📚 A-Level Physics: Medical Physics Key Concepts Review | A-Level物理：医疗物理考点精讲
Medical physics applies the principles of physics to diagnose and treat diseases. For A-Level Physics, understanding the core imaging techniques—X‑rays, ultrasound, CT, PET, MRI, and endoscopy—is essential. This article breaks down each modality, covering production, interaction with matter, image formation, and clinical applications.
医疗物理将物理学原理应用于疾病诊断和治疗。对A-Level物理而言，掌握X射线、超声波、CT、PET、MRI及内窥镜等核心成像技术至关重要。本文逐一剖析各成像方式，涵盖产生机制、与物质相互作用、成像原理及临床应用。
1. X-ray Production and Spectra | X射线的产生与谱
X-rays are produced when high-speed electrons are decelerated upon striking a metal target (usually tungsten). Electrons are emitted from a heated filament (cathode) via thermionic emission and accelerated through a high potential difference of 20–150 kV towards a rotating anode.
高速电子撞击金属靶（通常为钨）减速时产生X射线。电子通过热电子发射从加热灯丝（阴极）逸出，经20–150 kV的高压加速，飞向旋转阳极。
Two main processes contribute to the X-ray spectrum: bremsstrahlung (braking radiation) gives a continuous spectrum as electrons are decelerated by the nuclei of the target atoms; characteristic radiation produces sharp peaks when incident electrons eject inner‑shell electrons and outer electrons cascade down, emitting photons of specific energies.
X射线谱的贡献主要来自两个过程：轫致辐射 (bremsstrahlung) 产生连续谱，因电子被靶原子核减速；特征辐射产生尖锐峰，当入射电子击出内层电子、外层电子跃迁回落时，发射特定能量的光子。
Minimum wavelength: λmin = hc / eV
最短波长：λmin = hc / eV
The cut‑off wavelength depends only on the accelerating voltage V; increasing the tube current increases intensity of all wavelengths but does not change λmin.
截止波长仅取决于加速电压V；增加管电流可提高所有波长的强度，但不改变λmin。
2. X-ray Attenuation and Half‑Value Thickness | X射线衰减与半值层
As a beam of X‑rays passes through matter, its intensity I decreases exponentially with thickness x: I = I0 e–μx, where μ is the linear attenuation coefficient, dependent on photon energy and material.
X射线束穿过物质时，其强度I随厚度x呈指数衰减：I = I0 e–μx，其中μ是线性衰减系数，取决于光子能量和材料。
The half‑value thickness (HVT) or half‑value layer is the thickness required to reduce the intensity by half: x½ = ln 2 / μ. This concept is crucial for designing shielding and for understanding contrast in imaging.
半值层 (HVT) 是将强度减弱一半所需的厚度：x½ = ln 2 / μ。这一概念对设计屏蔽和理解成像对比度至关重要。
Mass attenuation coefficient μ/ρ removes density dependence, enabling comparison across materials. Attenuation is primarily due to photoelectric absorption (dominant at low energies) and Compton scattering at diagnostic energies.
质量衰减系数 μ/ρ 消除了密度依赖性，便于不同材料间的比较。衰减主要来源于光电吸收（低能时占主导）和康普顿散射（诊断能量范围内）。
3. X-ray Imaging and CT Scans | X射线成像与CT扫描
In conventional radiography, X‑rays passing through the body are detected by a flat‑panel detector or a scintillator coupled with a CCD. An image intensifier can be used to convert X‑rays to visible light, amplify brightness, and reduce patient dose.
常规X射线摄影中，穿透人体的X射线由平板探测器或闪烁体耦合CCD检测。图像增强器可将X射线转换为可见光，放大亮度，降低患者辐射剂量。
Contrast media such as barium sulfate or iodine compounds improve visibility of soft tissues. Digital subtraction angiography subtracts a pre‑contrast image from post‑contrast images to highlight blood vessels.
硫酸钡或碘化合物等造影剂能提高软组织可见度。数字减影血管造影通过扣除注入对照前的影像突出血管。
Computed tomography (CT) produces cross‑sectional images. A thin fan beam of X‑rays rotates around the patient; detectors measure transmitted intensity at many angles. A computer reconstructs a 2D slice, assigning each voxel an attenuation coefficient expressed in Hounsfield units.
计算机断层扫描 (CT) 生成横截面图像。一束薄扇形X射线围绕患者旋转，探测器测量多个角度的透射强度。计算机重建二维切片，为每个体系赋以一个用亨氏单位表示的衰减系数。
Compared to conventional X‑rays, CT offers superior contrast resolution and eliminates overlapping structures, but delivers a higher radiation dose.
与传统X射线相比，CT对比度分辨率更优，且消除了结构重叠，但辐射剂量更高。
4. Ultrasound Basics and Piezoelectric Effect | 超声波基础与压电效应
Ultrasound refers to sound waves with frequencies above 20 kHz. In medical imaging, frequencies of 1–15 MHz are generated using the piezoelectric effect. A piezoelectric crystal (e.g., lead zirconate titanate) deforms when a potential difference is applied, producing pressure waves.
超声波指频率高于20 kHz的声波。医学成像使用1–15 MHz频率，通过压电效应产生。压电晶体（如锆钛酸铅）在施加电压时发生形变，产生压力波。
The same crystal acts as a receiver: returning echoes compress the crystal, generating an electrical signal. The transducer emits short pulses of ultrasound and listens for reflections from tissue interfaces.
同一晶体还用作接收器：返回的回波压缩晶体，产生电信号。换能器发射短脉冲超声波，并接收来自组织界面的反射。
Imaging modes include A‑scan (amplitude‑modulated, one‑dimensional depth profile) and B‑scan (brightness‑modulated, producing a 2D cross‑sectional image by combining many A‑scans). Real‑time B‑scanners provide moving images.
成像模式包括A型扫描（幅度调制，一维深度图谱）和B型扫描（亮度调制，组合多个A扫描生成二维截面图像）。实时B型扫描仪提供动态影像。
5. Acoustic Impedance and Ultrasound Scanning | 声阻抗与超声扫描
Acoustic impedance Z of a medium is given by Z = ρc, where ρ is density and c is speed of sound. When ultrasound encounters a boundary between two media with impedances Z1 and Z2, some energy is reflected.
介质的声阻抗 Z = ρc，ρ为密度，c为声速。当超声波遇到声阻抗分别为Z1与Z2的两种介质界面时，部分能量被反射。
Reflection coefficient for intensity: R = (Z2 − Z1)2 / (Z2 + Z1)2
强度反射系数：R = (Z2 − Z1)2 / (Z2 + Z1)2
To minimize reflection at the transducer‑skin interface, a coupling gel is used, with impedance close to that of soft tissue. Most modern systems utilise phased array transducers to steer and focus the beam electronically.
为减小换能器–皮肤界面的反射，需使用阻抗接近软组织的耦合凝胶。多数现代系统采用相控阵换能器，通过电子方式控制波束偏转与聚焦。
Ultrasound is non‑ionising, safe for fetal imaging, and gives real‑time information, but resolution is limited by wavelength and penetration depth is restricted at high frequencies.
超声波无电离，对胎儿成像安全，且提供实时信息，但分辨率受波长限制，高频时穿透深度有限。
6. PET Scanning Principles | PET扫描原理
Positron Emission Tomography (PET) relies on a radiotracer labelled with a positron‑emitting isotope, most commonly fluorine‑18 (FDG). The tracer accumulates in metabolically active tissues.
正电子发射断层扫描 (PET) 依赖标记有正电子发射同位素的放射性示踪剂，最常用氟‑18 (FDG)。示踪剂积聚在代谢活跃的组织中。
When a positron is emitted, it travels a short distance before annihilating with an electron, producing two 511 keV gamma photons travelling in opposite directions (conserving momentum).
正电子发射后行进极短距离即与电子湮灭，产生两个511 keV伽马光子，方向相反（动量守恒）。
A ring of detectors registers coincident events: if two photons arrive within a narrow time window, a line of response is defined. Tomographic reconstruction yields a 3D map of tracer concentration, highlighting cancerous or inflamed regions.
环形探测器记录符合事件：若两光子在一狭小时间窗内到达，则确定一条响应线。通过断层重建得到示踪剂浓度的三维分布，突出癌变或炎症区域。
PET is often combined with CT (PET‑CT) to provide both metabolic and anatomical information, improving diagnostic accuracy.
PET常与CT联合（PET‑CT），同时提供代谢与解剖信息，提高诊断准确性。
7. MRI Physics | MRI物理原理
Magnetic Resonance Imaging exploits the nuclear spin of hydrogen protons. In an external strong magnetic field B₀, protons precess around the field direction at the Larmor frequency: f = γ B₀ / (2π), where γ is the gyromagnetic ratio.
磁共振成像利用氢质子的核自旋。在外加强磁场B₀中，质子绕磁场方向进动，频率为拉莫尔频率：f = γ B₀ / (2π)，γ为旋磁比。
A radiofrequency (RF) pulse at the Larmor frequency tips the net magnetisation into the transverse plane. After the pulse, protons relax back to equilibrium, emitting RF signals that are detected by receiver coils.
频率等于拉莫尔频率的射频脉冲将净磁化矢量翻转到横向平面。脉冲结束后，质子弛豫恢复平衡，发射射频信号，由接收线圈检测。
Two relaxation times are key: T1 (spin‑lattice, longitudinal recovery) and T2 (spin‑spin, transverse decay). Differences in T1 and T2 among tissues generate image contrast. Gradient coils spatially encode the signals to build detailed tomographic images.
两个关键的弛豫时间：T1（自旋‑晶格，纵向恢复）和T2（自旋‑自旋，横向衰减）。组织间T1和T2的差异形成图像对比。梯度线圈对信号进行空间编码，构建精细断层图像。
MRI gives exceptional soft‑tissue contrast without ionising radiation, but it is expensive, time‑consuming, and cannot be used with patients who have certain metallic implants.
MRI具有卓越的软组织对比度，无电离辐射，但成本高、时间长，且不适用于某些带有金属植入物的患者。
8. Endoscopy and Optical Fibers | 内窥镜与光纤
Endoscopes use bundles of optical fibres to transmit light into the body and return an image. Each fibre consists of a high‑refractive‑index core surrounded by a lower‑index cladding, exploiting total internal reflection.
内窥镜利用光纤束将光传入体内并传回图像。每根光纤由高折射率纤芯和低折射率包层构成，基于全内反射原理工作。
Total internal reflection occurs when the angle of incidence at the core‑cladding interface exceeds the critical angle, allowing light to be guided with minimal loss. Coherent bundles preserve the relative positions of fibres, enabling pixel‑by‑pixel image transmission.
当纤芯‑包层界面的入射角超过临界角时发生全内反射，使得光几乎无损耗地在光纤中传导。相干光纤束保持纤维相对位置，实现逐像素传输图像。
Incoherent bundles are used simply for illumination. Endoscopes may also incorporate instrument channels for biopsy or surgery, and often attach a CCD camera for display.
非相干光纤束仅用于照明。内窥镜还可能包含器械通道用于活检或手术，并常连接CCD摄像头显示图像。
9. Comparison of Imaging Modalities | 成像方式比较
The table below summarises the key features, advantages, and disadvantages of the main medical imaging techniques studied at A‑level.
下表总结了A-Level课程中主要医学成像技术的关键特点、优势与不足。
| Modality | Physical principle | Ionising? | Main strengths | Limitations |
|---|---|---|---|---|
| X‑ray / CT | X‑ray attenuation; computed reconstruction | Yes | High spatial resolution, bone detail, fast | Radiation dose, poor soft‑tissue contrast without contrast media |
| Ultrasound | Reflection at impedance boundaries | No | Real‑time, safe, portable, good for soft tissues | Operator‑dependent, limited penetration, poor through bone/air |
| MRI | Nuclear magnetic resonance, proton relaxation | No | Excellent soft‑tissue contrast, no radiation, multiplanar | Expensive, slow, claustrophobia, contraindicated with metal |
| PET | Positron annihilation, coincidence detection | Yes (internal radionuclide) | Metabolic information, detects cancer spread | Radiation exposure, costly, lower spatial resolution |
| Endoscopy | Total internal reflection in fibres | No (visible light) | Direct visualisation, biopsy capability, minimally invasive | Invasive, limited to accessible cavities, risk of perforation |
Understanding the underlying physics allows clinicians to select the most appropriate technique for each clinical scenario, balancing diagnostic power against safety and cost.
理解背后的物理原理，临床医生才能为每种临床场景选择最合适的成像技术，在诊断效能、安全与成本间取得平衡。
Published by TutorHao | Physics Revision Series | aleveler.com
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