Chapter1 fundamental physics of radiation dosimetry

The main contents Production of Radiation（review） Interactions of ionizing radiation（r) Basic concepts in radiation dosimetry（r） Phantom Dose measurement methology

1.Production of Radiation The classification of radiation

1.Production of Radiation The classification of radiation

1.Production of Radiation The classification of radiation Both directly and indirectly ionizing radiations are used in treatment of disease, mainly but not exclusively malignant disease. The branch of medicine that uses radiation in treatment of disease is called radiotherapy, therapeutic radiology or radiation oncology. Diagnostic radiology and nuclear medicine are branches of medicine that use ionizing radiation in diagnosis of disease.

1.Production of Radiation The kind of rays can be used for radiation therapy： X-rays γ-rays Electron beam Neutron beam and proton beam

1.Production of Radiation X-rays were discovered by Roentgen in 1895 while studying cathode rays in a gas discharge tube. He observed that another type of radiation was produced (presumably by the interaction of electrons with the glass walls of the tube) which could be detected outside the tube. This radiation could penetrate opaque substances, produce fluorescence, blacken a photographic plate, and ionize a gas. He named the new radiation x-rays.

1.Production of Radiation 1.1 Production of X-Rays There are two different mechanisms by which x-rays are produced. One give rise to bremsstrahlung x-rays (braking radiation) and the other characteristic x-rays.

1.Production of Radiation 1.1.1 Kilovoltage units (eliminated through selection or contest )(千伏级x线机) Grenz-ray therapy: used to describe treatment with beams of very soft (low-energy) x-rays produced at potentials below 20kV Contact therapy: potentials of 40 to 50 kV Superficial therapy: from 50 to 150 kV Orthovoltage therapy or deep therapy: from 150 to 500 kV Supervoltage therapy(high-voltage): 500 to 1000 kV Megavoltage therapy: 1MV or greater

1.Production of Radiation 1.1.2 Medical linear accelerator(直线加速器) 4MV, 6MV, 8MV, 10MV, 15MV, 25MV 表1 钨靶x线管和加速器产生x线的效率 加速电压 40KV 70KV 100KV 150KV 4MeV 20MeV X线能（%） 0.4 0.6 0.8 1.3 36 70 热能（%） 99.6 99.4 99.2 98.7 64 30

1.Production of Radiation 1.2 γ-rays Source Ra-226(镭-226) Cs-137(铯-137) half of life :33y Co-60(钴-60) 5.27y 1.25MeV I-125(碘-125) used for brachytherapy Ir-192(铱-192) used for brachytherapy

Nucleus transformation

X线光子在生物组织中的吸收及其引起生物效应的过程

2. Interactions of ionizing radiation 2.1 Interactions of electron radiation Electron interacts with matter through Coulomb inter-actions with atomic orbital electrons and atomic nuclei. Through these collisions the electrons may lose their kinetic energy (collision and radiative losses) or change their direction of travel (scattering). Energy losses are described by stopping power; scattering is described by scattering power.

2. Interactions of ionizing radiation Interaction of an electron with an atom, where a is the atomic radius and b the impact parameter.

2. Interactions of ionizing radiation Interactions of electron radiation orbital electron interactions Coulomb interactions between the incident electron and orbital electrons of an absorber result in ionisations and excitations of absorber atoms: Ionisation: ejection of an orbital electron from absorber atom; Excitation: transfer of an orbital electron of the absorber atom from an allowed orbit to a higher allowed orbit (shell); Atomic excitations and ionisations result in collisional energy losses and are characterized by collision (ionisation) stopping powers.

2. Interactions of ionizing radiation Interactions of electron radiation Electron-nucleus interactions Coulomb interactions between the incident electron and nuclei of the absorber atom result in electron scattering and energy loss of the electron through production of x-ray photons (bremsstrahlung). These types of energy losses are characterized by radiative stopping

2. Interactions of ionizing radiation 2.2 Interactions of x or γ ray beam When an x or γ ray beam passes through a medium, interaction between photons and matter can take place with the result that energy is transferred to the medium. The initial step in the energy transfer involves the ejection of electrons from the atoms of absorbing medium. These high-speed electrons transfer their energy by producing ionization and excitation of the atoms along their paths.

2.Interactions of ionizing radiation If the absorbing medium consists of body tissues, sufficient energy may be deposited within the cells, destroying their reproductive capacity. However, most of the absorbed energy is converted into heat, producing no biologic effect.

2.Interactions of ionizing radiation The following are the action forms in the interaction between photon and medium. Photoelectric effect 光电效应 Compton effect 康普顿效应 Pair production 电子对产生 Coherent scattering 相干散射 Interaction of photon and nucleus光核反应

2.Interactions of ionizing radiation

2.Interactions of ionizing radiation 2.2.1 Photoelectric Effect The photoelectric effect is a phenomenon in which a photon interacts with an atom and ejects one of the orbital electrons from the atom. In this process,the entire energy hv of the photon is transferred to the atomic electron. The kinetic energy of the ejected electron (called the photoelectron) is equal to hv-EB,where EB is the binding energy of the electron . Interaction of this type can take place with electrons in K,L,M,or N shells.

Photoelectric effect

2.Interactions of ionizing radiation 光电效应发生的能量条件是：入射光子的能量必须等于或大于轨道电子的结合能。 光电效应的发生几率与物质的原子序数的4次方成正比，与入射线波长的3次方成正比即与光子能量的3次方成反比。

2.Interactions of ionizing radiation 2.2.2 Compton effect In the Compton process,the photon interacts with an atomic electron as though it were a “free” electron. The term“free” here means that the binding energy of the electron is much less than the energy of the bombarding photon. In this interaction the electron receives some energy from the photon and is emitted at an angle θ. The photon, with reduced energy, is scattered at an angle φ.

Compton effect

2.Interactions of ionizing radiation 康普顿效应的发生几率与入射线波长成正比，即与入射光子能量成反比。 理论推导得到散射光子的能量hv’、反冲电子的动能E分别为：

2.Interactions of ionizing radiation

2.Interactions of ionizing radiation 2.2.3 Pair Production If the energy of the photon is greater than 1.02 MeV, the photon may interact with matter through the mechanism of pair production. In this process, the photon interacts strongly with the electronmagnetic field of an atomic nucleus and gives up all its energy in the process of creating a pair consisting of a negative electron(e-) and a positive electron(e+).

2.Interactions of ionizing radiation 2.2.3 Pair Production 由于电子的静止能量等于0.51MeV,因此产生一对正、负电子所需的最小能量是1.02MeV 。 设ε＋、ε－分别表示正、负电子的动能，由能量守恒定律，得 正、负电子的动能并不一定相等，其能量是从0到最大值为E=hv－2m0c2 的连续能谱。

Pair production

2.Interactions of ionizing radiation 2.3 除上述三种主要相互作用过程外，与辐射防护相关的其它过程是相干散射和光核反应。 2.3.1相干散射 射线与物质相互作用而发生干涉的散射过程称为相干散射，也称为瑞利散射。入射光子被原子的内壳层电子吸收并激发到外层高能级上，遂即又跃迁回原能级，同时放出一个能量与入射光子相同，但传播方向发生改变的散射光子。实际上就是x线的折射。 是光子与物质相互作用中唯一不产生电离的过程

2.Interactions of ionizing radiation 2.3.2光核作用 即光子与原子核作用而发生的核反应。这是一个光子从原子核内击出数量不等的中子、质子和γ光子的作用过程。 对不同物质只有当光子能量大于该物质发生核反应的阈能时，光核反应才会发生。其发生率不足主要作用过程的5%。 光核反应在诊断射线能量范围内不可能发生，在医用电子加速器等高能射线的放疗中发生率也很低。

2.Interactions of ionizing radiation 总结（入射光子的能量hv、结合能Ei） hv < Ei 相干散射 hv ≥ Ei 光电效应 hv >> Ei 康普敦效应 hv ≥ 2mec2 电子对效应 hv 很高 光核反应 总减弱系数

三种主要效应的优势空间

3.Basic concept of radiation dosimetry 能量转移系数和能量吸收系数（energy transfer coeficient and energy absorb coeficient) 粒子注量与能量注量（particle fluence and energy fluence） 照射量(E, exposure) 比释动能(K, kerma) 吸收剂量( D, absorbed dose)

3.Basic concept of radiation dosimetry 3.1 energy transfer coeficient and energy absorb coeficient For use in radiation dosimetry two additional attenuation coefficients are defined: the energy transfer coefficient μtr and the energy absorption coefficient μab(often designated as μ en). The two coefficients are related to μ as follows: is the average energy transferred to charged particles (electrons and posi-trons) in the attenuator Is the average energy deposited by charged particles in the attenuator.

3.Basic concept of radiation dosimetry 3.2粒子注量与能量注量 粒子注量：进入具有单位截面积的小球的粒子数。如球体（通过球心P的）截面积为da，从各个方向进入该小球体的粒子的总数为dN，二者相除为P点处的粒子注量φ。即

3.Basic concept of radiation dosimetry 3.2粒子注量与能量注量 能量注量：进入单位截面积小球的所有粒子的能量的总和。如果进入截面积为da的球体内的所有粒子的能量总和为dEfL则能量注量ψ为：

3.Basic concept of radiation dosimetry 3.2粒子注量与能量注量 二者的关系（单能或者是非单能 ）

3.Basic concept of radiation dosimetry 3.3 照射量 X 或γ射线的光子在单位质量空气中产生出来的所有次级电子，当它们完全被空气所阻止时，在空气中所形成的任何一种符号离子的总电荷量的绝对值。即： 单位：库仑/千克（C/kg）。仍在沿用的照射量专用单位为伦琴（R）。 1R=2.58×10-4 C/kg

3.Basic concept of radiation dosimetry 3.4 比释动能 指间接致电离辐射与物质相互作用时，在单位质量物质中由间接致电离辐射所产生的全部带电粒子的初始动能之总和。即： 单位：焦耳/千克-1（J•kg-1）又名“戈瑞”，以“Gy”记。以此纪念为测量吸收剂量而奠定空腔电离理论基础的科学家H . Gray。1Gy=1 J•kg-1

3.Basic concept of radiation dosimetry 3.5 吸收剂量 辐射所授予单位质量介质dm的平均能量dEen定义为吸收剂量。 （dEen表示进入介质dm的全部带电粒子和不带电粒子能量的总和，与离开该体积的全部带电粒子和不带电粒子能量的总和之差，再减去在该体积内发生任何核反应所增加的静止质量的等效能量）即： 单位：焦耳/千克-1（J•kg-1）又名“戈瑞”，以“Gy”记之。

3.Basic concept of radiation dosimetry 辐射量 照射量 比释动能 吸收剂量 剂量学含义 表征X、γ射线在关心的体积内用于电离空气的能量 表征非带电粒子在所关心的体积内交给带电粒子的能量 表征任何辐射在所关心的体积内被物质吸收的能量 适用介质 空气 任何介质 适用辐射类型 X、γ射线 非带电粒子辐射 任何辐射

4.Phantoms 体模

4.1 Concept of Phantoms Introduction It is seldom possible to measure dose distribution directly in patients treated with radiation. Dada on dose distribution are almost entirely derived from measurement in phantoms----tissue equivalent materials, usually large enough in volume to provide full-scatter conditions for the given beam. These basic data are used in a dose calculation system devised to predict dose distribution in an actual patient.

4.1.1 Definition of phantom 采用人体组织的替代材料（tissue substitutes）构成的模型代替人的身体，简称模体(phantom). ICRU第30号报告中曾用组织等效材料(tissue-equivalent material)一词，将其定义为“对射线的散射和吸收的特性与人体组织的相同的材料”。这种定义因理解不同往往被乱用。因此ICRU第44号报告中建议使用组织替代材料一词，定义是“模拟人体组织与射线相互作用的材料”。

Introduction 显然这种替代材料必须具有与被模拟的组织与射线相互作用相同的有关的物理特点，如原子序数、电子密度、质量密度、甚至化学成分等。

物质的电子密度ρe与质量密度ρ m、原子量A和原子序数Z之间的关系是： NA：Avogadro’s常数 ai ：第i种元素的重量份额，该元素原子序数为Z i ，原子量为Ai。

一般情况下，适合X（γ）射线的组织替代材料一定是电子束的组织替代材料。 对中子束，因其主要与组织中的元素的原子核发生作用，替代材料的元素构成必须与被替代组织的相同，而且，它们的H、C、N、O的质量相对份数完全相等，这样才能保证替代材料与被替代组织对中子的吸收和散射相等。 对重离子，因其与组织的相互作用主要是电子碰撞，所以线性碰撞本领是选择组织替代材料的首要条件。 对负π介子，除考虑线性碰撞本领外，还应考虑被替代组织及组织替代材料的分子结构。

4.1.2 Water phantom and its characters Basic dose distribution data are usually measured in a water phantom which closely approximates the radiation absorption and scattering properties of muscle and other soft tissues. Another reasons for the choice of water as a phantom material is that it is universally available with reproducible radiation properties. A water phantom, however, poses some practical problems when used in conjunction with ion chamber and other detectors which are affected by water, unless they are designed to be waterproof. In most cases, however, the detector is encased in a thin plastic (water equivalent) sleeve before immersion into the water phantom.

Physical properties of various phantom materials Chemical Composition Mass Density(g/cm3) Number of electrons/g(×1023) Zeff Water H2O 1 3.34 7.42 Polystyrene (C8H8)n 1.03~1.05 3.24 5.69 Plexiglas (C5O2H8)n 1.16~1.20 6.48 Muscle 1.04 3.44 7.64 Fat 0.916 3.06 6.46 Bone 1.65 5.26 12.31

4.2 组织替代材料之间的转换 上述组织替代材料作为水的替代材料的效果，决定于被测射线与模体材料的相互作用。 对中高能X(γ)射线，康普敦效应为主要形式，当两种模体材料的电子密度相等时，则认为它们彼此等效。对水的等效厚度T水为：

式中 T水为T模体的等效水厚度， ρ模体为模体材料的物理密度， Z为材料的原子序数， A为材料的原子量。 1cm厚的有机玻璃相当于1.18×(0.540/0.555)=1.148cm水

对低能X射线，光电效应占主要，两种模体材料通过下式等效： 1cm厚的有机玻璃相当于 1.18×(6.48 / 7.42)3=0.79cm水

对高能X射线，电子对效应为主要形式，两种模体材料通过下式等效： 1cm厚的有机玻璃相当于 1.18×(5.85 / 6.60)=1.05 cm 水

对电子束，模体材料是通过模体中电子注量进行等效： R0为电子束在材料中的连续慢化近似射程(有效射程)，随能量而变化。

4.3 体模种类 由组织替代材料组成的模体是用于模拟各种射线在人体组织或器官中因散射和吸收所引起的变化，即模拟射线与人体组织或器官的相互作用的物理过程。ICRU第23号，第24号，第30号报告中对各种模体作了如下的分类和定义： 标准模体（standard phantom） 均匀模体（homogeneous phantom） 人体模体（anthropomorphic phantom） 组织填充模体（bolus）

4.3.1 Standard Phantom 长宽高分别为30cm的立方体水模，用于X（γ）射线、电子束、中子束吸收剂量的测定与比对。对低能电子束，水模体的高度可以薄一些，但其最低高度不能低于5cm。

4.3.2Homogeneous Phantom 用固态或干水组织替代材料加工成的片形方块，构成边长为30cm或者25cm的立方体，代替标准水模体作吸收剂量和能量的常规检查。

4.3.3 Anthropomorphic Phantom 分为均匀型和不均匀型，前者用均匀的固态材料替代组织加工成，类似标准人体外形或组织器官外形的模体；后者用人体各种组织（包括肺、骨、气腔等）的相应的组织替代材料加工而成，类似标准人体外形或组织器官外形的模体。 人体模体主要用于治疗过程中的剂量学研究，包括新技术的开发与验证、治疗方案的验证与测量等，不主张用它做剂量的常规校对与检查。

4.3.4 Bolus 用组织替代材料制成的组织补偿模体，直接放在射野入射侧的患者皮肤上，用于改变患者皮肤不规则轮廓对体内靶区或重要器官剂量分布的影响，提供附加的对线束散射、建成或衰减。与组织补偿器（tissue compensator）的区别是：前者必须用组织替代材料制作而且必须放在患者皮肤上；后者不必非用组织替代材料而且要远离患者皮肤一定距离。

5.Methology of radiation measurement 剂量测量装置的一般要求 电离室法 量热法 热释光剂量仪 胶片剂量仪 半导体剂量仪 化学方法

5.1 General requirement of dosimeter What is dosimeter? Radiation dosimeter is a device, instrument or system that measures or evaluates, either directly or indirectly, the quantities exposure, kerma, absorbed dose or equivalent dose, or their time derivatives (rates) or related quantities of ionizing radiation. A dosimeter along with its reader is referred to as a dosimetry system.

5.1 General requirement of dosimeter What is the requirement? Accuracy and precision Linearity Dose rate dependence Energy dependence Directional dependence Spatial resolution and physical size Readout convenience Convenience of use

5.1 General requirement of dosimeter Response characteristics of two dosimetry systems. Curve A first exhibits linearity with dose, then supralinear behavior, and finally saturation. Curve B first exhibits linearity and then saturation at high doses

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS Chambers and electrometers Free air chamber Standard method for Exposure measure Don’t suit for application Practical thumb chamber

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS The basic design of a cylindrical Farmer-type ionisation chamber.

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS Electrometer in feedback mode of operation.

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS Chambers and electrometers Cylindrical (thimble type) ionisation chambers Parallel-plate (plane-parallel) ionisation chambers Brachytherapy chambers Extrapolation chambers

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS (1) is the polarizing electrode; (2) is the measuring electrode; and (3) is the guard ring. (a) is the height (electrode separation) of the air cavity; (d) is the diameter of the polarizing electrode; (m) is the diameter of the collecting electrode; and (g) is the width of the guard ring (adapted from the IAEA TRS-381 dosimetry protocol).

5.2 IONISATION CHAMBER DOSIMETRY SYSTEMS The basic design of a brachytherapy well-type chamber

5.3 FILM DOSIMETRY Various types of films are available for radiotherapy work (e.g., direct exposure non-screen films for field size verification, phosphor screen films used with simulators, metallic screen films used in portal imaging, etc.). Ideally, the relationship between the dose and OD should be linear, but unfortunately this is not always the case. So the dose vs. OD curve, known as the sensitometric curve (also known as the characteristic or H&D curve, in honour of Hurter and Driffield who first investigated the relationship) must be established for each film before using it for dosimetry work.

5.3 FILM DOSIMETRY Typical sensitometric (characteristic H&D) curve for a radiographic film.

5.4 LUMINESCENCE DOSIMETRY Some materials, upon absorption of radiation, retain part of the absorbed energy in metastable states. When this energy is subsequently released in the form of ultraviolet, visible or infrared light, the phenomenon is called as luminescence. If the exciting agent is heat, the phenomenon is known as thermoluminescence and the material is called a thermoluminescent (TL) material or a thermoluminescent dosimeter (TLD) when used for purposes of dosimetry.

5.4 LUMINESCENCE DOSIMETRY TL dosimeters most commonly used in medical applications are LiF:Mg,Ti, LiF:Mg,Cu,P and Li2B4O7:Mn, because of their tissue equivalence. Other TLDs, used because of their high sensitivity, are CaSO4:Dy, Al2O3:C and CaF2:Mn. TLDs are available in various forms (e.g., powder, chips, rods, ribbon, etc.).

5.4 LUMINESCENCE DOSIMETRY Typical applications of TLD in radiotherapy are: in vivo dosimetry on patients (either as a routine QA procedure or for dose monitoring in special cases, e.g., complicated geometries, dose to critical organs, total body irradiation, in brachytherapy, etc.), verification of treatment techniques in various phantoms (e.g., Rando phantom), dosimetry audits (such as the IAEA/WHO TLD postal dose audit programme) and comparisons among hospitals.

5.4 LUMINESCENCE DOSIMETRY

5.4 LUMINESCENCE DOSIMETRY A typical glow-curve (thermogra) of LiF:Mg,Ti measured with a TLD reader at a low heating rate.

5.5 SEMICONDUCTOR DOSIMETRY Silicon diode dosimeter is a p-n junction diode. The diodes are referred to as n-Si or p-Si dosimeters, depending upon the base material. Radiation produces electron-hole (e-h) pairs in the body of the dosimeter including the depletion layer. They are swept across the depletion region under the action of the electric field due to the intrinsic potential. In this way a current is generated in the reverse direction in the diode.

5.5 SEMICONDUCTOR DOSIMETRY Silicon diode dosimeter is a p-n junction diode. The diodes are referred to as n-Si or p-Si dosimeters, depending upon the base material. Radiation produces electron-hole (e-h) pairs in the body of the dosimeter including the depletion layer. They are swept across the depletion region under the action of the electric field due to the intrinsic potential. In this way a current is generated in the reverse direction in the diode.

5.6 MAIN ADVANTAGES AND DISADVANTAGES OF FOUR COMMONLY USED DOSIMETRIC SYSTEMS

5.6 MAIN ADVANTAGES AND DISADVANTAGES OF FOUR COMMONLY USED DOSIMETRIC SYSTEMS

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