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AFRICA IS CAPABLE OF USING LINEAR ACCELERATORS IN
RADIOTHERAPY RATHER THAN COBALT UNITS
Written by Melissa McClement, Application Specialist, Tecmed Africa
December 2011
INTRODUCTION
Throughout the world, radiotherapy continues to play a major part in the fight against cancer.
Estimates are that about 60% of all cancer patients will require radiation treatment at one point or
another during the course of their disease.
Unfortunately, radiotherapy facilities are not available to the majority of cancer patients in Africa,
most of who are diagnosed late when the diseases are far advanced (1).
In the African countries where radiotherapy facilities are available, the departments are grossly ill-
equipped and understaffed. There are shortages of radiation oncologists, medical physicists and
radiotherapists (2).
Virtually all developed countries are using linear accelerators as a basic treatment machine.
This document aims to prove that Africa is not only good enough for cobalt radiotherapy treatment
units, but capable of handling, using and maintaining a linear accelerator.
CAUSES OF PROBLEMS WITH RADIOTHERAPY IN AFRICA
Before I discuss the machines that would be used to treat cancer, I would like to discuss the causes
of the problems in Africa surrounding cancer treatment.
According to the IAEA, some of the factors include:
- Lack of awareness by the competent authorities of the extent of the cancer problem in many
countries owing to an absence of cancer registries and statistics;
- Underestimation of the role of radiotherapy in cancer management;
- Low priority for cancer care against other diseases competing for scarce funds (Diseases
such as health problems associated with communicable and infectious diseases);
- Absence of health and cancer control policies in many African countries;
- High capital outlay involved in establishing the required infrastructure (Some medical
practitioners still cherish the old idea that cancer is not a curable disease. Consequently,
they believe they cannot justify the heavy financial investment involved in the establishment
of a radiotherapy facility);
- High cost of equipment purchase and maintenance;
- High cost of training staff and then keeping the trained people (The few successful
candidates are likely to immigrate to other countries where they are likely to obtain better
paying jobs than they would otherwise obtain in their home countries. This “brain drain
syndrome” is a major handicap to developmental efforts in many developing countries);
- Poor economies in almost all African countries;
- Poor budgetary allocation to health (3).
Certain strategies need to be put into place. Some of them including:
- The provision of adequate facilities for both curative as well as palliative treatments,
especially radiotherapy services;
- The encouragement to develop centres of excellence for radiotherapy and oncology through
pooled resources which ensure availability of adequate facilities and staff for efficient
services, research and training within the region (3).
THE CONTINUED RISE OF THE COBALT TREATMENT UNIT IN AFRICA
A WHO report on National Cancer Control Programmes, states that “relatively inexpensive cobalt
machines are quite easy to maintain and can provide adequate therapy or palliation for most
patients, thus making it unnecessary to invest in expensive linear accelerators and other high-energy
machines requiring sophisticated maintenance and frequent calibration. For the majority of
treatable cancers in developing countries, linear accelerators offer no advantage over cobalt therapy
units.” (4)
According to R. Ravichandran, a Cobalt-60 machine provides an acceptable megavoltage photon
beam for clinical applications. “If the 5mm build-up thickness is preserved by proper understanding
of physics, there will be no problem of skin morbidities. Modern cobalt machines have penumbra
trimmers, to cut down excess penumbra thereby reducing dose to critical structures adjacent to the
tumour volume.” (5)
The advantages of cobalt teletherapy units (to be discussed in more detail later) are well known in
the radiotherapy community.
THE VALUED INTRODUCTION OF LINEAR ACCELERATORS IN AFRICA
As complex radiotherapy techniques become more widespread, there is a tendency for departments
to move away from using cobalt units in favour of more sophisticated delivery techniques.
Linear Accelerators also have a large number of advantages in radiotherapy treatment (to be
discussed in detail later). A linear accelerator is easy to use and includes a large number of
automated processes and built in safety mechanisms as standard features. This level of automation
provides a logical working process for improved efficiency and safety. As a result, therapists can
concentrate on the much needed explanation of the process to the patient, rather than operating
the machine.
International guidelines recommend one megavoltage therapy unit for every 1, 2 million people, for
every 250 new patients providing about 6,250 treatments per year (6).
This number can be beaten by a linear accelerator.
Linear Accelerators started replacing Co-60 units about 35 years ago. These machines should last 15
years – it therefore makes sense to install the most up to date current technology, or in 10 years,
Africa will be 45 years behind the rest of the Radiation Oncology world.
My superior always says that she finds it condescending that Europe (where a lot of the support for
installation of Co-60 units in Africa comes from) makes the judgement that Africa can only handle
Co-60 units and that Linear Accelerator technology is not for Africa.
THE PRO’S AND CON’S
There are some very obvious comparisons which can be made between Linear Accelerators
and Cobalt-60 teletherapy units, such as the skin dose, the penetration, and radiation
leakage. These comparisons are tabulated in Table 1.
The other comparisons I would like to make is that of the five-year survival rate in
percentage from 1960 (the first Co-60 unit was designed in the 1950’s) to 2000. These
figures were generated from an average of 15 different diagnoses. Remember that the
linear accelerator was introduced in the 1970’s). In 1960 the 5 year survival rate was 37.5%,
in 1970 it was 44.6%, in 1980 it was 49.5%, in 1990 it was 53.5% and in 2000 it was 56.5%.
The increase in survival rate is definitely more pronounced since the introduction of linear
accelerators, and of course is steadily increasing due to new developments in cancer
treatment. Please see Table 2.
In a study done by E.J. Adams and A.P. Warrington from The Royal Marsden NHS Foundation
Trust and Institute of Cancer Research, cobalt and linear accelerator plans of different
anatomical regions were compared. They found that lung doses were increased for a cobalt
plan, due to the larger penumbra, for a thorax patient. They also found that cobalt plans
tend to show increased PTV inhomogeneity and that doses to the organs at risk were slightly
higher for cobalt plans than for linear accelerator plans (7).
When comparing the price between a cobalt teletherapy unit and a linear accelerator, the
cobalt unit will always triumph. But, with the enormously strict regulations and costs
regarding import and disposal of radioactive sources, the cobalt teletherapy unit becomes a
less likely option.
Cobalt-60 has a half-life of 5 years. This essentially indicates that only half the patients
treated in year 1, would be treated in year 5, in the same amount of time. Every 5 years the
source would have to be replaced, and there is increased pressure on physicists to
continually calculate new treatment times as the source decays.
A linear accelerator has dynamic wedges, electronic position readout with verification
possibilities, variable dose rate and a built in service and physics mode. Future upgrades
with multi-leaf collimators and portal imaging is a possibility as linear accelerators are
modular.
The electricity problem in African countries can easily be overcome with generators and
UPS’s, which are in itself developing each day.
TABLE 1: COMPARISON OF COBALT TREATMENT UNITS AND LINEAR ACCELERATORS
FEATURE LINEAR
ACCELERATOR
COBALT - 60
ENERGY Higher, so treats deep seated
tumours with better doses
Inferior in matter of deep
seated tumour
DOSE RATE Does not change every month Reduces with time due to
radioactive decay
PRECISION More precise as there is
continuous dose monitoring
and recording
Less accurate
MINIMUM FIELD SIZE 0.5 x 0.5cm, hence very small
areas can be treated
5 x 5cm
ELECTRON BEAM Is present hence superficial
tumours can be treated without
harming deep structures
Not possible
STEREOTACTIC RADIOTHERAPY Possible Not possible
SOURCE DISPOSAL Nil, hence better safety profile Major environmental problem
SOURCE CHANGE None Every 5 years
RADIATION LEAK Once machine is off there is no
radiation in the room
Some radiation is always in the
room and never zero
SKIN DOSE 40 – 50% 15 – 25%
PENUMBRA Sharp beam field definition 80% 90 – 10% is 1.5cm field
definition 50%
BEAM COLLIMATION MLC, Assymetric collimators MLC being tried
IRREGULAR FIELDS MLC Achievable with blocks
SHAPE OF ISODOSE CURVES Flattened with special filter Rounded beyond central zone
BUILD-UP 28 - 35mm 5mm
SOURCE DISTANCE 100cm 80cm
Adapted from Reference number 5 and study done by Patel Hospital.
TABLE 2: OVERALL CANCER THERAPY (5 YEAR SURVIVAL RATE %)
1960 1970 1980 1990 2000
PROSTATE 50 68 75 90 98
MALE BLADDER 62 78 90 95 95
HODGKIN’S 54 80 90 92 92
BREAST 62 65 75 80 88
UTERINE 75 78 78 80 85
CERVIX 59 62 68 69 70
LARYNX 60 65 68 68 67
SARCOMAS 24 38 49 62 65
COLORECTAL 42 48 52 60 62
PHARYNX 45 50 52 53 55
BRAIN 19 21 25 28 33
OESOPHAGEAL 3 4 5 7 16
LUNG 8 11 13 14 15
PANCREAS 0 1 1 2 3
GLIOBLASTOM
A
0 0 1 2 3
CONCLUSION
Through what I have discussed, it is quite apparent that the opinion that Africa is not ready, able or
developed enough to handle linear accelerators is not only incorrect but also uncalled for.
Yes, a cobalt teletherapy treatment unit has its advantages, but a linear accelerator has so much
more to offer a Radiation Oncology department.
As a trained radiotherapist, I can say with utter conviction that working on a cobalt
teletherapy unit is not ideal. The fear of the source getting stuck, the fear of continuous
radiation exposure when working on the unit, and the fear of incorrectly treating a patient
becomes unbearable.
I implore departments in Africa to not be patronized by global opinion, but to aim for the
best. The time for Cobalt – 60 teletherapy treatment units in Africa has passed. African
patients deserve the best and newest treatment techniques in radiation oncology, and this
is only possible with linear accelerators.
REFERENCES
1) “Cancer patients in Nigeria: Causes of delay in diagnosis and treatment,” by F.A. Durosinmi-
Etti, Nig. Qtly. J. Hosp. Med. 3 (1) (1985).
2) “Situation actuelle de la radiotherapie en Afrique,” by A. Mouele-Sane, F.A. Durosinmi-Etti,
M.M. Mahfouz, P. Bey and A. Lougier, presentation at IAEA / WHO seminar for Africa on
Organization and training in Radiotherapy, Cairo (1989).
3) “Radiotherapy in Africa: Current needs and prospects,” by F.A. Durosinmi-Etti, M. Nofal, and
M.M. Mahfouz, IAEA Bulletin, 4/1991.
4) “Treatment of cancer: Policies and Managerial Guidelines,” by Geneva: World Health
Organization, 1995. National Cancer control programmes; pp.70 – 81.
5) “Has the time come for doing away with Cobalt-60 teletherapy for cancer treatments,” by R.
Ravichandran, J Med Phys. 2009 Apr-Jun; 34(2): 63 – 65.
6) “Radiation Oncology in integrated cancer management: Report of the Inter-Society Council
for Radiation Oncology (ISCRO),” USA, Dec. 1991.
7) “A comparison between cobalt and linear accelerator-based treatment plans for conformal
and intensity-modulated radiotherapy,” by E.J. Adams and A.P. Warrington from the Joint
Department of Physics, The Royal Marsden NHS Foundation Trust and Institute of Cancer
Research. The British Journal of Radiology, 81 (2008), 304 – 310.
1) “Cancer patients in Nigeria: Causes of delay in diagnosis and treatment,” by F.A. Durosinmi-
Etti, Nig. Qtly. J. Hosp. Med. 3 (1) (1985).
2) “Situation actuelle de la radiotherapie en Afrique,” by A. Mouele-Sane, F.A. Durosinmi-Etti,
M.M. Mahfouz, P. Bey and A. Lougier, presentation at IAEA / WHO seminar for Africa on
Organization and training in Radiotherapy, Cairo (1989).
3) “Radiotherapy in Africa: Current needs and prospects,” by F.A. Durosinmi-Etti, M. Nofal, and
M.M. Mahfouz, IAEA Bulletin, 4/1991.
4) “Treatment of cancer: Policies and Managerial Guidelines,” by Geneva: World Health
Organization, 1995. National Cancer control programmes; pp.70 – 81.
5) “Has the time come for doing away with Cobalt-60 teletherapy for cancer treatments,” by R.
Ravichandran, J Med Phys. 2009 Apr-Jun; 34(2): 63 – 65.
6) “Radiation Oncology in integrated cancer management: Report of the Inter-Society Council
for Radiation Oncology (ISCRO),” USA, Dec. 1991.
7) “A comparison between cobalt and linear accelerator-based treatment plans for conformal
and intensity-modulated radiotherapy,” by E.J. Adams and A.P. Warrington from the Joint
Department of Physics, The Royal Marsden NHS Foundation Trust and Institute of Cancer
Research. The British Journal of Radiology, 81 (2008), 304 – 310.

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AFRICA IS CAPABLE OF USING LINEAR ACCELERATORS IN RADIOTHERAPY RATHER THAN COBALT UNITS

  • 1. AFRICA IS CAPABLE OF USING LINEAR ACCELERATORS IN RADIOTHERAPY RATHER THAN COBALT UNITS Written by Melissa McClement, Application Specialist, Tecmed Africa December 2011
  • 2. INTRODUCTION Throughout the world, radiotherapy continues to play a major part in the fight against cancer. Estimates are that about 60% of all cancer patients will require radiation treatment at one point or another during the course of their disease. Unfortunately, radiotherapy facilities are not available to the majority of cancer patients in Africa, most of who are diagnosed late when the diseases are far advanced (1). In the African countries where radiotherapy facilities are available, the departments are grossly ill- equipped and understaffed. There are shortages of radiation oncologists, medical physicists and radiotherapists (2). Virtually all developed countries are using linear accelerators as a basic treatment machine. This document aims to prove that Africa is not only good enough for cobalt radiotherapy treatment units, but capable of handling, using and maintaining a linear accelerator.
  • 3. CAUSES OF PROBLEMS WITH RADIOTHERAPY IN AFRICA Before I discuss the machines that would be used to treat cancer, I would like to discuss the causes of the problems in Africa surrounding cancer treatment. According to the IAEA, some of the factors include: - Lack of awareness by the competent authorities of the extent of the cancer problem in many countries owing to an absence of cancer registries and statistics; - Underestimation of the role of radiotherapy in cancer management; - Low priority for cancer care against other diseases competing for scarce funds (Diseases such as health problems associated with communicable and infectious diseases); - Absence of health and cancer control policies in many African countries; - High capital outlay involved in establishing the required infrastructure (Some medical practitioners still cherish the old idea that cancer is not a curable disease. Consequently, they believe they cannot justify the heavy financial investment involved in the establishment of a radiotherapy facility); - High cost of equipment purchase and maintenance; - High cost of training staff and then keeping the trained people (The few successful candidates are likely to immigrate to other countries where they are likely to obtain better paying jobs than they would otherwise obtain in their home countries. This “brain drain syndrome” is a major handicap to developmental efforts in many developing countries); - Poor economies in almost all African countries; - Poor budgetary allocation to health (3). Certain strategies need to be put into place. Some of them including: - The provision of adequate facilities for both curative as well as palliative treatments, especially radiotherapy services; - The encouragement to develop centres of excellence for radiotherapy and oncology through pooled resources which ensure availability of adequate facilities and staff for efficient services, research and training within the region (3).
  • 4. THE CONTINUED RISE OF THE COBALT TREATMENT UNIT IN AFRICA A WHO report on National Cancer Control Programmes, states that “relatively inexpensive cobalt machines are quite easy to maintain and can provide adequate therapy or palliation for most patients, thus making it unnecessary to invest in expensive linear accelerators and other high-energy machines requiring sophisticated maintenance and frequent calibration. For the majority of treatable cancers in developing countries, linear accelerators offer no advantage over cobalt therapy units.” (4) According to R. Ravichandran, a Cobalt-60 machine provides an acceptable megavoltage photon beam for clinical applications. “If the 5mm build-up thickness is preserved by proper understanding of physics, there will be no problem of skin morbidities. Modern cobalt machines have penumbra trimmers, to cut down excess penumbra thereby reducing dose to critical structures adjacent to the tumour volume.” (5) The advantages of cobalt teletherapy units (to be discussed in more detail later) are well known in the radiotherapy community. THE VALUED INTRODUCTION OF LINEAR ACCELERATORS IN AFRICA As complex radiotherapy techniques become more widespread, there is a tendency for departments to move away from using cobalt units in favour of more sophisticated delivery techniques. Linear Accelerators also have a large number of advantages in radiotherapy treatment (to be discussed in detail later). A linear accelerator is easy to use and includes a large number of automated processes and built in safety mechanisms as standard features. This level of automation provides a logical working process for improved efficiency and safety. As a result, therapists can concentrate on the much needed explanation of the process to the patient, rather than operating the machine. International guidelines recommend one megavoltage therapy unit for every 1, 2 million people, for every 250 new patients providing about 6,250 treatments per year (6). This number can be beaten by a linear accelerator. Linear Accelerators started replacing Co-60 units about 35 years ago. These machines should last 15 years – it therefore makes sense to install the most up to date current technology, or in 10 years, Africa will be 45 years behind the rest of the Radiation Oncology world. My superior always says that she finds it condescending that Europe (where a lot of the support for installation of Co-60 units in Africa comes from) makes the judgement that Africa can only handle Co-60 units and that Linear Accelerator technology is not for Africa.
  • 5. THE PRO’S AND CON’S There are some very obvious comparisons which can be made between Linear Accelerators and Cobalt-60 teletherapy units, such as the skin dose, the penetration, and radiation leakage. These comparisons are tabulated in Table 1. The other comparisons I would like to make is that of the five-year survival rate in percentage from 1960 (the first Co-60 unit was designed in the 1950’s) to 2000. These figures were generated from an average of 15 different diagnoses. Remember that the linear accelerator was introduced in the 1970’s). In 1960 the 5 year survival rate was 37.5%, in 1970 it was 44.6%, in 1980 it was 49.5%, in 1990 it was 53.5% and in 2000 it was 56.5%. The increase in survival rate is definitely more pronounced since the introduction of linear accelerators, and of course is steadily increasing due to new developments in cancer treatment. Please see Table 2. In a study done by E.J. Adams and A.P. Warrington from The Royal Marsden NHS Foundation Trust and Institute of Cancer Research, cobalt and linear accelerator plans of different anatomical regions were compared. They found that lung doses were increased for a cobalt plan, due to the larger penumbra, for a thorax patient. They also found that cobalt plans tend to show increased PTV inhomogeneity and that doses to the organs at risk were slightly higher for cobalt plans than for linear accelerator plans (7). When comparing the price between a cobalt teletherapy unit and a linear accelerator, the cobalt unit will always triumph. But, with the enormously strict regulations and costs regarding import and disposal of radioactive sources, the cobalt teletherapy unit becomes a less likely option. Cobalt-60 has a half-life of 5 years. This essentially indicates that only half the patients treated in year 1, would be treated in year 5, in the same amount of time. Every 5 years the source would have to be replaced, and there is increased pressure on physicists to continually calculate new treatment times as the source decays. A linear accelerator has dynamic wedges, electronic position readout with verification possibilities, variable dose rate and a built in service and physics mode. Future upgrades with multi-leaf collimators and portal imaging is a possibility as linear accelerators are modular. The electricity problem in African countries can easily be overcome with generators and UPS’s, which are in itself developing each day.
  • 6. TABLE 1: COMPARISON OF COBALT TREATMENT UNITS AND LINEAR ACCELERATORS FEATURE LINEAR ACCELERATOR COBALT - 60 ENERGY Higher, so treats deep seated tumours with better doses Inferior in matter of deep seated tumour DOSE RATE Does not change every month Reduces with time due to radioactive decay PRECISION More precise as there is continuous dose monitoring and recording Less accurate MINIMUM FIELD SIZE 0.5 x 0.5cm, hence very small areas can be treated 5 x 5cm ELECTRON BEAM Is present hence superficial tumours can be treated without harming deep structures Not possible STEREOTACTIC RADIOTHERAPY Possible Not possible SOURCE DISPOSAL Nil, hence better safety profile Major environmental problem SOURCE CHANGE None Every 5 years RADIATION LEAK Once machine is off there is no radiation in the room Some radiation is always in the room and never zero SKIN DOSE 40 – 50% 15 – 25% PENUMBRA Sharp beam field definition 80% 90 – 10% is 1.5cm field definition 50% BEAM COLLIMATION MLC, Assymetric collimators MLC being tried IRREGULAR FIELDS MLC Achievable with blocks SHAPE OF ISODOSE CURVES Flattened with special filter Rounded beyond central zone BUILD-UP 28 - 35mm 5mm SOURCE DISTANCE 100cm 80cm Adapted from Reference number 5 and study done by Patel Hospital. TABLE 2: OVERALL CANCER THERAPY (5 YEAR SURVIVAL RATE %)
  • 7. 1960 1970 1980 1990 2000 PROSTATE 50 68 75 90 98 MALE BLADDER 62 78 90 95 95 HODGKIN’S 54 80 90 92 92 BREAST 62 65 75 80 88 UTERINE 75 78 78 80 85 CERVIX 59 62 68 69 70 LARYNX 60 65 68 68 67 SARCOMAS 24 38 49 62 65 COLORECTAL 42 48 52 60 62 PHARYNX 45 50 52 53 55 BRAIN 19 21 25 28 33 OESOPHAGEAL 3 4 5 7 16 LUNG 8 11 13 14 15 PANCREAS 0 1 1 2 3 GLIOBLASTOM A 0 0 1 2 3 CONCLUSION
  • 8. Through what I have discussed, it is quite apparent that the opinion that Africa is not ready, able or developed enough to handle linear accelerators is not only incorrect but also uncalled for. Yes, a cobalt teletherapy treatment unit has its advantages, but a linear accelerator has so much more to offer a Radiation Oncology department. As a trained radiotherapist, I can say with utter conviction that working on a cobalt teletherapy unit is not ideal. The fear of the source getting stuck, the fear of continuous radiation exposure when working on the unit, and the fear of incorrectly treating a patient becomes unbearable. I implore departments in Africa to not be patronized by global opinion, but to aim for the best. The time for Cobalt – 60 teletherapy treatment units in Africa has passed. African patients deserve the best and newest treatment techniques in radiation oncology, and this is only possible with linear accelerators. REFERENCES
  • 9. 1) “Cancer patients in Nigeria: Causes of delay in diagnosis and treatment,” by F.A. Durosinmi- Etti, Nig. Qtly. J. Hosp. Med. 3 (1) (1985). 2) “Situation actuelle de la radiotherapie en Afrique,” by A. Mouele-Sane, F.A. Durosinmi-Etti, M.M. Mahfouz, P. Bey and A. Lougier, presentation at IAEA / WHO seminar for Africa on Organization and training in Radiotherapy, Cairo (1989). 3) “Radiotherapy in Africa: Current needs and prospects,” by F.A. Durosinmi-Etti, M. Nofal, and M.M. Mahfouz, IAEA Bulletin, 4/1991. 4) “Treatment of cancer: Policies and Managerial Guidelines,” by Geneva: World Health Organization, 1995. National Cancer control programmes; pp.70 – 81. 5) “Has the time come for doing away with Cobalt-60 teletherapy for cancer treatments,” by R. Ravichandran, J Med Phys. 2009 Apr-Jun; 34(2): 63 – 65. 6) “Radiation Oncology in integrated cancer management: Report of the Inter-Society Council for Radiation Oncology (ISCRO),” USA, Dec. 1991. 7) “A comparison between cobalt and linear accelerator-based treatment plans for conformal and intensity-modulated radiotherapy,” by E.J. Adams and A.P. Warrington from the Joint Department of Physics, The Royal Marsden NHS Foundation Trust and Institute of Cancer Research. The British Journal of Radiology, 81 (2008), 304 – 310.
  • 10. 1) “Cancer patients in Nigeria: Causes of delay in diagnosis and treatment,” by F.A. Durosinmi- Etti, Nig. Qtly. J. Hosp. Med. 3 (1) (1985). 2) “Situation actuelle de la radiotherapie en Afrique,” by A. Mouele-Sane, F.A. Durosinmi-Etti, M.M. Mahfouz, P. Bey and A. Lougier, presentation at IAEA / WHO seminar for Africa on Organization and training in Radiotherapy, Cairo (1989). 3) “Radiotherapy in Africa: Current needs and prospects,” by F.A. Durosinmi-Etti, M. Nofal, and M.M. Mahfouz, IAEA Bulletin, 4/1991. 4) “Treatment of cancer: Policies and Managerial Guidelines,” by Geneva: World Health Organization, 1995. National Cancer control programmes; pp.70 – 81. 5) “Has the time come for doing away with Cobalt-60 teletherapy for cancer treatments,” by R. Ravichandran, J Med Phys. 2009 Apr-Jun; 34(2): 63 – 65. 6) “Radiation Oncology in integrated cancer management: Report of the Inter-Society Council for Radiation Oncology (ISCRO),” USA, Dec. 1991. 7) “A comparison between cobalt and linear accelerator-based treatment plans for conformal and intensity-modulated radiotherapy,” by E.J. Adams and A.P. Warrington from the Joint Department of Physics, The Royal Marsden NHS Foundation Trust and Institute of Cancer Research. The British Journal of Radiology, 81 (2008), 304 – 310.