📚 IB Physics: Medical Physics Key Points | IB 物理：医疗物理 考点精讲
Medical physics is a fascinating applied branch of physics that powers diagnostic imaging, cancer therapy, and patient monitoring. For IB Physics students, the medical physics option demands a solid grasp of wave physics, atomic and nuclear processes, as well as practical safety considerations. This article distils the core concepts, essential equations, and comparative insights you need for revision, presented in clear bilingual form to reinforce understanding.
医学物理是一门迷人的应用物理分支，为诊断成像、癌症治疗和患者监护提供物理基础。对于 IB 物理学生而言，医疗物理选修部分要求扎实掌握波动物理、原子与核过程以及实际的安全考量。本文凝练了核心概念、必背公式和对比要点，并以清晰的双语形式呈现，帮助你巩固理解。
1. Introduction to Medical Physics | 医学物理简介
Medical physics applies the principles of physics to the prevention, diagnosis and treatment of human disease. The IB Physics syllabus covers imaging techniques that exploit different parts of the electromagnetic spectrum and mechanical waves, as well as the use of ionising radiation in nuclear medicine and radiotherapy. Key themes include resolution, contrast, intensity, attenuation and biological effects of radiation.
医学物理将物理原理应用于人类疾病的预防、诊断和治疗。IB 物理课程涵盖了利用电磁波谱不同区域和机械波的成像技术，以及电离辐射在核医学与放射治疗中的应用。核心主题包括分辨率、对比度、强度、衰减和辐射的生物效应。
2. X-ray Imaging: Production and Properties | X 射线成像：产生与性质
X-rays are high-energy photons produced when fast-moving electrons are decelerated in a metal target. In an X-ray tube, a heated filament emits electrons via thermionic emission. They are accelerated by a high potential difference (ΔV) and strike a rotating anode. The kinetic energy of an electron just before impact is e × ΔV, and the maximum photon energy is given by Eₘₐₓ = h fₘₐₓ = e ΔV. The short-wavelength cut-off is λₘᵢₙ = hc / (e ΔV).
X 射线是高速电子在金属靶中减速时产生的高能光子。在 X 射线管中，加热灯丝通过热电子发射放出电子，电子被高压（ΔV）加速后撞击旋转阳极。电子撞击前的动能是 e × ΔV，产生的最大光子能量为 Eₘₐₓ = h fₘₐₓ = e ΔV。最短波长截止点为 λₘᵢₙ = hc / (e ΔV)。
The X-ray spectrum consists of a continuous bremsstrahlung background and characteristic peaks. Intensity of the beam depends on the tube current (mA), while penetration power depends on the accelerating voltage (kVp). Hard X-rays have higher energy and are more penetrating; soft X-rays are easily absorbed and are often filtered out.
X 射线能谱包含连续的轫致辐射本底和特征峰。射线束强度取决于管电流（mA），穿透能力取决于加速电压（kVp）。硬 X 射线能量高、穿透力强；软 X 射线容易被吸收，通常会被滤除。
Attenuation of a monochromatic X-ray beam in matter follows an exponential law:
I = I₀ e⁻ᵘˣ
where μ is the linear attenuation coefficient and x is the thickness. The half-value thickness (HVT) is x₁/₂ = ln2 / μ. For polyenergetic beams, beam hardening occurs because lower-energy photons are attenuated more rapidly.
单能 X 射线在物质中的衰减遵循指数规律：I = I₀ e⁻ᵘˣ，其中 μ 为线性衰减系数，x 为厚度。半值层厚度为 x₁/₂ = ln2 / μ。对于多能射线束，会发生射线硬化，因为低能光子衰减更快。
3. Factors Affecting X-ray Image Quality | 影响 X 射线图像质量的因素
Image quality in radiography is determined by contrast, sharpness and noise. Contrast depends on the differential absorption between tissues – bone absorbs much more than soft tissue due to higher effective atomic number. Contrast can be improved by using a lower kVp or by introducing a contrast medium such as barium or iodine.
射线摄影的图像质量取决于对比度、清晰度和噪声。对比度依赖于组织间吸收的差异——骨的有效原子序数较高，因此吸收远多于软组织。可通过使用较低的 kVp 或引入钡、碘等造影剂来改善对比度。
Geometric unsharpness arises because the X-ray source has a finite focal spot size. The magnified penumbra can be reduced by keeping the object close to the detector and using a greater source-to-image distance. Scattered radiation degrades contrast, so grids are used between the patient and the detector to absorb off-axis photons.
几何不清晰度源于 X 射线源的焦点并非无限小。放大的半影可通过将物体贴近探测器，并增大源到影像接收器的距离来减小。散射线会降低对比度，因此需要在患者与探测器之间使用滤线栅吸收斜射光子。
4. Computed Tomography (CT) Scanning | 计算机断层扫描 (CT)
A CT scanner rotates an X-ray tube and a bank of detectors around the patient to acquire multiple projections. Reconstruction software produces a cross-sectional image, where each pixel’s brightness represents the linear attenuation coefficient μ, displayed as Hounsfield units (HU): HU = 1000 × (μ − μwₐₜₑᵣ) / μwₐₜₑᵣ. The CT number for water is 0, air is –1000, and bone is +400 to +1000.
CT 扫描仪将 X 射线管和一组探测器围绕患者旋转，获取多个投射。重建软件生成横截面图像，每个像素的亮度代表线性衰减系数 μ，并以亨氏单位（HU）显示：HU = 1000 × (μ − μ水) / μ水。水的 CT 值为 0，空气为 –1000，骨为 +400 至 +1000。
CT provides excellent 3D anatomical detail and removes superposition, but it delivers a higher radiation dose than a single projection radiograph. Modern helical (spiral) CT allows rapid volume scanning. Image noise and spatial resolution must be balanced against patient dose.
CT 可提供出色的三维解剖细节并消除重叠，但辐射剂量高于单次投照X线片。现代螺旋 CT 可实现快速容积扫描。图像噪声和空间分辨率需与患者剂量之间取得平衡。
5. Ultrasound Imaging: Principles and Applications | 超声成像：原理与应用
Ultrasound uses high-frequency sound waves (typically 1–15 MHz) produced by the piezoelectric effect in a transducer. When an electric pulse is applied, the crystal vibrates and emits ultrasound. Returning echoes generate a voltage that is processed to form images. The key parameter is acoustic impedance Z = ρc, where ρ is density and c is speed of sound in the medium.
超声利用换能器中压电效应产生的高频声波（通常 1–15 MHz）。施加电脉冲时，晶体振动并发射超声波。返回的回波产生电压，经处理形成图像。关键参数是声阻抗 Z = ρc，其中 ρ 为密度，c 为介质中的声速。
At a boundary between two media, the intensity reflection coefficient for normal incidence is:
R = (Z₂ − Z₁)² / (Z₂ + Z₁)²
A large impedance mismatch (e.g. tissue–air) reflects most of the sound, so a coupling gel is used to eliminate air gaps. In imaging, the A-mode displays amplitude vs time, B-mode gives a 2D brightness image, and M-mode shows motion over time for heart valves etc.
在两种介质界面处，正入射的强度反射系数为：R = (Z₂ − Z₁)² / (Z₂ + Z₁)²。声阻抗失配大（如组织–空气）会反射大部分声波，因此需使用耦合凝胶消除空气间隙。成像中，A 型显示振幅–时间，B 型给出二维亮度图像，M 型用于显示瓣膜等随时间变化的运动。
Doppler ultrasound measures blood flow velocity using the Doppler shift: Δf = 2 f₀ v cosθ / c, where f₀ is the transmitted frequency, v is blood velocity, θ is the angle between the beam and flow direction, and c is the speed of sound in tissue (~1540 m/s). Colour Doppler adds flow direction information.
多普勒超声利用频移测量血流速度：Δf = 2 f₀ v cosθ / c，其中 f₀ 为发射频率，v 为血流速度，θ 为声束与血流方向的夹角，c 为组织中声速 (~1540 m/s)。彩色多普勒可以添加流向信息。
6. Endoscopy: Fibre Optics in Medicine | 内窥镜：医用纤维光学
An endoscope uses coherent bundles of optical fibres to transmit light and images into and out of the body. Total internal reflection (TIR) traps light within the core, provided the incidence angle at the core–cladding interface exceeds the critical angle. The critical angle is given by sin θc = n₂ / n₁, where n₁ > n₂.
内窥镜利用相干光纤束将光线和图像传入体内并传出体外。当光线在纤芯–包层界面的入射角大于临界角时，会发生全内反射，将光限制在纤芯内。临界角由 sin θc = n₂ / n₁ 给出，其中 n₁ > n₂。
The image quality depends on fibre diameter and packing fraction. Additional channels in an endoscope allow the insertion of surgical tools, irrigation, or a separate fibre for laser surgery. Endoscopy is minimally invasive and avoids ionising radiation, but it is limited to accessible cavities.
图像质量取决于光纤直径和填充率。内窥镜的附加通道可插入手术器械、冲洗管或用于激光手术的单独光纤。内窥镜属微创操作且无电离辐射，但仅限于可进入的腔体。
7. Nuclear Medicine: Gamma Camera and PET | 核医学：伽马相机与 PET
Nuclear medicine images physiological function by introducing a radiopharmaceutical that emits gamma rays. The gamma camera uses a collimator (usually a lead honeycomb) to accept only photons arriving perpendicularly, a NaI scintillator to convert gamma rays into visible light, and an array of photomultiplier tubes to determine the position of each scintillation event.
核医学通过引入发射伽马射线的放射性药物对人体生理功能进行成像。伽马相机使用准直器（通常为蜂窝状铅板）只接收垂直入射的光子，NaI 闪烁体将伽马射线转化为可见光，光电倍增管阵列确定每次闪烁事件的位置。
Radioactive tracers are chosen with an appropriate half-life: e.g., technetium‑99m (T₁/₂ = 6 h) emits 140 keV gamma rays. The activity A of a sample decays exponentially: A = A₀ e⁻λᵗ, where λ = ln2 / T₁/₂. The count rate measured by the camera must be corrected for attenuation and scatter.
选择具有适当半衰期的放射性示踪剂，例如：锝‑99m（T₁/₂ = 6 h）发射 140 keV 伽马射线。样品的活度 A 呈指数衰减：A = A₀ e⁻λᵗ，其中 λ = ln2 / T₁/₂。相机测量的计数率必须对衰减和散射进行校正。
Positron emission tomography (PET) uses radionuclides that decay via β⁺ emission (e.g., fluorine‑18). The emitted positron annihilates with a nearby electron, producing two 511 keV annihilation photons travelling in almost opposite directions. Coincidence detection by a ring of detectors removes the need for a physical collimator, improving sensitivity and enabling quantitative imaging.
正电子发射断层扫描（PET）使用通过 β⁺ 衰变的放射性核素（如氟‑18）。发射出的正电子与邻近电子湮灭，产生两个几乎沿相反方向传播的 511 keV 湮灭光子。环形探测器的符合探测无需物理准直器，提高了灵敏度并实现了定量成像。
8. Radiotherapy: Using Radiation to Treat Cancer | 放射治疗：用辐射治疗癌症
Radiotherapy aims to deliver a lethal dose of ionising radiation to a tumour while sparing surrounding healthy tissue. External beam therapy commonly uses high-energy X-rays (6–25 MV) from a linear accelerator. The depth–dose curve shows a build-up region, a maximum, and then a slow decline; the percentage depth dose is maximised for deep tumours by using multiple beams or arc therapy.
放射治疗旨在向肿瘤释放致死剂量的电离辐射，同时保护周围健康组织。外照射治疗通常使用直线加速器产生的高能 X 射线（6–25 MV）。深度–剂量曲线显示建成区、最大值、然后缓慢下降；利用多野照射或旋转调强可以使深部肿瘤的百分深度剂量最大化。
The biological effect depends on absorbed dose (Gy = J/kg), but both physical dose and relative biological effectiveness (RBE) are important. Fractionation – dividing the total dose into many small fractions – allows normal tissue to repair between treatments while tumour cells, often less efficient at repair, accumulate damage. Equivalent dose H (Sv) = D × wR, where wR is the radiation weighting factor.
生物效应取决于吸收剂量（Gy = J/kg），但物理剂量和相对生物效应（RBE）都重要。分割治疗——将总剂量分成多次小剂量——使正常组织在治疗间隔得到修复，而修复能力通常较差的肿瘤细胞则累积损伤。当量剂量 H（Sv）= D × wR，其中 wR 为辐射权重因子。
Brachytherapy places a sealed radioactive source close to or inside the tumour (e.g., iodine‑125 seeds for prostate cancer). The inverse‑square law ensures a steep dose fall‑off, limiting damage to distant tissues. Proton therapy exploits the Bragg peak – a sharp maximum in energy deposition at a specific depth – to confine dose to the tumour with sub‑millimetre precision.
近距治疗将密封放射源置于肿瘤附近或内部（如前列腺癌用的碘‑125 粒子）。距离平方反比规律确保剂量急剧下降，限制对远处组织的损伤。质子治疗利用布拉格峰——在特定深度处能量沉积的尖锐极大值——以亚毫米精度将剂量限制在肿瘤内。
9. Magnetic Resonance Imaging (MRI) | 磁共振成像 (MRI)
MRI exploits the magnetic properties of hydrogen nuclei (protons). In a strong external magnetic field B₀, protons precess at the Larmor frequency f = γ B₀ / (2π), where γ is the gyromagnetic ratio. A radiofrequency pulse at this frequency flips the magnetization into the transverse plane. When the RF pulse is switched off, the protons relax, emitting a signal that is used to construct images.
MRI 利用氢原子核（质子）的磁特性。在强外磁场 B₀ 中，质子以拉莫尔频率 f = γ B₀ / (2π) 进动，其中 γ 为旋磁比。此频率的射频脉冲将磁化矢量翻转至横向平面。射频脉冲关闭后，质子弛豫，发射的信号用于构建图像。
Two relaxation times characterise the tissue: T₁ (spin‑lattice) and T₂ (spin‑spin). By varying the pulse sequence, T₁-weighted or T₂-weighted images can be produced, highlighting different tissue types. MRI provides superb soft‑tissue contrast without ionising radiation, but it is expensive, noisy, and cannot be used with certain metal implants.
两种弛豫时间表征组织：T₁（自旋‑晶格）和 T₂（自旋‑自旋）。通过改变脉冲序列，可以生成 T₁ 加权或 T₂ 加权图像，凸显不同的组织类型。MRI 不涉及电离辐射，可提供极佳的软组织对比度，但价格昂贵、噪声大，且不能用于某些金属植入物。
10. Comparison of Imaging Techniques | 成像技术比较
The table below summarises key features of the main medical imaging modalities. Understanding these differences helps in deciding which technique is most appropriate for a given clinical question.
下表总结了主要医学成像模式的关键特征。理解这些差异有助于确定哪种技术最适合特定的临床问题。
| Imaging Method | Physical Principle | Radiation? | Soft‑Tissue Resolution | Typical Application |
|---|---|---|---|---|
| X-ray / Radiography | Attenuation of X-rays | Ionising | Poor | Bone fractures, chest |
| CT | Multiple X-ray projections, μ maps | Ionising (higher dose) | Good | Head trauma, tumour staging |
| Ultrasound | Echoes at impedance boundaries | Non‑ionising | Moderate | Obstetrics, abdomen |
| Nuclear Medicine (γ camera) | Gamma emission from radiotracer | Ionising | Functional only | Bone scans, thyroid |
| PET | Coincident annihilation photons | Ionising | Functional, high sensitivity | Cancer staging, brain metabolism |
| MRI | NMR of protons in magnetic field | Non‑ionising | Excellent | Brain, joints, spine |
11. Safety and Risks in Medical Physics | 医疗物理中的安全与风险
Any technique using ionising radiation must follow the ALARA principle – keeping doses As Low As Reasonably Achievable. Stochastic effects (e.g., cancer induction) have a probability increasing with dose, while deterministic effects (e.g., skin erythema) occur above a threshold. Staff wear film badges or TLDs to monitor cumulative exposure.
任何使用电离辐射的技术都必须遵循 ALARA 原则——即尽可能合理地降低剂量。随机性效应（如诱发癌症）的发生概率随剂量增加，确定性效应（如皮肤红斑）则存在阈值。工作人员佩戴胶片徽章或热释光剂量计监测累积剂量。
Ultrasound and MRI are generally considered safe for the patient, but ultrasound can cause tissue heating and cavitation at very high intensities. MRI safety requires rigorous screening for ferromagnetic implants, pacemakers and metallic foreign bodies, because the strong static field and gradient switching can cause projectile injuries or heating.
超声和 MRI 通常被认为对患者是安全的，但超声在极高强度下可能引起组织加热和空化。MRI 安全需严格筛查铁磁性植入物、起搏器和金属异物，因为强大的静磁场及梯度切换可造成抛射伤害或发热。
12. Summary and Key Equations | 总结与关键方程
Medical physics integrates wave mechanics, nuclear physics and electronics to visualise and treat the human body. The IB exam will expect you to recall the fundamental equations and apply them to straightforward numerical problems. Below are the essential formulas you should have at your fingertips.
医学物理综合运用波动学、核物理和电子学来可视化并治疗人体。IB 考试期望你记住基本方程，并将其应用于简单的数值计算。以下是你必须烂熟于心的公式。
- X-ray photon energy: Eₘₐₓ = h fₘₐₓ = e ΔV ; λₘᵢₙ = hc/(e ΔV) — 最大光子能量和最短波长
- Exponential attenuation: I = I₀ e⁻ᵘˣ ; HVT = ln2 / μ — 指数衰减和半值层厚度
- Ultrasound intensity reflection coefficient: R = (Z₂ − Z₁)²/(Z₂ + Z₁)² ; Z = ρc — 声强反射系数和声阻抗
- Doppler shift: Δf = 2 f₀ v cosθ / c — 多普勒频移测速
- Radioactive decay: A = A₀ e⁻λᵗ ; λ = ln2 / T₁/₂ — 衰变定律
- CT Hounsfield unit: HU = 1000 × (μ − μwₐₜₑᵣ) / μwₐₜₑᵣ — CT 值定义
- Larmor frequency (MRI): f = γ B₀ / (2π) — 拉莫尔进动频率
- Radiation equivalent dose: H = D × wR — 当量剂量
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