be recorded electronically. If not a
radiographer, then a healthcare professional, in
gaining consent from a patient, should be sufciently knowledgeable and informed to answer
routine questions and must be able to call upon
the expert advice of either a radiographer or radiologist prior to the appointment or examination.
In signing consent, a patient should be satised
that all questions have been answered sufciently
and that the benets, risks, and side effects of the
examination have been explained to them.
3.6 Risks Associated withCTC
Procedures
There are risks associated with a CTC study. It
involves a CT examination where there is a risk
of ionising radiation damage to tissues. Patients
need to be informed of this risk prior to conducting a CTC examination [19]. This could be a verbal explanation or included in the patient
preparation leaet provided prior to the
examination.
An explanation of the risks should include the
following
• Risk of perforation
• Anaphylactic reaction from the use of contrast
agents (see Chap. 8)
• Risk of harm from ionising radiation explained
as a dose equivalent of a CT scan (see Chaps.
5 and 6)
• In the case of patients undergoing CTC screening, the risk of psychological harm in incidence of false positives and false negatives
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• Risk of harm from an incidental nding when
the examination is being carried out. CTC
examinations also demonstrate intra- abdominal
and pelvic organs; approximately 10% of cases
[20] demonstrate signicant pathology, e.g.
underlying lymphomas or early cancers of the
kidney and ovaries may be identied (see Chap.
18)
• Risk of wrong diagnosis, either human or
through AI algorithm recommendations as
detailed above
In addition, there should be an explanation of
the following
• Side effects and discomfort, e.g. bloating arising from the insufation of air, and dehydration arising from an electrolyte imbalance
caused by the contrast agents
• Alternative options, if appropriate
3.7 The Duty ofConsent
andtheRole ofaCTC
Radiographer
One of the current dilemmas in gaining informed
consent lies in the question of ‘whose responsibility is it to gain informed consent?’ Does this
responsibility lie with the referring physician or
does the responsibility lie with the practitioner
conducting the examination? In the case of
radiographer-led CTC, the question is, ‘would
the radiographer in charge of carrying out the
examination be responsible?’
Interestingly, the results of a recent survey
conducted to radiographers [21] revealed that
radiographers were of the opinion that a
patient’s referring physician was responsible
for obtaining informed consent. When an examination involves the risk of ionising radiation,
only trained experts in the eld of medical ionising radiation are qualied to inform patients
of the risks of the procedure and explain the
benet of having the examination in spite of the
risks. If radiographers are of the opinion that it
is not their responsibility, then they are of the
belief that the referring physician is fully
knowledgeable and competent to inform the
patient of risks and benets of ionising
radiation.
Radiographers are the experts in their eld,
and using the lowest radiation dose for the best
image quality, i.e. as low as reasonably achievable (ALARA), is the basis of radiography.
Radiographers should be able to condently
advise their patients of the dose of radiation
they are receiving and how this translates to a
risk experienced in their everyday lives (see
Chaps. 5 and 6).
The overall responsibility of obtaining
informed consent remains with a healthcare practitioner responsible for conducting the medical
intervention. In this case, if the procedure is
being carried out by a radiographer, then it is
their responsibility and not that of the referring
physician. If the examination is being carried out
by a radiologist the overall responsibility is theirs
even though they chose to delegate the responsibility to a radiographer or a radiology department
nurse. In the event of delegation, a radiologist
should be available to answer questions that may
arise or if a patient wishes to speak to them.
A CTC radiographer has a duty in ensuring
that a patient has been provided with sufcient
information on all aspects of the examination and
that they have given their informed consent prior
to the examination being carried out.
Radiographers must adhere to their respective
employer’s local policies and procedures in relation to consent and must be aware of and adhere
to guidance issued by the appropriate regulatory
body (e.g., Health and Care Professions Council)
in the country in which they practise [22].
3.8 Good Practice inInformation
Giving
The incidence of developing further cancer from
radiation depends on the radiation dose received.
It is therefore important that patients are sufciently informed of not just the nature of the
examination or procedure that they are about to
undergo, but also have been provided with adequate information that will enable them to make
an informed decision as to whether or not to
proceed.
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A. Ramlaul and T. Gregory
The language used in the information leaets
needs to be comprehensible to a lay person and
should avoid the use of medical jargon.
Furthermore, the information leaet is likely to
be read by a patient’s family and as such its readability (see Sect. 2.9 in Chap. 2) is of utmost
importance for maximising understanding of the
procedure and its requirements. This ultimately
can affect a patient’s experience and the overall
quality and outcome of the procedure patientcentred communication is discussed in Chap. 2.
In addition, CTC radiographers need to ensure
that they do not present an overwhelming amount
of information that may affect a patient’s
decision- making ability [8]. The more complex a
medical imaging examination and/or its side
effects, the greater the risks involved. It is therefore crucial to have formal records of patient
consent.
Information should be given in advance of the
day of examination to enable a patient to take
time to read and understand the information and
ask questions before their examination. This is
one of the key areas that enables consent to be
informed [8]. The associated risks need to be
dened in advance and clearly articulated within
patient information leaets.
In keeping with a patient-centred care
approach, the entire process of information giving and gaining consent should be patient
focussed taking into account a patient’s culture
and beliefs and being able to identify when alternate methods of communication may be required,
for example, in cases where English may not be
their rst language or if a patient has special care
considerations, for example, dementia (see
Chap. 2).
With regard to duty of care, a CTC radiographer must inform a patient of the benets of the
procedure in addition to the risks. Patients must
also be informed of what the likely alternative
options may be as well as the risk involved in not
having the examination at all, i.e. doing nothing
[8].
Patients are naturally concerned about the
harmful effects of ionising radiation, not only to
themselves, but also to their future offspring.
Care should be taken to use appropriate language
when discussing the risks and benets of the
examination so that they are able to understand
the consequences.
In the case of patients undergoing CTC screening, information regarding risks applicable to
them must include, in addition to those already
mentioned, the risk of psychological harm from
over or under diagnosis that may result from false
positives or false negatives. In addition, there is a
risk of distress from the discovery of extracolonic
pathologies or conditions that may present itself
as incidental ndings during the screening procedure. Extracolonic ndings are discussed in detail
in Chap. 18.
3.9 Clinical Audit toInclude
Informed Consent
andPatient Information
CTC examinations must be audited against best
practice standards for compliance with the standard, to ensure standards of practice are optimal,
and to improve patient outcomes and experience.
Informed consent is one of several CTC standards. Patient experience of the entire CTC process is an auditable outcome [23]. The principles
of a clinical audit are presented in Chap. 27.
Key Messages
• Patients have the fundamental legal and ethi-
cal right to determine what happens to their
own bodies. Ensuring that consent is informed
plays a pivotal role in enabling patients to
exercise their autonomy.
• A radiographer has a duty of care to inform
each patient of the benets and risks of the
CTC examination. Patients must also be
informed of the likely alternative options as
well as the risk involved if they do not have
the examination at all.
• The responsibility of obtaining informed con-
sent lies with the healthcare practitioner
responsible for conducting the medical
intervention.
• Written consent is required for invasive proce-
dures, which are considered to involve signi-
cant risks or side effects.
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• If a patient fails to fully understand the nature
of the examination, including the risks that it
involves, then the consent given by such a
patient is not considered to be valid.
• The language used in information leaets
needs to be devoid of medical jargon and must
be written in a comprehensible style that is
understood by a layperson.
• When explaining the extent of the risk from
radiation to patients, liken the radiation dose
to other acceptable risks in society that they
can identify with on a daily basis.
• The experience of a CTC patient is an auditable outcome.
3.10 Summary
Informed consent is an important patient right
and fundamental within medical law. There are
two aspects to the law of informed consent. One
is the act of a practitioner giving information to a
patient. The other is receiving and processing of
information by a patient: asking questions and
then signing a consent form thus providing a
written gesture of acceptance of the examination.
If an examination is conducted in the absence of
consent, a patient may sue for compensation on
the grounds of ‘trespass to the person’. All practitioners have a duty of care to their patients. Part
of this duty of care is to provide sufcient information about all aspects of a CTC procedure.
Failure to give sufcient information could result
in a patient bringing about an action for
negligence.
Radiographers must work within their scope
of practice and the expectations set by their professional and regulatory bodies in order for high
standards in professional practice to be
maintained.
References
1. World Medical Association. The physician’s pledge.
Declaration of Geneva adopted in 1948, amended
by the 68th WMA General Assembly, Chicago,
United States, October 2017. Ferney-Voltaire: World
Medical Association. 2017. https://www.who.int/
publications/i/item/9789240047785. Accessed 21
Nov 2022.
2. World Health Organisation. Ethics and medical
radiological imaging: a policy brief for health-care
providers. 2022. https://www.who.int/publications/i/
item/9789240047785. Accessed 21 Nov 2022.
3. Department of Health. Reference guide to consent for
examination or treatment. 2nd ed. 2009. https://assets.
publishing.service.gov.uk/government/uploads/
system/uploads/attachment_data/file/138296/
dh_103653__1_.pdf. Accessed 21 Nov 2022.
4. Shala KK, Patra AP, Das S. The importance of
informed consent in medicine. Sch J Appl Med
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sjams.2013.v01i05.0025455.
5. NHS Bowel Cancer Screening Programme (BCSP).
Bowel cancer screening: guidelines for CTC imaging.
2021. Bowel cancer screening: guidelines for CTC
imaging—GOV.UK. www.gov.uk. Accessed 21 Nov
2022.
6. Mental Capacity Act. 2005. https://www.legislation.
gov.uk/ukpga/2005/9/contents. Accessed 21 Nov
2022.
7. Mental Capacity (Amendment) Act. 2019.
https://www.legislation.gov.uk/ukpga/2019/18/
enacted#:~:text=2019%20CHAPTER%20
18,consent%3B%20and%20for%20connected%20
purposes. Accessed 21 Nov 2022.
8. Society and College of Radiographers (SCoR).
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obtaining- consent- a- clinical- guideline- for- the- dia.
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9. General Medical Council. Decision making and consent. 2020. https://www.gmc- uk.org/ethical- guidance/
ethical- guidance- for- doctors/decision- making- andconsent. Accessed 21 Nov 2022.
10. World Health Organization. Ethics and governance
of articial intelligence for health: WHO guidance. 2021. https://www.who.int/publications/i/
item/9789240029200. Accessed 21 Nov 2022.
11. Amann J, Blasimme A, Vayena E, Frey D, Madai
VI. Explainability for articial intelligence in
healthcare: a multidisciplinary perspective. BMC
Med Inform Decis Mak. 2020;20:310. https://doi.
org/10.1186/s12911- 020- 01332- 6.
12. European Society of Radiology (ESR). What the radiologist should know about articial intelligence—an
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https://doi.org/10.1186/s13244- 019- 0738- 2.
13. Kim TW, Routledge BR. Why a right to an explanation of algorithmic decision-making should exist: a
trust-based approach. Bus Ethics Q. 2022;32(1):75–
102. https://doi.org/10.1017/beq.2021.3.
14. Astromskė K, Peičius E, Astromskis P. Ethical and
legal challenges of informed consent applying articial intelligence in medical diagnostic consultations.
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AI & Soc. 2021;36:509–20. https://doi.org/10.1007/
s00146- 020- 01008- 9.
15. Dimond BC.Legal aspects of radiography and radiology. Oxford: Wiley-Blackwell; 2008.
16. Ramlaul A, Gregory T. Ethical and legal considerations in professional practice. In: Ramlaul A, Vosper
M, editors. Patient centred care in medical imaging
and radiotherapy. London: Churchill Livingstone;
2013. p.255–69.
17. Hersch J, Barratt A, Jansen J, etal. Use of a decision aid including information on overdetection
to support informed choice about breast cancer
screening: a randomised controlled trial. Lancet.
2015;385(9978):1642–52. https://doi.org/10.1016/
S0140- 6736(15)60123- 4.
18. Society and College of Radiographers (SCoR).
Guidelines for the provision of a safe and effective
CT colonography service. 2018. https://www.sor.
org/learning- advice/professional- body- guidanceand- publications/documents- and- publications/
policy- guidance- document- library/national- bestpractice- guidelines- for- the- ct- colon. Accessed 21
Nov 2022.
19. Doudenkova V, Bélisle Pipon JC. Duty to inform
and informed consent in diagnostic radiology:
how ethics and law can better guide practice. HEC
Forum. 2016;28:75–94. https://doi.org/10.1007/
s10730- 015- 9275- 7.
20. Bortz JH. An approach for performing a successful
computed tomography colonography examination. S
Afr J Radiol. 2014;18(1):607. https://doi.org/10.4102/
sajr.v18i1.607.
21. Friedrich-Nel H, Munro L. Radiographers’ opinions
on patients’ rights to informed consent: results of an
online survey. SAR. 2015;53(1):27–33.
22. Health and Care Professions Council. Standards of
conduct, performance and ethics. London: Health and
Care Professions Council; 2016.
23. British Society of Gastrointestinal and Abdominal
Radiology and Royal College of Radiologists.
Standards of practice for computed tomography
colonography (CTC). 2021. https://www.rcr.ac.uk/
system/files/publication/field_publication_files/
bfcr201- standards- of- practice- for- computedtomography- colonography- ctc.pdf. Accessed 21
Nov 2022.
Principles ofCT andHybrid
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Imaging
ChristophJ.Trauernicht
4
4.1 Introduction
Computed tomography (CT) entered its sixth
decade of clinical use and has proved an exceptionally valuable and useful imaging tool. The
rst head CT scanner was introduced in 1972.
Each pair of slices took over 4min of scan time
and over 1 min of reconstruction time. While
this would be considered quite terrible by
today’s standards, it was considered revolutionary at the time and earned Godfrey Hounseld
and Allan Cormack the Nobel Prize in Medicine
in 1979.
4.2 Principles ofCT
4.2.1 The X-ray Tube
At the heart of a CT scanner is an X-ray tube
(Fig.4.1). A tungsten lament is heated and emits
electrons by a process known as thermionic emission. The emitted electrons, having a negative
charge, are accelerated across a potential difference towards a copper anode, which sits at a positive potential. All this happens inside an evacuated
glass housing. The vacuum is required to prevent
C. J. Trauernicht (*)
Division of Medical Physics, Tygerberg Hospital and
Stellenbosch University, Cape Town, South Africa
e-mail: cjt@sun.ac.za
electrons from interacting with any materials
inside the housing, other than the tungsten
target.
When energetic electrons come into the vicinity of an atomic nucleus, the positively charged
nucleus attracts the negatively charged electrons,
and these are decelerated in the process. The
electric eld of the nucleus exerts a force on the
incoming electron and forces it to change its
velocity (i.e., energy) and direction.
The energy difference of the initial electron
energy and the deected electron energy shows
up as an X-ray photon. This process is known as
bremsstrahlung (Fig.4.2), which is the German
word for “braking radiation”. Bremsstrahlung
production depends on the square of the number
of protons (Z) in the target nucleus; therefore, the
target should consist of a material with a high
atomic number, like tungsten (Z = 74).
Bremsstrahlung production is very inefcient,
only around 0.9% for 100 keV electrons, the
other 99% of energy is lost through other interactions that do not produce X-rays, but that do
result in heat. Therefore, there must be a cooling
mechanism for the X-ray target, and the target
material must have a high melting point.
An electron that is travelling close to a
nucleus will experience a larger force of attraction to the nucleus than one that is passing the
nucleus at a larger distance. The electron will
experience a larger energy loss, resulting in a
higher energy X-ray photon. If the potential dif-
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
J. H. Bortz et al. (eds.), CT Colonography for Radiographers,
https://doi.org/10.1007/978-3-031-30866-6_4
29
30
copper anode
oltage
heated tungsten filament
v
emitted radiation
electron
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oltage –
C. J. Trauernicht
electrons
+ v
Fig. 4.1 Simplied diagram of an X-ray tube
Fig. 4.2 Bremsstrahlung production
ference between the tungsten lament and the
target is, for example, 120.000V (or 120 kVp),
then the resultant X-rays will have an energy
range from near zero up to 120 kVp. When the
operator selects a kVp before the acquisition of
an image series, this adjusts the potential difference inside the X-ray tube through the use of a
transformer. If the kVp is increased, the energy
of the X-rays is increased. This is often referred
to as beam quality. In addition, bremsstrahlung
production becomes more efcient at higher
energies, resulting in more X-rays. This is
referred to as the “quantity”. Dose to the patient
increases with the square of the kVp. It should
be noted that the average X-ray energy is only
about 1/3–1/2 of the peak kilovoltage. The very
low energy X-rays do not contribute to useful
image information and are ltered out before the
beam enters the patient. Additionally, superimposed on the continuous bremsstrahlung X-ray
spectrum are discrete peaks (characteristic radiation) that happen when electrons transition from
one energy shell to another one inside the target
material after they were knocked out of their
shell by the incoming energetic electrons. The
manipulation of this spectrum is important in
dual-energy CT (DECT). Principles of DECT
are presented in Chap. 26.
nucleus
evacuated glass housing
tungsten target
X-rays
X-rays
A direct current (DC) must be used to accelerate the electrons in the tube housing; an alternating
current (AC) would result in electrons being
accelerated back and forth in the tube, without
any useful output. There are additional circuits in
an X-ray tube (not indicated in Fig. 4.1), for
example, to provide power to focusing cups for
the electrons before they are accelerated, so that
they travel in a more focused beam towards the
anode. The tungsten lament also has its own circuit, and the number of electrons that are emitted
can be increased by increasing the lament current, which results in more heat in the lament,
and thus more emitted electrons. When an operator adjusts the mA on the control console, this
refers to the number of electrons that are accelerated in the X-ray tube, i.e. the beam current.
Increasing the mA on the console increases the
current to the lament, which means more electrons are emitted and accelerated. Increasing the
mA does not affect the beam energy (or beam
quality) but does increase the number of X-rays
(quantity). Dose is linearly proportional to the
beam current or the current-time product (mAs).
CT scanner X-ray tubes have substantially
higher requirements than ordinary X-ray tubes
because they do not just take a single image, but a
series of many projection images. One way in
which the additional heat that is generated is dissipated, is by situating the tungsten target inside
the X-ray tube on a rotating anode disk, which
rotates at a few thousand revolutions per minute. If
a rotating anode has a focal track radius of 5cm
and a 1mm track width, then the annular area that
the electrons hit is 314 times (2πr) larger than that
of a xed anode with a focal spot of 1mm × 1mm,
resulting in substantially improved heat loading.
I I
x
nd
=×
−++++
()
×
0
µµ µµ
,
1
x
×
attenuation
detector
attenuation
detector
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31
Of course, the X-ray tube must be shielded.
X-rays are uncharged photons, and it is thus not
possible to steer or focus these. The only way to
stop them from going where they shouldn’t is to
either shield or collimate them. An X-ray tube
has an exit window that allows X-rays to escape
in a particular direction: the rest of the tube is
shielded. For a more detailed description of X-ray
tubes and computed tomography, the reader is
referred to [1–3].
4.2.2 What Are WeImaging?
A planar X-ray of a patient is, in essence, a representation of how the X-ray beam was attenuated
through the body of a patient. This is shown visually for a single line of response, also known as a
ray, in Fig.4.3. The initial beam intensity I0 gets
reduced as the beam penetrates through the
patient. An attenuated beam intensity Ix arrives at
the detector. In mathematical terms, this is given
by Ix=I0 × e
patient and μ (Greek letter “mu”) represents the
linear attenuation coefcient.
If we now superimpose a matrix over a patient
(Fig.4.4), then the total attenuation along the line
of response will be the sum of each pixel attenuation contribution along the same line of response.
This is given by:
where d is the pixel dimension and μ1 to μn is the
linear attenuation coefcient of each pixel in that
line of response.
−μ × x
, where x is the thickness of the
123
e
X-ray tube
X-ray tube
µ
1
µ
2
.
.
µ
n
Fig. 4.4 Pixel map
For a CT image a third dimension, the slice
thickness, is included as well. Therefore, each
pixel on a CT image represents the average attenuation properties of the tissue in this volume element (voxel). A series of rays that pass through
the patient at the same orientation is called a view
or a projection. A single axial CT image may
involve about 800 rays taken at 1000 different
projection angles. A typical CT slice has dimensions of 512 × 512 pixels.
One of the biggest advantages of CT imaging
is the reconstruction of many projections into
cross-sectional images. Interestingly, the maths
for this was developed in 1917 already, when
Johann Radon showed that the image of a threedimensional object can be constructed from an
innite number of two-dimensional images of the
object.
4.3 Tomographic Reconstruction:
Backprojection
In the previous section, the relationship between
the initial and transmitted beam intensity for each
ray was given by Ix=I0 × e
sity can be determined by doing a blank scan (as
is done every morning), and Ix is measured with
the patient in the beam. Therefore, the equation
can be rearranged to solve for μ, the linear attenuation coefcient, the only unknown in the equa-
tion: μ =
ln (I0/Ix).
−μ × x
. The initial inten-
Fig. 4.3 Attenuation
This can ultimately be done for each pixel
along each line of response by tomographic
reconstruction, the simplest of which is the back-
32
ab
cd
https://t.me/medicina_free
Fig. 4.5 Simple backprojection explained
C. J. Trauernicht
Step 3
Another 45° rotation gives us the third projection
angle as shown in step 4.
projection algorithm. The following example
will explain this algorithm for a 2 × 2 matrix and
four projection angles. In this recipe, each pixel
has a unique value (a, b, c, or d), which represents the linear attenuation coefcient for that
pixel as shown in Fig.4.5. The rst part of the
recipe requires the acquisition of the four
projections.
4.3.1 Backprojection: AnExample
The rst ray of the rst projection angle is shown
in step 1.
Step 1
The second ray of the rst projection angle is
shown in step 2.
Step 4
Finally, the last projection angle for the backprojection example is shown in step 5.
Step 5
At this point, all projections have been acquired,
now the reconstruction begins, the second component of the recipe. This is done as follows:
since the attenuation coefcients in each pixel are
not known, they are initially all set to zero. Then
each line of response must be backprojected (step
6) into the empty matrix, starting with the rst
line of response from step 1 above.
Step 2
This is the rst projection angle. The second
angle, after a 45° rotation, is shown next in step
3.
Step 6
Since the values of a and b are not known at this
point and only their sum is known for this particular ray, that value is backprojected into each
pixel along that line of response to give step 7—
rst line of response backprojected.
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