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In vivo dosimetry for brachytherapy

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Aims

To learn of in vivo dosimetry for brachytherapy including appropriate detectors.

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Specific Learning Objectives

• In vivo dosimetry - the rationale, role of in vivo dosimetry in brachytherapy

• Various dosimeters available, their advantages, disadvantages, limitations, challenges, applications and the future.

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In vivo dosimetry

Rationale:• Brachytherapy is delivered without any

record and verification system as in EBRT which may lead to errors in treatment delivery (ICRP 86,97 & IAEA 3RS 17).- Change of Transfer tubes -Change in Indexer lengths- Mechanical errors- Incorrect input of dose, reconstruction errors etc

In BT, in vivo dosimetry has not become popular, due to practical difficulties, however it is very important to continue the research of the use of in vivo dosimetry in BT, not least because record and verify systems are still not widely clinically implemented in BT.

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In vivo dosimetry

Rationale cont...• Only way to know the actual dose delivered• Movement of the applicators• Organ deformation or movement

- Bladder filling- Rectum gas- Movement of sigmoid colon

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Role of in vivo dosimetry in BT

• Quality control of patient treatments- Confirmation of delivered dose- Detection of errors- Can provide meaningful data for evaluation of

treatment outcomes (TCP & NTCP)- Commissioning of a new treatment technique -

In vivo measurements in phantom

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Ideal BT in vivo dosimeter

• Robust dosimetry system• Small detectors with high S/N ratio• High spatial resolution• Energy independent• Dose rate independent• High accuracy and reproducibility• Linear dose response over a broad range• No directional dependence• Rugged and reliable (for sterilization)• Minimally intrusive to the patient• Fast, reliable and real time readout• High sensitivity and specificity• Affordable

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Challenges - specific to BT in in vivo dosimetry

• High dose gradients and detector positioning• Energy dependence of detectors• Poor sensitivity and specificity• Extra invasive procedure• Other uncertainties

■ Source calibration■ Dose calculation algorithm■ Positional and temporal accuracy of afterloader

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High dose gradients and detector positioning

• High dose gradient in BT (~ 20% per mm) leads to significant uncertainties in dose measurements.

• Detector placement is a balance between SNR and the ability to reduce positional uncertainties.

• For bladder and rectum, difficult to establish a stable dosimeter position directly adjacent to the most exposed part of the organ wall.

• The anatomy of the urethra is more favorable for performing in vivo dosimetry in prostate BT since this organ is smaller and less deformable.

The BT dose distributions are characterized by steep dose gradients that depend strongly on the distance from the detector to the source.Several challenges regarding optimal dosimeter positioning could be solved withdedicated clinical components, e.g., urethral catheters and rectal or bladder balloons,that would both stabilize and offer accessibility at desired dosimetry sites.

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Energy dependence of detectors

• Most commonly used detectors exhibit a higher energy- dependence than in megavoltage beams, since the photoelectric effect causes an over-response in the BT energy range.

• The detector response may change with depth in tissue from the source because the BT photon energy spectrum changes as function of source distance.

• The absorbed dose sensitivity must be corrected for if the source is calibrated with a radiation source different from the BT source used.

This is due to the fact that detector response depends more on the mass-attenuation absorption coefficients (large cavities) than on the mass-collisional stopping powers (small cavities: satisfying the Bragg-Gray conditions). Therefore, the energy dependence (absorbed dose sensitivity) needs to be determined for the type of detector used for the specific radioactive source since the energy spectrum depends also on the source model (especially for low-energy sources).

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Energy dependence of detector response (diode and MOSFET)

Cygler et al, Med Phys 17 (1990) 172-177 Kron et al, Phys Med Biol 43 (1998) 3235-3259I Figure reproduced with permission courtesy of AAPM I [ Reproduced by permission of IOP Publishing

These graphs show that the MOSFET and diode have energy dependent response. So it is very important to calibrate these dosimeters in the clinically used situations.

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Detectors

• Luminescence based detectors- TLD (Thermo Luminescence Dosimeter)- RL (Radio Luminescence)- RPLGD (Radio Photo Luminescence Glass Dosimeters)- OSL (Optically stimulated luminescence)

• Semiconductor diodes• MOSFETs (Metal Oxide Semiconductor Field Effect

Transistor)• Alanine chemical dosimeters• Plastic scintillators

The list shows the types of in vivo dosimeters used in BT.

Summary of various detectorsTLD Diode MOSFET Alanine RL PSD

Size + +/- +Z++ ++ ++Sensitivity + ++ + - ++ +/++Energy dependence + - - + - ++Angular dependence ++ - + + ++ ++Dynamic range ++ ++ + - ++ ++Calibration + ++ ++ - -/+ +/++procedures, QA.stability, robustness.size of system, easeof operationCommercial ++ ++ ++ ++ - +availabilityOnline dosimetry - ++ + - ++ ++Main advantages No cables, well Commercial Small size. Limited energy Small size, high Small size, no

studied system systems at commercial system dependence, no sensitivity angular and energyreasonable price. at reasonable price cables dependence.well studied system sensitivity

Main disadvantages Tedious procedures Angular and energy Limited life of Not sensitive to low Needs frequent Stem effectfor calibration and dependence detectors, energy doses, tedious recalibration, stemreadout, not online dependence procedures for effect, notdosimetry' calibration and commercially

readout, not online availabledosimetry.expensive readoutequipment notavailable in clinics

Tanderup et al, Med Phys 40 (2013) 070902 | Table reproduced with permission courtesy of AAPM

Characteristics of detectors and dosimetry systems of importance for precise routine usein in vivo dosimetry in brachytherapy. The items are rated according to:advantageous (++), good (+), and inconvenient (-).

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Luminescence based detectors

These type of detectors store energy in meta­stable states, which can be released later by an external stimulant:• Heat stimulated energy release - TLD• Light Stimulated energy release - OSL• Radio Luminescence - RL

Fluorescence - Spontaneous process 10-8 -10_1° secPhosphorescence - Delayed luminescence useful in

dosimetry

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TLD

• TLDs come in various materials forms and shapes• Easy to fit in various areas of interest.• Lithium fluoride (LiF) TLD rods are the most widely

used form, because they can be easily inserted into catheters

• Require special preparation annealing, individual calibration, careful handling, fading correction

• TLDs have been used for HDR 192lr BT to measure the dose to the urethra and/or rectum during prostate treatments

• Not a real time dosimeter

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TLD principleOn exposure to radiation, the electrons are created and trapped in meta­stable states. On heating, the electrons emit light which is proportional to the amount of radiation dose absorbed.

The trapped electrons and holes (Mg sites) in TLDs are recombined by heating the material promoting the electrons back into the conduction band before recombination (Ti sites), which makes them reusable.

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TLD readout systemTLDs are readout by systems which essentially consists of a heating and light measurement system.

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Physical form of TL detectors

Courtesy P Olko, Institute of Nuclear Physics (IFJ). Krakow, Poland

• Powder• Pellets• Chips• Rods

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TL materials and dose range

Material Detector Dose range

LiF:Mg,Ti TLD-100, -600,-700, GR-100, 206,-207 MTS-N, -6, -7

100 mGy-10 Gy

LiF:Mg,Cu,P TLD-100H, GR-200 MCP-N

1 mGy - 10 Gy

CaSO4:Dy 10 mGy -1 Gy

CaF2:Tm TLD-300 100 mGy-10 Gy

AI2O3:C Landauer, USA 1 mGy - 10 Gy

Courtesy: Cygler JE

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Pin worm TLDs

Pin-worm TLD train measurements have been performed with an 192 Ir source in a phantom. The results plotted as dose response relative to the maximum dose (100%) show excellent agreement to dose predicted by a TPS. See for example Hood et al, LiF:Mg,Cu,P 'pin worms': miniature detectors for brachytherapy dosimetry, Rad Prot Dosim, 101,407-410, 2002.

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Advantages and Disadvantages of TLDs

Disadvantages

• Not a real timedosimeter(delay in reading) Light sensitivity FadingBatch calibration needed Hard to track Difficulty to handle Long preparation time No permanent dose record

Advantages

► Most widely used & well established dosimetry method.

» Small dependency on dose- rate, energy and temperature

» Wide dose range • Small » Portable » No bias required » Low cost

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Optically stimulated luminescence (OSL) system

Picture courtesy: Landauer, Cygler JE

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Riso OSL - optical fiber coupled dosimetry system

Figure 1. Measurement protocol for RL and OSL RL is collected vshilc the beam is on. whereas OSL is measured once the irradiation has been completed and the laser has been switched on.

Aznar et al, Phys Med Biol 49 (2004) 1655-69 Picture courtesy: C Anderson Riso, Cygler JE

In vivo measurements of a brachytherapy patient

Cervix recurrence above the vaginal wallTreated with 15 needles, OSL in 2 needles30Gy delivered in 50pulses over 50 hoursOSL measured pulse dose between each pulse RL signal integrated to give pulse doseTPS with +/- 1mm uncertainty

Courtesy: C Anderson Riso, Cygler JE

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Advantages and Disadvantages of OSL

Advantages• Riso detector

- Size- Real-time dosimeter- Reusable

• Nano dot- Fast readout- Easier to process than TLD- Reusable

Disadvantages• Energy dependence

-Zeff = 11.3 for AI2O3:C• Sensitive to light• Size-for nanoDot• Some temperature

dependence (0.2%/K)• Not waterproof• One vendor for nano-Dots• No commercial product

for RL

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RPLGD

• Have a similar reading process to TLDs, except UV (not heat) is used to stimulate the detector.

• Irradiation of the silver-activated phosphate glass converts silver ions to stable luminescent centers

• When exposed to UV light, the luminescent centers produce fluorescence in proportion to the absorbed radiation dose.

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RPLGD example

• HDR interstitial BT for head-and-neck cancer (61 patients) and pelvic malignancies (66 patients).

• For pelvis cases, RPLGDs were sutured to the anterior wall of the rectum or positioned inside a Foley catheter inside the urethra.

• For pelvis cases, deviations greater than 20% were found between the measured and calculated doses and were attributed to the independent movement of the organs and applicators between the planning and treatment delivery times.

Nose et al, Int J Radiat Oncol Biol Phys 61 (2005) 945-953 Nose et al, Int J Radiat Oncol Biol Phys 70 (2008) 626-633

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Semiconductor diodes• Commonly used in-vivo dosimeter for

EBRT & Brachytherapy.• Semiconductor solid-state dosimeters

based on silicon.• P type diodes suitable for dosimetry• Must be characterized in phantom

before clinical use for the specific radiation source or application.

• Flexible diode array commercially available (PTW) - Rectal probes consisting of five diodes (separated by 15 mm) and bladder probes consisting of a single diode is available.

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Rectal and bladder dose measurements for prostate and GYN Brachytherapy

• Dose variation of -31 % to +90% (mean 11%) for the rectum and -27% to +26%(mean 4%) for the bladder was reported.

• Dose variation of more than 10% was attributed to probe shift of 2.5 mm for rectum and 3.5 mm for bladder.

• Seymour et al reported a variation ranged from -42% to +35% (with 71% of the measurements within 10% of the predicted values).

• The overall uncertainty involved in phantom dose measurement, after correcting for all the factors affecting diode response were ±7 to10% (SD).

Seymour et al, Med Phys 38 (2011) 4785-4794

Waldhausl et al., Radiother Oncol 77 (2005) 310-317

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Advantages and Disadvantages of diodes

AdvantagesHigh sensitivity

Real - time dosimeter

Good mechanical stability

Water proof

Durable

Efficient (fast) in use

Small size

DisadvantagesEnergy dependence (Silicon Z = 14)

Angular dependence

Temperature dependence

Change of sensitivity due to radiation damageCumbersome cables on most systems

Different detectors for photon and electron fields

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MOSFETsMOSFETs are miniature n- or p-type silicon (Si) semiconductors.For dosimetry, mostly p-type detectors are used.Can operate in active (positive bias on gate during radiation) or passive modeAV is a function of absorbed dose T That function is linear when the MOSFET operates in the biased mode during the irradiation.Absorbed dose linearity region increases with the increase of the bias voltage

Soubra et al, Med Phys 21 (1994) 567-572

| Figures reproduced with permission courtesy of AAPM

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Types of MOSFET detectors

• Single bias, single MOSFET- Temperature dependence- Instability of response

• Dual-bias, dual-MOSFET- Proposed by Soubra, Cygler et. al. in Med. Phys. (1994)- Two MOSFETs on same silicon chip operating at two different gate

biases- Better sensitivity, reproducibility, and stability than single MOSFET- Minimal temperature effects

• Unbiased single MOSFET- Temperature dependence- Instability of response, frequently used as disposable detectors- Shorter dose linearity range than biased MOSFETs

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MOSFET Detectors

• BEST Medical (Thomson-Nielsen)- Mobile MOSFET system (single

detectors and arrays)- Portable Dosimeter, based on dual-

bias-dual-MOSFET

• Two Physical detector sizes- Standard (8 x 2.5 x1.3 mm3)- MicroMOSFETs (3.5 x1 x1 mm3)

• Two sensitivities- Standard (0.2 x 0.2x 5 x10'4 mm3)- High (0.2x0.2x1 x 10’3 mm3)

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Use of MOSFET in HDR prostate implants

The radio-opaque marker of the array’s tip, helps with visualization under CT or radiograph of MOSFETs’ positions relative to the internal bladder wall (at the lower edge of the Foley balloon).

Courtesy: Cygler JE

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Use of MOSFET in HDR prostate implants

calculated initial pre-plan (•) measured post implant (^)

0 10 20 30 40 50 60 70 80 90 100 110Distance (mm)

Cygler et al, Radiother Oncol 80 (2006) 296-301, copyright Elsevier, reproduced with permission

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Advantages and Disadvantages of MOSFET

Advantages DisadvantagesVery small size/active volume Not tissue equivalent, which makes

the dose response vary with radiation quality

Real time dosimetry Limited life time

Temperature independence for single Temperature dependence of somedual MOSFET dual bias detector MOSFET array

Efficient - doesn’t consume much timeWater proof

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Alanine dosimeter

• Irradiation of the amino acid alanine produces stable free radicals.

• The concentration of these radicals is proportional to absorbed dose and can be measured by EPR spectroscopy.

• Alanine exist in a form of powder or in the shape of rods, pellets, films.

Courtesy: Schultka K & Cygler JE

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Alanine in vivo dosimetry in brachytherapy

• Schultka et al. study for gynecological insertions- Alanine capsules inside Foley’s

catheter placed in rectum or in vagina- Different visualization methods: wire,

radio-opaque thread, cupronickel frame

• Radiographs of detectors placed in vagina.The schemes beside radiograph shows placement of cupronickel frame allowing localization of the detectors on the radiographs

«•»

Schultka et al, Rad Prot Dos 120 (2006) 171-175

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Advantages and Disadvantages of Alanine dosimeter

Advantages

Independent of dose rate and energy

Disadvantages

Expensive EPR equipment, not easily available in radiotherapy clinics

Can be packed into small packets, portableNon destructive type of measurement, very little fading with time

Wide dose range

Delayed read out

Insensitive for lower doses(<2Gy)

Some dependence on temperature and humidity

no bias is required, no cables

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Plastic Scintillation detector PSD

• PSDs are composed of organic scintillation material (scintillator or scintillating optical fiber) that emits light proportionally to the dose deposited in their detector volume.

Spring loaded circular plate

MgO Reflector Opaque plastic Leac

BC-430 Light pipe

High-Z build up material

Teflon tapeAirgap

• The light produced in the detector is optically coupled to a fiber-optic light guide and transmitted toward a photo­detector.

• Cerenkov light production analogous to stem effect is a challenge.

• Accuracy of better than 1 % has been demonstrated.- L. Archambault et al., Int. J. Radiat. Oncol. Biol.

Phys. 78 (2010) 280-287

Beddar et al, Phys Med Biol 39 (1994) 253-263 Reproduced by permission of IOP Publishing

Picture courtesy: Cygler JE

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PSD in brachytherapy - Phantom study

• Developed for HDR BT by Lambert et al• PSDs could be cut and shaped in size that can be easily inserted into

catheters or arranged around applicators that are commonly used in BT• 1 and 0.5 mm fibres• Phantom studies showed good correlation between the measured and

the predicted dose from TPS (Therriault-Proulx et al, Med Phys 38 (2011) 2542-2551, Cartwright et al, Med Phys 37 (2010) 2247-2255)

Reproduced by permission of IOP Publishing Lambert et al, Phys Med Biol 51 (2006) 5505-5516

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PSD in brachytherapy - In Vivo Dosimetry (urethral dose)

• First patient in vivo measurements using PSD in BT, urethral dose in Prostate BT• A maximum of 9% deviation was reported with the improved dosimetry• Dose variation was attributed to the changes in the anatomy• Recommended that patient outcome should be correlated with the in vivo dosimetry

Suchowerska et al, Int J Radiat Oncol Biol Phys 79 (2011) 609-615

Picture courtesy: Cygler JE

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Multiple different color mPSD

• Single optical transmission line• Additional “carrier catheters” sutured

within the vicinity of the implant• The extraction of each corresponding color

from the total spectrum measured will provide the dose deposited at corresponding color PSD.

• This type of detector has the advantage ofsimultaneous dose rate measurements in Image reproduced with permission of American Association of Physicists in

Medicine

multiple points with the potential to improve error detection capabilities.

Tanderup et al, Med Phys 40 (2013) 070902

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Advantages and Disadvantages of PSD

Advantages Disadvantages• Water equivalent No commercial product• Real time dosimeter• Small size - high spatial resolution• Linear response to dose• Dose rate independence• Energy independence in MVrange• Rugged, simple to construct &cost effective• Good stability and reproducibility• No high-voltage bias• Remote operation and reset

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New Dosimeters - 4D dosimetry system RADPOS*

• Combination of electromagnetic positioning sensor and MOSFET dosimeter

• Simultaneous measurements of dose and spatial position• Software developed: sample position and dose manually/automaticall

monitored.• Real-time treatment verification tool for

■ Patient motion■ Accuracy of delivered dose.

• Can be used in brachytherapy.

Slide courtesy: Cygler JE

*RADPOS, A. Saoudi, J.E. Cygler, R.W. Ashton, US Patent 7831016 Cherpak et al, Med Phys 36 (2009) 1672-1726; Med Phys 38 (2011) 179-187; Radiother Oncol 102 (2012) 290- 296

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RADPOS array

Detector placed in urethral catheter during seed implantation.Intra-fraction motion, dose profile along urethra (with and without trans-rectal ultrasound probe in place)10 patients, compared measurements to ultrasound, treatment planning system

distance/mm

Cherpak et al, Med Phys 38 (2011) 3577Real-Time Measurement of Urethral Dose and Position Using a RADPOS Array during Permanent Seed Implantation for Prostate Brachytherapy, reproduced with permission courtesy of AAPM

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In vivo dosimetry - summary

• In vivo dosimetry is the only way to verify what dose was actually delivered to the tumour and/or organs at risk

• Variety of systems and detectors are available:- No single detector is perfect for all situations- User has to understand pros and cons of each system to select the best

one for the task• Careful calibration to account for the following:

- Energy dependence- Angular dependence- Accurate localization

• IVD in BT is currently not well established in clinical practice for sensitive and specific error detection

• However, IVD can detect accidental over- and under-exposure resulting from undetected errors

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Bibliography

• ANDERSEN, C. E., et al., Characterization of a fiber-coupled AI2O3:C luminescence dosimetry system for online in vivo dose verification during 192lr brachytherapy, Med. Phys. 36 (2009) 708-718.

• ARCHAMBAULT, L., et al., Toward a real-time in vivo dosimetry system using plastic scintillation detectors, Int J Radiat Oncol Biol Phys 78 (2010) 280-287.

• AZNAR, M. C., et al., Real-time optical-fibre luminescence dosimetry for radiotherapy: physical characteristics and applications in photon beams, Phys. Med. Biol. 49 (2004) 1655-1669.

• BEDDAR, A. S., A new scintillator detector system for the quality assurance of 60Co and high-energy therapy machines, Phys Med Biol 39 (1994) 253-263.

• CHERPAK, A., DING, W„ HALLIL, A., CYGLER, J. E„ Evaluation of a novel 4D in vivo dosimetry system, Med Phys 36 (2009) 1672-1679.

• CHERPAK, A., SERBAN, M„ SEUNTJENS, J., CYGLER, J. E„ 4D dose-position verification in radiation therapy using the RADPOS system in a deformable lung phantom, Med Phys 38 (2011) 179- 187.

• CHERPAK, A., CYGLER, J., PERRY, G., Real-time measurement of urethral dose and position using a RADPOS array during permanent seed implantation for prostate brachytherapy, Med Phys 38 (2011) 3577.

• CHERPAK, A. J., et al., Clinical use of a novel in vivo 4D monitoring system for simultaneous patient motion and dose measurements, Radiother Oncol 102 (2012) 290-296.

• CYGLER, J„ SZANTO, J., SOUBRA, M„ ROGERS, D. W„ Effects of gold and silver backings on the dose rate around an 1251 seed, Med. Phys. 17 (1990) 172-178.

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Bibliography

• CYGLER, J. E„ SAOUDI, A., PERRY, G„ MORASH, C„ E, C„ Feasibility study of using MOSFET detectors for in vivo dosimetry during permanent low-dose-rate prostate implants, Radiother. Oncol. 80 (2006)296-301.

• HOOD, C., et al., LiF:Mg,Cu,P 'pin worms': miniature detectors for brachytherapy dosimetry, Radiat. Prot. Dosimetry 101 (2002)407-410.

• HUYSKENS, D. P., et al., Practical Guidelines for the Implementation of in Vivo Dosimetry with Diodes in External Radiotherapy with Photon Beams (Entrance Dose), ESTRO Booklet No. 5, ESTRO, Brussels (2001).

• INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Prevention of Accidental Exposures to Patients Undergoing Radiation Therapy, ICRP Publication No. 86, ICRP, Pergamon (2000).

• INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Prevention of High-Dose-Rate Brachytherapy Accidents, ICRP Publication No. 97 - Annals of the ICRP 35 (2), 2005, ICRP, Oxford (2005).

• INTERNATIONAL ATOMIC ENERGY AGENCY, Lessons Learned from Accidental Exposures in Radiotherapy, Safety Reports Series No. 17, IAEA, Vienna (2000).

• INTERNATIONAL ATOMIC ENERGY AGENCY, Development of Procedures for In Vivo Dosimetry in Radiotherapy, Human Health Reports No. 8, IAEA, Vienna (2013).

• KRON, T., et al., Dose response of various radiation detectors to synchrotron radiation, Phys. Med. Biol. 43(1998) 3235-3259.

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Bibliography

• LAMBERT, J., MCKENZIE, D. R„ LAW, S„ ELSEY, J., SUCHOWERSKA, N„ A plastic scintillation dosimeter for high dose rate brachytherapy, Phys Med Biol 51 (2006) 5505-5516.

• NOSE, T., et al., In vivo dosimetry of high-dose-rate brachytherapy: study on 61 head-and-neck cancer patients using radiophotoluminescence glass dosimeter, Int. J. Radiat. Oncol. Biol. Phys. 61 (2005) 945-953.

• NOSE, T., et al., In vivo dosimetry of high-dose-rate interstitial brachytherapy in the pelvic region: use of a radiophotoluminescence glass dosimeter for measurement of 1004 points in 66 patients with pelvic malignancy, Int. J. Radiat. Oncol. Biol. Phys. 70 (2008) 626-633.

• SCHULTKA, K., et al., EPR/alanine dosimetry in LDR brachytherapy--a feasibility study, Radiat Prot Dosimetry 120 (2006) 171-175.

• SEYMOUR, E. L., DOWNES, S. J., FOGARTY, G. B., IZARD, M. A., METCALFE, P., In vivo real-time dosimetric verification in high dose rate prostate brachytherapy, Med Phys 38 (2011) 4785-4794.

• SOUBRA, M., CYGLER, J., MACKAY, G., Evaluation of a dual bias dual metal oxide-silicon semiconductor field effect transistor detector as radiation dosimeter, Med Phys 21 (1994) 567-572.

• SUCHOWERSKA, N., et al., Clinical trials of a urethral dose measurement system in brachytherapy using scintillation detectors, Int J Radiat Oncol Biol Phys 79 (2011) 609-615.

• TANDERUP, K„ BEDDAR, S„ ANDERSEN, C. E„ KERTZSCHER, G„ CYGLER, J. E„ In vivo dosimetry in brachytherapy, Med. Phys. 40 (2013) 070902.

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Bibliography

WALDHAUSL, C„ WAMBERSIE, A., POTTER, R„ GEORG, D„ In-vivo dosimetry for gynaecological brachytherapy: physical and clinical considerations, Radiother. Oncol. 77 (2005) 310-317.YORKE, E., et al., Diode in Vivo Dosimetry for Patients Receiving External Beam in Radiation Therapy: Report of AAPM Task Group 62, AAPM Report No. 87, Medical Physics Publishing, Madison, Wl (2005).