A-Level WJEC Physics: Medical Physics Revision | A-Level WJEC 物理：医疗物理考点精讲

📚 A-Level WJEC Physics: Medical Physics Revision | A-Level 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 A-Level specification, this topic covers imaging techniques such as X-rays, ultrasound, and endoscopy, as well as nuclear medicine and radiotherapy. A sound understanding of wave behaviour, ionising radiation, and atomic structure is essential for mastering these concepts.

医疗物理将物理学原理应用于疾病的诊断和治疗。在 WJEC A-Level 课程中，该主题涵盖 X 射线、超声波、内窥镜等成像技术，以及核医学和放射治疗。扎实理解波的行为、电离辐射和原子结构对于掌握这些概念至关重要。

1. Production of X-rays | X 射线的产生

X-rays are produced when high-speed electrons collide with a metal target, typically tungsten. In an X-ray tube, a heated filament emits electrons via thermionic emission. These electrons are accelerated through a high potential difference (typically 50-150 kV) and strike the rotating anode, where their kinetic energy is converted into X-ray photons and heat.

高速电子撞击金属靶（通常是钨）时会产生 X 射线。在 X 射线管中，加热灯丝通过热电子发射释放电子。这些电子在高电势差（通常 50-150 kV）下加速，撞击旋转阳极，其动能转化为 X 射线光子和热量。

The X-ray spectrum consists of a continuous bremsstrahlung (braking radiation) background and characteristic line peaks. The minimum wavelength λmin depends on the accelerating voltage V: λmin = hc / eV. The intensity of X-rays can be controlled by adjusting the tube current (mA) and exposure time, while the penetrating power (beam quality) is determined by the kVp.

X 射线谱包含连续的轫致辐射背景和特征线峰。最短波长 λmin 取决于加速电压 V：λmin = hc / eV。X 射线的强度可通过调节管电流（mA）和曝光时间来控制，而穿透能力（射束质量）则由 kVp 决定。

The efficiency of X-ray production is low, about 1%, with most energy lost as heat. This is managed by using a rotating anode and cooling systems. Filtration of the beam removes low-energy photons that would increase patient dose without contributing to the image.

X 射线产生效率很低，约 1%，大部分能量以热的形式散失。这通过使用旋转阳极和冷却系统来管理。射束过滤可去除低能光子，这些光子只会增加患者剂量而对成像无贡献。

2. X-ray Interaction and Attenuation | X 射线的相互作用与衰减

When X-rays pass through matter, they are attenuated by photoelectric absorption and Compton scattering. The intensity I after passing through a thickness x of material is given by I = I₀ e⁻μx, where μ is the linear attenuation coefficient. The half-value thickness (HVT) is the thickness required to reduce intensity by half: HVT = ln2 / μ.

X 射线穿过物质时，通过光电吸收和康普顿散射而衰减。穿过厚度为 x 的材料后的强度 I 由 I = I₀ e⁻μx 给出，其中 μ 为线性衰减系数。半值厚度（HVT）是将强度减半所需的厚度：HVT = ln2 / μ。

Photoelectric absorption dominates at lower photon energies and depends strongly on atomic number Z (∝ Z³). This is why bone (containing calcium) absorbs much more than soft tissue, providing excellent contrast in radiographic images. Compton scattering dominates at higher energies and is independent of Z, reducing image quality by creating background fog.

光电吸收在较低光子能量下占主导地位，并与原子序数 Z 密切相态（∝ Z³）。这就是为什么骨骼（含钙）的吸收远多于软组织，在放射图像中提供出色的对比度。康普顿散射在较高能量下占主导地位，与 Z 无关，通过产生背景灰雾降低图像质量。

In medical imaging, contrast can be improved by lowering kVp to emphasise photoelectric effect differences, but this increases patient dose. Alternatively, contrast media (e.g., barium or iodine) with high Z can be introduced to enhance visibility of soft tissues.

在医疗成像中，降低 kVp 可突出光电效应差异以增强对比度，但这会增加患者剂量。或者，可引入高 Z 的造影剂（如钡或碘）来增强软组织的可见性。

3. X-ray Imaging and Safety | X 射线成像与安全

Radiography uses a point source of X-rays and a detector (film, digital sensor, or image intensifier) to form a two-dimensional shadow image. The sharpness of the image is limited by the source size and beam divergence; a smaller focal spot and increased source-to-detector distance improve resolution. Scattered radiation can be reduced by a grid between the patient and detector.

放射摄影使用 X 射线点源和探测器（胶片、数字传感器或图像增强器）形成二维阴影图像。图像的清晰度受源尺寸和射束发散的限制；较小的焦点和增大的源到探测器距离可提高分辨率。患者与探测器之间的滤线栅可减少散射辐射。

Patient safety follows the ALARA principle (As Low As Reasonably Achievable). Dose is measured in sieverts (Sv) but for diagnostic X-rays, effective dose is typically in mSv. Factors reducing dose include proper beam filtration, collimation to the area of interest, shielding of radiosensitive organs, and minimising repeat exposures. The risk-to-benefit ratio must always be justified.

患者安全遵循 ALARA 原则（合理可达的尽可能低）。剂量以西弗特（Sv）衡量，但对于诊断 X 射线，有效剂量通常以 mSv 计。降低剂量的因素包括适当的射束过滤、准直到感兴趣区域、屏蔽辐射敏感器官以及尽量减少重复曝光。风险与收益比必须始终经得起论证。

4. Ultrasound Principles and Transducers | 超声原理与换能器

Ultrasound uses sound waves with frequencies above 20 kHz, typically 1-15 MHz for medical diagnosis. The waves are generated and detected by a piezoelectric transducer, which converts electrical pulses into mechanical vibrations and vice versa. The transducer is made of a piezoelectric crystal such as lead zirconate titanate (PZT).

超声使用频率高于 20 kHz 的声波，医学诊断通常为 1-15 MHz。这些波由压电换能器产生和检测，换能器将电脉冲转换为机械振动，反之亦然。换能器由压电晶体制成，例如锆钛酸铅（PZT）。

The resolution of an ultrasound image depends on the wavelength: axial resolution (along the beam) is approximately half the pulse length, and lateral resolution is limited by beam width. Higher frequencies give better resolution but poorer penetration due to attenuation. Attenuation in tissue is mainly due to absorption and scattering, with the attenuation coefficient approximately proportional to frequency.

超声图像的分辨率取决于波长：轴向分辨率（沿射束方向）约为脉冲长度的一半，横向分辨率受射束宽度限制。更高的频率给出更好的分辨率，但由于衰减增加，穿透力变差。组织中的衰减主要由于吸收和散射，衰减系数约与频率成正比。

5. Ultrasound Imaging Modes | 超声成像模式

A-mode (amplitude mode) displays the amplitude of the returning echo as a function of time, used primarily for distance measurement. B-mode (brightness mode) converts echo amplitudes into grey-scale dots, producing a two-dimensional cross-sectional image. Modern systems use real-time B-mode, refreshing the image many times per second to show motion.

A 模式（幅度模式）将返回回波的幅度显示为时间的函数，主要用于距离测量。B 模式（亮度模式）将回波幅度转换为灰度点，产生二维截面图像。现代系统使用实时 B 模式，每秒多次刷新图像以显示运动。

M-mode (motion mode) is used to study moving structures like heart valves, displaying a B-mode line over time. Doppler ultrasound shifts in frequency occur when sound is reflected from moving red blood cells. The frequency shift Δf is given by Δf = (2f₀ v cosθ) / c, where v is blood velocity, f₀ the transmitted frequency, c the speed of sound, and θ the angle between the beam and flow.

M 模式（运动模式）用于研究心脏瓣膜等运动结构，随时间显示一条 B 模式线。多普勒超声中，当声音从运动的红细胞反射时会发生频率偏移。频率偏移 Δf 由 Δf = (2f₀ v cosθ) / c 给出，其中 v 为血流速度，f₀ 为发射频率，c 为声速，θ 为射束与血流方向的夹角。

6. Fibre Optics and Endoscopy | 光纤与内窥镜

An endoscope uses bundles of optical fibres to illuminate internal cavities and transmit an image to the eyepiece or camera. Total internal reflection confines light within the core of each fibre, provided the angle of incidence exceeds the critical angle. The critical angle is given by sin θc = n₂/n₁, where n₁ is the core refractive index and n₂ the cladding index.

内窥镜使用光纤束照亮内部腔体并将图像传输到目镜或相机。只要入射角超过临界角，全内反射就会将光限制在每根光纤的纤芯内。临界角由 sin θc = n₂/n₁ 给出，其中 n₁ 为纤芯折射率，n₂ 为包层折射率。

Coherent bundles are used for imaging; each fibre corresponds to one pixel, and the relative positions must be maintained. Incoherent bundles are used for illumination only. For medical applications, the fibres must be flexible, biocompatible, and sterilizable. Endoscopes may also incorporate channels for instruments, fluids, and air.

相干光纤束用于成像；每根光纤对应一个像素，相对位置必须保持。非相干光纤束仅用于照明。在医疗应用中，光纤必须柔韧、生物相容且可消毒。内窥镜还可包含用于器械、液体和空气的通道。

7. Radioactive Tracers and Gamma Camera | 放射性示踪剂与伽马相机

Nuclear medicine uses radiopharmaceuticals that emit gamma rays to image organ function. The most commonly used radionuclide is technetium-99m (Tc-99m), which has a half-life of 6 hours and emits gamma photons of 140 keV, ideal for detection by a gamma camera. Tc-99m is produced in a molybdenum-technetium generator and can be attached to various biological compounds to target specific organs.

核医学使用发射伽马射线的放射性药物对器官功能进行成像。最常用的放射性核素是锝-99m (Tc-99m)，其半衰期为 6 小时，发射 140 keV 的伽马光子，非常适合伽马相机检测。Tc-99m 在钼-锝发生器中产生，并可附着于各种生物化合物以靶向特定器官。

A gamma camera consists of a collimator (usually parallel-hole type) to ensure only photons travelling perpendicular to the detector are accepted, a scintillation crystal (sodium iodide with thallium doping) that converts gamma photons into visible light, an array of photomultiplier tubes (PMTs) that amplify the light and determine the position of the scintillation by centroid calculation, and electronics to construct the image.

伽马相机由准直器（通常为平行孔型）确保只有垂直于探测器行进的光子被接收，闪烁晶体（铊掺杂的碘化钠）将伽马光子转换为可见光，光电倍增管（PMT）阵列放大光并通过重心计算确定闪烁位置，以及构建图像的电子电路组成。

8. Positron Emission Tomography (PET) | 正电子发射断层扫描 (PET)

PET imaging uses positron-emitting radionuclides such as fluorine-18 (¹⁸F), typically incorporated into fluorodeoxyglucose (FDG), a glucose analogue. After a positron is emitted, it annihilates with an electron within about 1 mm, producing two 511 keV gamma photons travelling in opposite directions. Coincidence detection of these two photons allows reconstruction of the emission point along the line of response (LOR).

PET 成像使用正电子发射放射性核素，如氟-18 (¹⁸F)，通常结合到氟代脱氧葡萄糖 (FDG)（一种葡萄糖类似物）中。正电子发射后，与电子在约 1 mm 内湮灭，产生两个沿相反方向飞行的 511 keV 伽马光子。对这两个光子进行符合探测，可沿响应线 (LOR) 重建发射点。

The spatial resolution of PET is limited by positron range and the non-collinearity of the annihilation photons. Attenuation correction is essential and often performed using a CT scan combined with PET in a PET/CT scanner. The standardised uptake value (SUV) quantifies tracer uptake and aids in distinguishing malignant from benign lesions.

PET 的空间分辨率受正电子射程和湮灭光子的非共线性的限制。衰减校正是必不可少的，通常使用与 PET 结合的 CT 扫描在 PET/CT 扫描仪中进行。标准化摄取值 (SUV) 量化示踪剂摄取，帮助区分恶性和良性病变。

9. Radiation Therapy | 放射治疗

Radiotherapy uses ionising radiation to destroy cancer cells by damaging their DNA. External beam radiotherapy employs a linear accelerator (linac) to produce high-energy X-rays (4-25 MV) or electron beams. Conformal techniques such as intensity-modulated radiotherapy (IMRT) shape the dose to the tumour while sparing surrounding healthy tissue.

放射治疗使用电离辐射通过损伤 DNA 来破坏癌细胞。外照射放疗使用直线加速器（linac）产生高能 X 射线（4-25 MV）或电子束。适形技术，如调强放疗 (IMRT)，可使剂量塑形以适应肿瘤，同时避开周围健康组织。

Brachytherapy involves placing sealed radioactive sources directly into or near the tumour, delivering a high dose locally with minimal damage to surrounding tissues. The biological effectiveness of radiation depends on dose, fractionation, tumour type, and the presence of oxygen (oxygen enhancement ratio). The linear energy transfer (LET) and relative biological effectiveness (RBE) also play crucial roles.

近距离治疗涉及将密封放射源直接置入或靠近肿瘤，局部施以高剂量，对周围组织的损伤最小。辐射的生物有效性取决于剂量、分次照射、肿瘤类型和氧的存在（氧增强比）。线性能量转移 (LET) 和相对生物有效性 (RBE) 也起着关键作用。

10. Safety and Risk in Medical Physics | 医疗物理中的安全与风险

All uses of ionising radiation carry a stochastic risk (cancer induction, genetic effects) and deterministic effects (at high doses, e.g., skin burns, cataract). The effective dose accounts for different tissue sensitivities using tissue weighting factors. Pregnant patients require special consideration, with foetal dose limits as low as 1 mSv during the entire pregnancy.

任何电离辐射的使用都伴随随机性风险（诱发癌症、遗传效应）和确定性效应（高剂量时，如皮肤灼伤、白内障）。有效剂量使用组织权重因子考虑不同组织的敏感性。怀孕患者需特殊考虑，整个孕期内胎儿剂量限值低至 1 mSv。

Non-ionising imaging methods (ultrasound, endoscopy) are generally safer but still require careful application: ultrasound can cause heating and cavitation at high intensities, and endoscopy carries infection and perforation risks. Quality assurance programmes in hospitals ensure equipment performance and dose optimisation. Regulatory bodies enforce exposure limits for radiation workers and the public.

非电离成像方法（超声、内窥镜）通常更安全，但仍需小心应用：高强度超声可导致加热和空化效应，内窥镜有感染和穿孔风险。医院的质量保证计划确保设备性能和剂量优化。监管机构执行对放射工作人员和公众的照射限值。

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A-Level WJEC Physics: Medical Physics Revision | A-Level WJEC 物理：医疗物理 考点精讲