📚 IGCSE WJEC Physics: Medical Physics Key Points | IGCSE WJEC 物理：医疗物理 考点精讲
Medical physics applies the principles of physics to the diagnosis and treatment of disease. In the WJEC IGCSE Physics specification, you are expected to understand how X‑rays, ultrasound, and radioactive isotopes are used in medicine, how images are formed, and how safety measures protect patients and staff. This article covers the essential concepts, key equations, and typical exam questions to help you master medical physics.
医疗物理将物理原理应用于疾病的诊断和治疗。在 WJEC IGCSE 物理考纲中，你需要理解 X 射线、超声波和放射性同位素在医学中的应用、图像是如何形成的，以及如何通过安全措施保护患者和医护人员。本文涵盖核心概念、关键公式和典型考题，帮助你掌握医疗物理。
1. X‑rays: Production and Properties | X 射线：产生与性质
X‑rays are high‑energy electromagnetic waves with wavelengths around 10⁻¹⁰ m. They are produced when fast‑moving electrons are suddenly decelerated upon hitting a metal target (often tungsten) in an X‑ray tube. The kinetic energy of the electrons is converted into X‑ray photons.
X 射线是一种高能电磁波，波长约为 10⁻¹⁰ m。当高速电子撞击 X 射线管中的金属靶（通常是钨）并急剧减速时，就会产生 X 射线。电子的动能转化为 X 射线光子。
Key properties of X‑rays include: they travel in straight lines, are unaffected by electric and magnetic fields (no charge), can penetrate materials that absorb visible light, and can ionise atoms. The beam intensity decreases with distance following the inverse square law.
X 射线的主要性质包括：沿直线传播、不受电场和磁场影响（不带电）、可穿透吸收可见光的材料、能使原子电离。射束强度随距离增加而减弱，遵循平方反比定律。
The energy of an X‑ray photon is given by E = h f lanck constant (6.63 × 10⁻³⁴ J·s) and f is the frequency. Since c = f λ, we can also write E = h c / λ. The accelerating voltage V in the tube determines the maximum photon energy: Eₘₐₓ = e V.
X 射线光子的能量由 E = h f 给出，其中 h 是普朗克常数（6.63 × 10⁻³⁴ J·s），f 是频率。由于 c = f λ，也可写成 E = h c / λ。管电压 V 决定了光子能量的最大值：Eₘₐₓ = e V。
E = h f Eₘₐₓ = e V
2. X‑ray Imaging and Contrast | X 射线成像与对比度
X‑ray images are produced because different tissues absorb X‑rays by different amounts. Dense materials such as bone contain calcium and absorb X‑rays strongly, appearing white on the image. Soft tissues absorb less, so they appear darker. The image is a shadow graph based on differential absorption.
X 射线图像的产生是因为不同组织对 X 射线的吸收程度不同。骨骼等致密材料含有钙，会强烈吸收 X 射线，在图像上呈白色。软组织吸收较少，因此显得较暗。这种图像是基于差别吸收的阴影图。
To enhance contrast in soft‑tissue examinations, patients may be given a contrast medium such as barium sulfate (for GI tract) or iodine (for blood vessels). These substances have a high atomic number and absorb X‑rays strongly, outlining the organ clearly.
为了增强软组织检查的对比度，患者可能会被给予造影剂，如硫酸钡（用于胃肠道）或碘（用于血管）。这些物质原子序数高，能强烈吸收 X 射线，清晰地勾勒出器官轮廓。
The intensity of X‑rays after passing through a material of thickness x obeys the exponential attenuation law: I = I₀ e⁻^μx, where μ is the linear attenuation coefficient. This formula is not required for calculations in the IGCSE exam but helps explain why thicker or denser tissue reduces the beam more.
X 射线穿过厚度为 x 的材料后，其强度遵循指数衰减规律：I = I₀ e⁻^μx，其中 μ 是线衰减系数。该公式在 IGCSE 考试中不要求计算，但有助于解释较厚或较密的组织为何会使射束衰减更多。
3. CT Scans: Slicing through the Body | CT 扫描：身体切片成像
A CT (Computed Tomography) scanner uses a rotating X‑ray tube and a ring of detectors to take many X‑ray images from different angles. A computer combines these images to produce a cross‑sectional slice or a 3D volume of the body.
CT（计算机断层扫描）扫描仪利用旋转的 X 射线管和环形探测器阵，从不同角度拍摄大量 X 射线图像。计算机将这些图像合成，产生身体的横截面切片或三维立体图像。
CT scans provide far more detail than conventional X‑rays because they can distinguish between soft tissues of similar density. This allows doctors to see tumours, internal bleeding, and organ damage. However, a CT scan delivers a much higher radiation dose to the patient than a single X‑ray image.
CT 扫描比传统 X 射线提供更多细节，因为它可以区分密度相似的软组织。这让医生能够看到肿瘤、内出血和器官损伤。然而，CT 扫描给予患者的辐射剂量远高于单次 X 射线成像。
The advantages and disadvantages are often assessed in exams. Advantages: high resolution 3D images, quick, and non‑invasive. Disadvantages: high radiation dose, expensive equipment, and some patients may have allergic reactions to contrast agents.
考试中常考查其优点与缺点。优点：高分辨率三维图像、快速、无创。缺点：辐射剂量高、设备昂贵，部分患者可能对造影剂过敏。
4. Ultrasound: Sound beyond Human Hearing | 超声波：超越人耳的声音
Ultrasound refers to sound waves with frequencies above the upper limit of human hearing (>20,000 Hz). In medical applications, frequencies between 1 MHz and 15 MHz are typical. Ultrasound is produced and detected by a transducer that uses the piezoelectric effect.
超声波是指频率超过人耳听觉上限（>20,000 Hz）的声波。在医学应用中，典型频率介于 1 MHz 至 15 MHz 之间。超声波由利用压电效应的换能器产生和检测。
A piezoelectric crystal vibrates when an alternating voltage is applied, generating ultrasound pulses. When the returning echo hits the crystal, it produces a voltage signal. The same transducer acts as both transmitter and receiver.
对压电晶体施加交变电压时，它会振动并产生超声脉冲。返回的回声撞击晶体时，它会产生电压信号。同一换能器既充当发射器又充当接收器。
Ultrasound imaging relies on the pulse‑echo principle. The time delay between sending a pulse and receiving its echo is used to calculate the depth of a reflecting surface: distance = speed × (time / 2). The factor 1/2 accounts for the round trip.
超声成像基于脉冲回波原理。发送脉冲与接收其回波之间的时间延迟用于计算反射面的深度：距离 = 速度 × (时间 / 2)。因子 1/2 是因为往返路径。
d = (v × t) / 2
The speed of sound in soft tissue is approximately 1540 m/s. You may be asked to calculate the depth of a boundary given the echo time.
声音在软组织中的速度约为 1540 m/s。你可能会被要求根据回波时间计算边界深度。
5. Ultrasound Imaging: A‑scans and B‑scans | 超声成像：A 型与 B 型扫描
An A‑scan (amplitude scan) displays the amplitude of returning echoes against time on an oscilloscope. It is used to measure distances, for example, the length of the eye before cataract surgery. Spikes correspond to reflections from boundaries.
A 型扫描（振幅扫描）在示波器上显示回波振幅随时间的变化。它用于测量距离，例如白内障手术前的眼轴长度。尖峰对应来自各界面的反射。
A B‑scan (brightness scan) produces a 2D image by recording the echoes as varying dots of brightness. By moving the transducer across the body, a cross‑sectional image is built up. B‑scans are routinely used to monitor foetal development because ultrasound is non‑ionising and considered safe.
B 型扫描（亮度扫描）通过将回波记录为亮度变化的点来产生二维图像。将换能器在体表移动，即可建立横截面图像。B 型扫描常用于监测胎儿发育，因为超声波非电离辐射，被认为是安全的。
Ultrasound cannot pass through bone or gas‑filled spaces, which limits its use in brain imaging or lungs. The resolution depends on wavelength: shorter wavelengths (higher frequencies) give finer detail but less penetration.
超声波无法穿透骨骼或充满气体的空间，这限制了它在脑部或肺部成像中的应用。分辨率取决于波长：波长越短（频率越高），细节越精细，但穿透力越弱。
6. Refraction and Acoustic Impedance | 折射与声阻抗
When ultrasound waves pass from one medium to another, they are partially reflected and partially transmitted at the boundary. The amount of reflection depends on the difference in acoustic impedance Z of the two media, where Z = ρ × c (ρ is density, c is speed of sound).
当超声波从一种介质进入另一种介质时，在边界处一部分被反射，一部分被透射。反射量取决于两种介质的声阻抗 Z 之差，其中 Z = ρ × c（ρ 为密度，c 为声速）。
ansmission into the body, a coupling gel is used between the transducer and the skin to eliminate air gaps (air has very low impedance, causing almost total reflection).
强度反射系数 α = (Z₂ − Z₁)² / (Z₂ + Z₁)²。为使超声波最大程度传入体内，在换能器和皮肤之间涂抹耦合凝胶，以消除空气间隙（空气的声阻抗极低，会导致几乎全反射）。
You do not need to memorise the formula for α at IGCSE, but you should know that a large impedance mismatch causes strong reflection, while a small mismatch allows more transmission. Coupling gel is a key experimental detail.
在 IGCSE 阶段你无需记住 α 的公式，但应知道：阻抗差异大会导致强反射，而差异小则允许更多的透射。耦合凝胶是一个关键的实验细节。
7. Doppler Effect in Ultrasound | 超声多普勒效应
The Doppler effect is the change in observed frequency when a wave source and observer move relative to each other. In medical ultrasound, it is used to measure blood flow velocity. Red blood cells reflect ultrasound; their motion causes a frequency shift of the echo.
多普勒效应是当波源与观察者相对运动时，所观测频率发生变化的现象。在医疗超声中，它被用于测量血流速度。红细胞反射超声波；它们的运动导致回波发生频移。
The Doppler shift equation for reflected ultrasound is Δf = (2 f v cos θ) / c, where f is the transmitted frequency, v is the blood velocity, θ is the angle between the beam and the flow, and c is the speed of sound in tissue. Even if the formula is not required, you should interpret that a larger frequency shift means faster flow.
反射超声的多普勒频移方程为 Δf = (2 f v cos θ) / c，其中 f 是发射频率，v 是血流速度，θ 是波束与血流方向的夹角，c 是组织中的声速。即使不要求记忆公式，你也应能解释：频移越大表示流速越快。
Δf ≈ (2 f v) / c (when θ = 0°)
Doppler ultrasound is widely used to detect narrowed arteries, heart valve problems, and foetal heartbeats. Colour Doppler adds colour to B‑scan images to indicate direction and speed of flow.
超声多普勒广泛用于检测动脉狭窄、心脏瓣膜问题以及胎儿心跳。彩色多普勒在 B 型扫描图像上添加色彩，以指示血流方向和速度。
8. Radioactive Isotopes in Medicine: Tracers | 医用放射性同位素：示踪剂
Radioactive tracers are isotopes that emit gamma radiation and are introduced into the body (by injection or ingestion) to investigate internal organs. The gamma rays are detected outside the body using a gamma camera, and the distribution of the tracer reveals organ function.
放射性示踪剂是释放 γ 射线的同位素，通过注射或吞服引入体内，以检查内部器官。γ 射线在体外用 γ 照相机检测，示踪剂的分布可揭示器官功能。
Technetium‑99m (⁹⁹ᵐTc) is the most commonly used tracer because it has a short half‑life of 6 hours, emits gamma rays (easily detected and less ionising than alpha or beta), and can be easily combined into various chemical compounds that target specific organs (e.g., bone, thyroid, kidneys).
锝-99m (⁹⁹ᵐTc) 是最常用的示踪剂，因为它半衰期短（6 小时），释放 γ 射线（易于探测且比 α 或 β 射线电离能力弱），并且易于结合到各种针对特定器官（如骨骼、甲状腺、肾脏）的化学化合物中。
The ideal tracer properties are: short half‑life (to minimise patient dose but long enough for measurement), pure gamma emitter (alpha and beta would be absorbed by the body without useful detection), and chemical compatibility with the organ being studied.
理想的示踪剂性质包括：短半衰期（以减少患者剂量，但要足够长以完成测量），纯 γ 发射体（α 和 β 射线会被身体吸收而无法有效探测），以及与所研究器官的化学相容性。
9. PET Scans | 正电子发射断层扫描
PET (Positron Emission Tomography) uses a tracer that emits positrons (β⁺ particles). The most common is fluorodeoxyglucose (FDG) tagged with fluorine‑18. The emitted positron annihilates with an electron in the body, producing two identical gamma photons that travel in opposite directions (each of 511 keV).
PET（正电子发射断层扫描）使用的是发射正电子（β⁺ 粒子）的示踪剂。最常见的是用氟‑18 标记的氟代脱氧葡萄糖 (FDG)。发射出的正电子与体内的一个电子湮灭，产生两个完全相同、沿相反方向运动的 γ 光子（每个能量为 511 keV）。
Detectors arranged in a ring around the patient detect both photons simultaneously (coincidence). These signals allow the computer to build a 3D image showing areas of high metabolic activity, such as cancer tumours, because they consume more glucose.
环绕患者排列成环形的探测器同时检测这两个光子（符合探测）。这些信号使计算机能够构建三维图像，显示高代谢活动区域，如癌症肿瘤，因为它们消耗更多葡萄糖。
PET scans are often combined with CT (PET‑CT) to provide both functional and anatomical detail. The main disadvantage is the high cost and the need for a cyclotron to produce the short‑lived isotopes.
PET 扫描常与 CT 结合（PET‑CT），以同时提供功能和解剖细节。主要缺点是成本高昂，且需要回旋加速器来生产短寿命同位素。
10. Radiotherapy: Treating Cancer | 放射治疗：治疗癌症
Radiotherapy uses ionising radiation to destroy cancer cells. The goal is to maximise dose to the tumour while minimising damage to surrounding healthy tissue. External beam radiotherapy uses a linear accelerator to direct high‑energy X‑rays (or gamma rays from cobalt‑60) at the tumour from multiple directions.
放射治疗利用电离辐射摧毁癌细胞。目标是最大化对肿瘤的剂量，同时最小化对周围健康组织的损伤。外照射放疗使用直线加速器，从多个方向将高能 X 射线（或钴‑60 的 γ 射线）射向肿瘤。
Brachytherapy involves placing a sealed radioactive source (e.g., iodine‑125 or iridium‑192) directly inside or very close to the tumour. This gives a high local dose while sparing distant tissues.
近距离放射治疗是将密封的放射源（如碘‑125 或铱‑192）直接置于肿瘤内部或极近处。这样可以实现高局部剂量，同时避免远隔组织受损。
Fractionation – dividing the total dose into many smaller treatments over weeks – allows healthy cells to repair between fractions, while cancer cells (poor at repair) accumulate damage. This is a crucial concept for exams.
分割治疗——将总剂量分成数周内的多次小剂量治疗——可使健康细胞在每次照射之间得到修复，而癌细胞（修复能力差）则累积损伤。这是考试的重要概念。
11. Radiation Dose and Safety | 辐射剂量与安全
Ionising radiation can damage DNA and cause cell death or mutations. In medical physics, radiation dose is measured in sieverts (Sv) or millisieverts (mSv). Typical doses: chest X‑ray ~0.1 mSv, CT head ~2 mSv, whole body CT ~10 mSv. Background radiation is about 2–3 mSv per year.
电离辐射会损伤 DNA，导致细胞死亡或突变。在医疗物理中，辐射剂量以希沃特 (Sv) 或毫希沃特 (mSv) 计量。典型剂量：胸部 X 射线约 0.1 mSv，头部 CT 约 2 mSv，全身 CT 约 10 mSv。背景辐射约为每年 2–3 mSv。
The ALARA principle (As Low As Reasonably Achievable) is the guiding safety philosophy. For staff, protection involves time (minimise exposure time), distance (maximise distance from source, following inverse square law), and shielding (lead aprons, lead‑lined walls, lead glass).
ALARA 原则（合理可行尽量低）是指导性的安全理念。对医护人员而言，防护包括：时间（尽量减少暴露时间）、距离（与放射源保持最大距离，遵循平方反比定律）以及屏蔽（铅围裙、铅衬墙、铅玻璃）。
Patients receive a benefit‑risk assessment before any exposure. Pregnant women are not given abdominal X‑rays unless absolutely necessary, as the foetus is especially sensitive to radiation.
患者在接受任何辐射暴露前都应进行获益‑风险评估。除非绝对必要，否则孕妇不做腹部 X 射线检查，因为胎儿对辐射特别敏感。
12. Comparing Imaging Techniques | 成像技术对比
Exam questions often ask you to compare X‑rays, ultrasound, CT, and MRI (though MRI is not always in the IGCSE WJEC core). Based on the WJEC specification, focus on X‑rays, CT, ultrasound, and nuclear medicine.
试题常要求比较 X 射线、超声波、CT 和 MRI（尽管 MRI 并非总在 WJEC IGCSE 核心中）。根据 WJEC 考纲，应重点关注 X 射线、CT、超声波和核医学。
| Technique | Wave/Radiation | Image | Ionising? | Key Use |
|---|---|---|---|---|
| X‑ray | X‑rays (EM) | 2D shadow | Yes | Bone fractures, chest |
| CT | X‑rays | 3D slices | Yes (higher dose) | Brain, abdomen, trauma |
| Ultrasound | Sound (non‑EM) | 2D real‑time | No | Foetal, soft tissue |
| Gamma camera | Gamma rays | Functional map | Yes | Organ function, tumours |
Understanding the underlying physics (wave type, interaction with matter, resolution, safety) allows you to justify the choice of technique for a given clinical scenario. Practice linking properties to specific medical applications.
理解背后的物理原理（波的类型、与物质的相互作用、分辨率、安全性），你就能为给定的临床情境选择合适的技术并说明理由。练习将性质与具体的医学应用联系起来。
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