📚 Medical Physics Essentials for A-Level CIE | A-Level CIE 物理：医疗物理 考点精讲
Medical physics brings together core principles of waves, electromagnetism, radioactivity and materials to diagnose and treat disease. In the CIE A‑Level syllabus, this topic demands a confident grasp of how X‑rays, ultrasound, nuclear medicine and MRI work, as well as the physics behind image formation, attenuation and safety. This article systematically unpacks each required concept so that you can tackle structured questions and longer written answers with precision.
医疗物理将波、电磁学、放射性和材料等核心原理结合起来，用于疾病的诊断和治疗。在 CIE A‑Level 大纲中，这一主题要求你扎实掌握 X 射线、超声波、核医学和磁共振成像的工作原理，以及图像形成、衰减和安全背后的物理学原理。本文系统地梳理了每个必备概念，帮助你精准应对结构题和长篇书面作答。
1. Production of X‑rays | X 射线的产生
X‑rays are produced when fast‑moving electrons are suddenly decelerated upon striking a metal target. In an X‑ray tube, a heated filament emits electrons via thermionic emission. A high potential difference (typically 30–150 kV) accelerates these electrons toward a rotating tungsten anode. When the electrons hit the target, most of their kinetic energy is converted into heat, but a small fraction produces X‑rays via two mechanisms: Bremsstrahlung (braking radiation) and characteristic radiation.
X 射线是快速运动的电子撞击金属靶时突然减速而产生的。在 X 射线管中，加热的灯丝通过热电子发射释放电子。高电势差（通常 30–150 kV）将这些电子加速飞向旋转钨阳极。当电子击中靶时，其大部分动能转化为热量，但一小部分通过两种机制产生 X 射线：轫致辐射和特征辐射。
Bremsstrahlung occurs when an electron is deflected by the Coulomb field of a tungsten nucleus, losing kinetic energy. The lost energy is emitted as an X‑ray photon of energy E = hf, where f can take a continuous range of values up to a maximum fmax determined by the accelerating voltage V: hfmax = eV. This gives the short‑wavelength cut‑off of the X‑ray spectrum: λmin = hc / eV.
轫致辐射发生在电子被钨原子核的库仑场偏转、损失动能之时。损失的能量以 X 射线光子形式释放，光子能量 E = hf，f 的取值范围连续，最大值 fmax 由加速电压 V 决定：hfmax = eV。由此得到 X 射线光谱的短波截止波长：λmin = hc / eV。
Characteristic radiation arises when an incident electron ejects a bound electron from an inner shell of a target atom. When an outer‑shell electron falls to fill the vacancy, a photon is emitted with energy equal to the difference between the two energy levels. Because this energy difference is fixed for a given element, characteristic X‑rays form sharp peaks superimposed on the continuous Bremsstrahlung spectrum.
特征辐射发生在入射电子将靶原子内壳层的一个束缚电子击出时。当外壳层电子跃迁填补空位时，会发射一个能量等于两个能级差的光子。由于这一能量差对于给定元素是固定的，特征 X 射线在连续轫致辐射谱上叠加形成尖锐的峰。
2. X‑ray Spectra and Factors Affecting Intensity | X 射线光谱及影响强度的因素
A typical X‑ray spectrum (intensity versus photon energy or wavelength) shows a broad continuous curve with sharp characteristic peaks. Changing the tube voltage V shifts the entire spectrum to higher maximum photon energies (hfmax = eV) and increases the overall intensity. The intensity is approximately proportional to V2 and to the tube current I, which is controlled by the filament temperature.
典型的 X 射线光谱（强度随光子能量或波长变化）显示一条宽阔的连续曲线，上面叠加有尖锐的特征峰。改变管电压 V 会将整个光谱推向更高的最大光子能量（hfmax = eV），并增加总强度。强度近似与 V2 和管电流 I 成正比，而管电流由灯丝温度控制。
The area under the continuous spectrum represents the total X‑ray energy output. Hardness of the beam refers to its penetrating ability; increasing V produces harder (more penetrating) X‑rays. In clinical practice, filters (usually aluminium) are placed in the beam path to absorb low‑energy photons, which would otherwise increase patient dose without contributing to the image, thus hardening the beam.
连续谱下的面积代表 X 射线总能量输出。射束的硬度指其穿透能力；提高 V 会产生更硬（穿透性更强）的 X 射线。在临床实践中，束流路径中会放置滤线器（通常为铝），以吸收低能光子——这些光子只会增加患者剂量而不对成像做贡献——从而使射束变硬。
3. Attenuation of X‑rays | X 射线的衰减
As an X‑ray beam passes through matter, its intensity I decreases exponentially with thickness x: I = I₀ e–μx, where μ is the linear attenuation coefficient, which depends on photon energy and the material’s atomic number and density. The half‑value thickness (HVT) is the thickness required to reduce the intensity by half: HVT = ln 2 / μ.
当 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，取决于光子能量以及材料的原子序数和密度。半值层（HVT）是将强度减小一半所需的厚度：HVT = ln 2 / μ。
Attenuation occurs via the photoelectric effect, Compton scattering and pair production (above 1.02 MeV). In the diagnostic energy range (20–150 keV), the photoelectric effect dominates in materials of high atomic number like bone, making them appear white on a radiograph, while Compton scattering reduces image contrast. The differential attenuation between tissues is what creates contrast in X‑ray imaging.
衰减通过光电效应、康普顿散射和电子对产生（能量高于 1.02 MeV）发生。在诊断能量范围（20–150 keV）内，光电效应在骨骼等高原子序数材料中占主导地位，使它们在 X 光片上呈白色，而康普顿散射会降低图像对比度。组织间的差异衰减正是 X 射线成像对比度的来源。
4. Computed Tomography (CT) Scanning | 计算机断层扫描（CT）
CT scanning builds a three‑dimensional image from many X‑ray attenuation measurements taken at different angles. An X‑ray tube and a bank of detectors rotate around the patient, collecting data for multiple slices. A computer processes the attenuation values to reconstruct cross‑sectional images, displaying each small volume element (voxel) with a CT number (Hounsfield unit): CT number = (μtissue – μwater) / μwater × 1000.
CT 扫描通过从不同角度采集大量 X 射线衰减测量值来构建三维图像。X 射线管和一组探测器围绕患者旋转，收集多层数据。计算机处理衰减值以重建横截面图像，用 CT 值（亨氏单位）显示每个小体积元素（体素）：CT 值 = (μ组织 – μ水) / μ水 × 1000。
Compared to conventional radiography, CT provides superior contrast resolution and eliminates the superimposition of structures. However, the patient dose is significantly higher, and iodine‑based contrast agents may be injected to enhance visibility of blood vessels. Modern helical (spiral) CT acquires data continuously as the patient moves through the gantry, reducing scan time and radiation exposure while improving image quality.
与传统 X 光摄影相比，CT 具有更好的对比度分辨率，并消除了结构重叠。然而，患者剂量显著更高，并且可注射碘基造影剂以提高血管可见度。现代螺旋 CT 在患者穿过机架时连续采集数据，缩短了扫描时间和辐射暴露，同时提高了图像质量。
5. Ultrasound: Production and Detection | 超声波的产生与检测
Ultrasound refers to sound waves with frequencies above 20 kHz, typically 1–15 MHz in medical imaging. These longitudinal mechanical waves are generated and detected using a piezoelectric transducer. When an alternating voltage is applied across a piezoelectric crystal (e.g., lead zirconate titanate, PZT), it vibrates at the same frequency, sending short ultrasonic pulses into the body.
超声波指频率高于 20 kHz 的声波，医学成像中通常为 1–15 MHz。这些纵波通过压电换能器产生和检测。当交变电压施加在压电晶体（如锆钛酸铅，PZT）上时，它以相同频率振动，向体内发射短超声波脉冲。
When reflected echoes return, they cause the same crystal to vibrate, generating a voltage signal that is amplified and processed. The transducer acts as both transmitter and receiver. To maximise energy transfer into the body, an acoustic matching layer is placed on the crystal surface, and a gel eliminates air gaps between the probe and the skin.
当反射回波返回时，它们使同一晶体振动，产生一个电压信号，进而被放大和处理。换能器同时充当发射器和接收器。为了最大限度地提高能量向体内的传递，晶体表面放置有声学匹配层，并且使用耦合凝胶消除探头与皮肤之间的空气间隙。
6. Ultrasound in Medical Diagnostics: A‑scan and B‑scan | 超声波医学诊断：A 型扫描和 B 型扫描
An A‑scan (amplitude scan) displays a graph of echo amplitude against time. The time delay between the transmitted pulse and each returning echo gives the depth of a reflecting boundary: d = (c × t) / 2, where c ≈ 1540 m s⁻¹ in soft tissue. A‑scans are used in ophthalmology to measure eye‑length and to detect retinal detachment.
A 型扫描（振幅扫描）显示回波振幅随时间变化的曲线图。发射脉冲与每个返回回波之间的时间间隔给出反射界面的深度：d = (c × t) / 2，其中软组织中 c ≈ 1540 m s⁻¹。A 型扫描在眼科中用于测量眼轴长度和检测视网膜脱落。
A B‑scan (brightness scan) produces a two‑dimensional cross‑sectional image. The probe is swept across the skin, and many A‑scan lines are combined; the amplitude of each echo is represented as the brightness of a dot on the screen. B‑scans are widely used in obstetrics, cardiology and abdominal imaging, providing real‑time visualisation of soft tissues without ionising radiation.
B 型扫描（亮度扫描）生成二维横截面图像。探头在皮肤上扫查，将多条 A 型扫描线组合在一起；每个回波的振幅用屏幕上点的亮度表示。B 型扫描广泛用于产科、心脏病学和腹部成像，无需电离辐射即可实时显示软组织结构。
7. Doppler Ultrasound for Blood Flow | 多普勒超声用于血流检测
The Doppler effect is the change in observed frequency when a wave source and an observer move relative to each other. In medical ultrasound, a moving red blood cell reflects the incident ultrasound; the frequency shift Δf between the transmitted and received signal is given by Δf = 2f₀v cos θ / c, where v is the blood velocity, θ the angle between the ultrasound beam and the vessel, f₀ the transmitted frequency and c the speed of sound in blood.
多普勒效应是波源与观察者之间相对运动时观测频率发生改变的现象。在医学超声中，移动的红细胞反射入射超声波；发射信号与接收信号之间的频率偏移 Δf 由公式 Δf = 2f₀v cos θ / c 给出，其中 v 为血流速度，θ 为超声波束与血管的夹角，f₀ 为发射频率，c 为血液中的声速。
Continuous wave Doppler provides a simple velocity readout, while pulsed Doppler selects a specific sample volume to measure velocity at a known depth. Colour Doppler overlays a colour map onto the B‑scan image, with red typically indicating flow toward the probe and blue flow away. Doppler ultrasound is essential for assessing vascular disease, heart valve regurgitation and foetal circulation.
连续波多普勒提供简单的速度读数，而脉冲多普勒选择特定的取样区域，在已知深度处测量速度。彩色多普勒将彩色图叠加在 B 型扫描图像上，通常红色表示血流朝向探头，蓝色表示远离。多普勒超声对于评估血管疾病、心脏瓣膜反流和胎儿循环至关重要。
8. Nuclear Medicine: Tracers and the Gamma Camera | 核医学：示踪剂与伽马相机
Nuclear medicine uses radiopharmaceuticals—radioactive isotopes attached to biologically active molecules—that concentrate in specific organs or tissues. A technetium‑99m (⁹⁹ᵐTc) is the most common radionuclide because of its short half‑life (6 h), emission of 140 keV gamma photons and ability to label many compounds. The patient is injected with the tracer, and a gamma camera detects the emitted gamma rays to form an image.
核医学使用放射性药物——即将放射性同位素附着在生物活性分子上——这些药物会聚集在特定器官或组织中。锝‑99m (⁹⁹ᵐTc) 是最常用的放射性核素，因其半衰期短（6 小时）、发射 140 keV 伽马光子，且能标记多种化合物。患者被注射示踪剂后，伽马相机探测发射的伽马射线以形成图像。
The gamma camera consists of a collimator (typically a lead plate with many parallel holes) that selects gamma photons arriving perpendicularly, a large NaI scintillation crystal that converts gamma rays into visible light, an array of photomultiplier tubes that amplify the light signal, and pulse‑height analysis circuitry to reject scattered photons. The positions of detected events are used to construct a 2‑D projection image, providing functional information about organ perfusion or metabolism.
伽马相机由准直器（通常为带有多个平行孔的铅板，用于筛选垂直入射的伽马光子）、将伽马射线转化为可见光的大尺寸 NaI 闪烁晶体、放大光信号的光电倍增管阵列以及用于剔除散射光子的脉冲高度分析电路组成。探测事件的位置被用来构建二维投影图像，提供器官灌注或代谢的功能信息。
9. Positron Emission Tomography (PET) | 正电子发射断层扫描（PET）
PET uses radionuclides that decay by positron emission (β⁺ decay), e.g., fluorine‑18 incorporated into fluorodeoxyglucose (FDG). The emitted positron travels a short distance before annihilating with an electron, producing two 511 keV gamma photons that travel in opposite directions. These are detected simultaneously by a ring of detectors surrounding the patient, and only coincidence events are recorded, which gives PET its unique spatial accuracy.
PET 使用通过正电子发射（β⁺ 衰变）衰变的放射性核素，例如被掺入氟代脱氧葡萄糖（FDG）的氟‑18。发射的正电子在湮没于电子之前行进很短的距离，产生两个沿相反方向行进的 511 keV 伽马光子。这些光子同时被环绕患者的探测器环检测，并且仅记录符合事件，这赋予了 PET 独特的空间精度。
A computer reconstructs a 3‑D map of the tracer concentration, reflecting metabolic activity. PET is powerful in oncology because malignant tumours often exhibit high glucose uptake, appearing as ‘hot spots’. Combined PET‑CT scanners co‑register metabolic PET images with anatomical CT images, greatly improving diagnostic accuracy.
计算机重建出示踪剂浓度的三维图谱，反映代谢活动。PET 在肿瘤学中非常强大，因为恶性肿瘤往往表现出高葡萄糖摄取，显示为“热点”。PET‑CT 联合扫描仪将代谢性 PET 图像与解构性 CT 图像配准，极大地提高了诊断准确性。
10. Magnetic Resonance Imaging (MRI) Principles | 磁共振成像（MRI）原理
MRI exploits the magnetic properties of hydrogen nuclei (protons), abundant in water and fat. When a patient is placed in a strong static magnetic field B₀ (typically 1.5–3 T), protons align either parallel (low energy) or anti‑parallel (high energy) to the field, with a slight excess in the low‑energy state. This produces a net magnetisation vector along B₀.
MRI 利用氢原子核（质子）的磁特性，氢在水分和脂肪中含量丰富。当患者被置于强静磁场 B₀（通常 1.5–3 T）中时，质子要么平行（低能量）要么反平行（高能量）于磁场排列，处于低能态的质子数量略多。这产生了一个沿 B₀ 方向的净磁化矢量。
A radiofrequency (RF) pulse at the Larmor frequency (f = γ B₀ / 2π, where γ is the gyromagnetic ratio) is applied to tip the magnetisation into the transverse plane. When the RF pulse is switched off, the net magnetisation relaxes back to equilibrium, emitting an RF signal that is detected by receiver coils. The relaxation times T₁ (longitudinal) and T₂ (transverse) differ among tissues, providing excellent soft‑tissue contrast.
施加一个频率为拉莫尔频率（f = γ B₀ / 2π，其中 γ 为旋磁比）的射频脉冲，将磁化矢量翻转到横向平面。当射频脉冲关闭后，净磁化弛豫回到平衡状态，并发射射频信号，被接收线圈检测到。不同组织的弛豫时间 T₁（纵向）和 T₂（横向）各不相同，提供了极佳的软组织对比度。
Magnetic field gradient coils linearly vary the field strength with position, so that nuclei at different locations precess at slightly different Larmor frequencies. This spatial encoding allows a computer to reconstruct a 3‑D image without any ionising radiation. MRI is the method of choice for imaging the brain, spinal cord, joints and soft tissues.
磁场梯度线圈使场强随位置线性变化，从而使不同位置的原子核以略微不同的拉莫尔频率进动。这种空间编码使计算机能够在不使用任何电离辐射的情况下重建三维图像。MRI 是脑、脊髓、关节和软组织成像的首选方法。
11. Comparing Medical Imaging Modalities | 医学影像方法的比较
Each imaging technique has strengths and weaknesses related to radiation dose, resolution, cost and the type of information provided. A summary table helps synthesise these differences for exam answers.
每种成像技术都有其与辐射剂量、分辨率、成本以及所提供信息类型相关的优点和缺点。总结表格有助于综合这些差异，用于考试答题。
| Modality / 模态 | Ionising radiation? / 电离辐射？ | Spatial resolution / 空间分辨率 | Contrast mechanism / 对比机制 | Clinical application / 临床应用 |
|---|---|---|---|---|
| X‑ray / X 射线 | Yes / 是 | ~0.1 mm | Attenuation (electron density, atomic number) / 衰减（电子密度、原子序数） | Bone fractures, chest / 骨折、胸部 |
| CT / CT | Yes (higher dose) / 是（剂量更高） | ~0.5–1 mm | Attenuation (3‑D) / 衰减（三维） | Head trauma, cancer staging / 头部创伤、癌症分期 |
| Ultrasound / 超声 | No / 否 | ~1–2 mm | Acoustic impedance mismatch / 声阻抗不匹配 | Foetal imaging, abdominal / 胎儿、腹部 |
| Gamma camera / 伽马相机 | Yes (internal source) / 是（内源） | ~5–10 mm | Functional (tracer uptake) / 功能性（示踪剂摄取） | Bone scans, thyroid / 骨扫描、甲状腺 |
| PET / PET | Yes (internal) / 是（内源） | ~4–6 mm | Metabolic activity / 代谢活动 | Oncology, brain function / 肿瘤学、脑功能 |
| MRI / MRI | No / 否 | ~1 mm | Proton density, T₁/T₂ relaxation / 质子密度、T₁/T₂ 弛豫 | Neurology, orthopaedics / 神经学、骨科 |
12. Safety and Non‑ionising vs Ionising Radiation Risks | 安全以及非电离与电离辐射风险
Ionising radiation (X‑rays, CT, nuclear medicine) can ionise atoms, breaking chemical bonds and damaging DNA, which increases the risk of cancer. The effective dose is measured in sieverts (Sv) and is kept as low as reasonably achievable (ALARA principle). Pregnant women and children are particularly sensitive, and examinations must be justified by a clear clinical benefit.
电离辐射（X 射线、CT、核医学）可以电离原子，破坏化学键并损伤 DNA，从而增加患癌风险。有效剂量以希沃特（Sv）为单位，应尽可能合理降低（ALARA 原则）。孕妇和儿童特别敏感，检查必须有明确的临床获益作为依据。
Ultrasound and MRI are regarded as non‑ionising and are not associated with these stochastic risks. However, ultrasound can cause tissue heating and cavitation at high intensities; diagnostic scanners operate within safe acoustic output limits. MRI uses strong magnetic fields and RF pulses; the main hazard is the projectile effect on ferromagnetic objects and potential heating of metal implants, but no genetic damage mechanism has been identified. Understanding these safety aspects is essential for evaluating the choice of imaging modality in a given clinical scenario.
超声波和 MRI 被视为非电离辐射，不伴随这些随机风险。然而，高强度超声波可引起组织发热和空化效应；诊断扫描仪在安全的声输出限值内工作。MRI 使用强磁场和射频脉冲；主要危险是对铁磁性物体的投射效应以及金属植入物可能被加热，但尚未发现基因损伤机制。理解这些安全要点对于在给定临床情境下评估成像方式的选择至关重要。
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