📚 A-Level OCR Physics: Medical Physics Key Points | 医疗物理考点精讲
Medical physics is a crucial applied topic in OCR A-Level Physics, covering the principles behind diagnostic and therapeutic techniques used in modern medicine. Understanding the production, interaction, and detection of ionising radiation, ultrasound, and optical fibres is essential for explaining how diseases are diagnosed and treated. This article presents a structured revision guide with key concepts, equations, and clinical applications aligned to the OCR specification.
医疗物理是 OCR A-Level 物理中的重要应用模块，涵盖现代医学中诊断与治疗技术背后的物理原理。理解电离辐射的产生、相互作用与探测，以及超声波和光纤的工作原理，对于解释疾病的诊断和治疗过程至关重要。本文提供一份结构化复习指南，梳理关键概念、方程和临床应用，紧密贴合 OCR 考纲。
1. Production of X-rays | X射线的产生
X-rays are produced when high-speed electrons are decelerated upon striking a metal target. In an X-ray tube, a filament is heated to emit electrons via thermionic emission. These electrons are accelerated through a large potential difference V, gaining kinetic energy eV.
X 射线由高速电子撞击金属靶标减速产生。在 X 射线管中，灯丝加热通过热电子发射释放电子。这些电子在高压加速下穿过电势差 V，获得动能 eV。
eV = ½ m v²
Less than 1% of the kinetic energy is converted into X-ray photons; the rest becomes heat, so the anode is often rotated and made of tungsten for its high melting point. The X-ray spectrum consists of a continuous bremsstrahlung background and characteristic peaks from atomic electron transitions in the target material.
不到 1% 的动能转化为 X 射线光子；其余变成热量，因此阳极通常旋转且用高熔点的钨制成。X 射线谱由连续的轫致辐射本底和靶材料原子电子跃迁产生的特征峰组成。
The maximum X-ray photon energy (and minimum wavelength) occurs when all the electron’s kinetic energy is converted into a single photon: eV = hf_max = hc/λ_min, giving λ_min = hc/eV. This relation allows calculation of the short-wavelength limit from the tube voltage.
当电子全部动能转化为单个光子时，产生最大 X 射线光子能量（及最短波长）：eV = hf_max = hc/λ_min，得 λ_min = hc/eV。该关系式可用于由管电压计算短波极限。
2. X-ray Attenuation and Imaging | X射线衰减与成像
As X-rays pass through matter, their intensity decreases exponentially with thickness due to absorption and scattering. The intensity I after travelling distance x is given by I = I₀ e⁻μx, where μ is the linear attenuation coefficient, which depends on photon energy and material atomic number. The half-value thickness x₁/₂ is the thickness required to reduce intensity by half, linked by x₁/₂ = ln 2 / μ.
X 射线穿过物质时，由于吸收和散射，其强度随厚度呈指数衰减。传播距离 x 后的强度 I 由 I = I₀ e⁻μx 给出，其中 μ 为线性衰减系数，与光子能量和材料原子序数有关。半价层 x₁/₂ 是将强度减半所需的厚度，关系为 x₁/₂ = ln 2 / μ。
Contrast in an X-ray image arises from differential attenuation by tissues (e.g., bone vs. soft tissue) due to differences in μ. High atomic number materials like bone absorb more, appearing white on the radiograph. Soft tissues have similar attenuation, making contrast low unless artificial contrast media (e.g., barium or iodine) are used.
X 射线图像的对比度源于不同组织（如骨骼与软组织）因 μ 不同产生的衰减差异。高原子序数材料如骨骼吸收更多，在 X 光片上呈白色。软组织衰减相近，对比度低，除非使用人工造影剂（如钡或碘）。
Intensity can also be controlled by adjusting tube current (mAs) and voltage (kVp), which affect quantity and energy of photons, optimizing image quality while minimising patient dose.
强度还可以通过调整管电流（mAs）和管电压（kVp）来控制，影响光子数量和能量，在优化图像质量的同时尽量降低患者剂量。
3. CT Scanning | CT扫描
Computed Tomography (CT) produces three-dimensional images by rotating an X-ray tube and detector array around the patient, measuring attenuation along many projections. A computer reconstructs cross-sectional slices using algorithms such as filtered back projection. The resulting image is a map of linear attenuation coefficients, expressed as Hounsfield Units (HU).
计算机断层扫描 (CT) 通过绕患者旋转 X 射线管和探测器阵列，测量多个投影路径上的衰减，生成三维图像。计算机使用滤波反投影等算法重建横断面切片。最终图像是线性衰减系数的分布图，以亨氏单位 (HU) 表示。
Hounsfield scale is defined as: HU = (μ_tissue – μ_water) / μ_water × 1000. By definition, water has HU = 0 and air HU = -1000. Bone has HU up to +1000 or more. CT provides superior contrast resolution compared to conventional radiography, making it possible to distinguish soft tissue structures, but it delivers a higher radiation dose.
亨氏单位标度定义为：HU = (μ_tissue – μ_water) / μ_water × 1000。按定义，水的 HU = 0，空气 HU = -1000。骨骼 HU 可达 +1000 或更高。与传统 X 射线摄影相比，CT 提供更好的对比度分辨率，可区分软组织结构，但辐射剂量更高。
Modern multi-slice CT scanners use helical scanning and multiple detector rows to reduce scan time and enable volumetric imaging. The use of contrast agents further enhances visibility of specific organs or blood vessels.
现代多层 CT 扫描仪采用螺旋扫描和多排探测器，缩短扫描时间并实现容积成像。使用造影剂可进一步增强特定器官或血管的可见度。
4. Ultrasound Principles | 超声波原理
Ultrasound refers to sound waves with frequencies above 20 kHz; medical diagnostic ultrasound typically uses 2–18 MHz. These waves are produced and detected by piezoelectric transducers that convert electrical pulses into ultrasound and vice versa. When ultrasound encounters a boundary between tissues with different acoustic impedances, part of the wave is reflected.
超声波指频率超过 20 kHz 的声波；医学诊断超声通常使用 2–18 MHz。这些波由压电换能器产生和探测，将电脉冲转换为超声，反之亦然。当超声波遇到具有不同声阻抗的组织边界时，部分波会被反射。
Acoustic impedance Z is defined as Z = ρ c, where ρ is density and c is speed of sound in the medium. The intensity reflection coefficient for normal incidence is R = (Z₂ – Z₁)² / (Z₂ + Z₁)². A large impedance mismatch (e.g., soft tissue–air) reflects almost all ultrasound, which is why gel is used to exclude air between the transducer and skin.
声阻抗 Z 定义为 Z = ρ c，其中 ρ 为密度，c 为介质中的声速。垂直入射时的强度反射系数为 R = (Z₂ – Z₁)² / (Z₂ + Z₁)²。阻抗失配大（如软组织–空气）几乎反射全部超声，因此需使用耦合凝胶排除换能器与皮肤之间的空气。
5. Ultrasound Scanning Techniques | 超声波扫描技术
The pulse-echo technique is the foundation of ultrasound imaging. Short pulses of ultrasound are emitted, and echoes returning from tissue interfaces are timed. The distance to a reflector is d = (c × Δt) / 2, where Δt is the round-trip time and c is the speed of sound in tissue (~1540 m s⁻¹). The amplitude of the echo provides brightness information, forming a B-mode (brightness mode) image.
脉冲回波技术是超声成像的基础。发射短超声脉冲，记录从组织界面返回的回波时间。到反射体的距离为 d = (c × Δt) / 2，其中 Δt 为往返时间，c 为组织中的声速（约 1540 m s⁻¹）。回波幅度提供亮度信息，形成 B 型（亮度模式）图像。
Doppler ultrasound measures the frequency shift of reflected ultrasound from moving red blood cells to determine blood flow velocity. The Doppler shift equation for a reflector moving directly towards or away from the transducer is Δf = (2 f v cos θ) / c, where v is blood velocity and θ is the angle between beam and flow. Colour Doppler overlays flow information on the B-mode image.
多普勒超声测量红细胞的反射超声频率偏移，以确定血流速度。对于直接朝向或远离换能器运动的反射体，多普勒频移方程为 Δf = (2 f v cos θ) / c，其中 v 为血流速度，θ 为声束与血流方向夹角。彩色多普勒将流动信息叠加在 B 型图像上。
Ultrasound is safe because it uses non-ionising radiation, has no known hazards at diagnostic intensities, and provides real-time imaging. It is widely used in obstetrics, cardiology, and abdominal investigations. Resolution improves with higher frequency but penetration depth decreases, requiring a compromise.
超声安全，因为它使用非电离辐射，诊断强度下无已知危害，并实现实时成像。它广泛用于产科、心脏病学和腹部检查。频率越高分辨率越好，但穿透深度减小，需权衡取舍。
6. Endoscopy and Optical Fibres | 内窥镜与光纤
An endoscope uses bundles of optical fibres to transmit light into the body and carry an image back to the viewer. Each fibre consists of a high-refractive-index core surrounded by a lower-index cladding, enabling total internal reflection (TIR) to confine light inside the core with minimal loss.
内窥镜使用光纤束将光传入体内并将图像传回观察者。每根光纤由高折射率纤芯和低折射率包层组成，使得全内反射 (TIR) 将光限制在纤芯内传播，损耗极低。
TIR occurs when the angle of incidence at the core–cladding boundary exceeds the critical angle θ_c, where sin θ_c = n_cladding / n_core. This allows light to travel along curved paths, essential for accessing internal organs via natural openings or small incisions. A coherent bundle preserves spatial information for imaging, while an incoherent bundle is used for illumination.
当纤芯–包层界面的入射角超过临界角 θ_c 时发生全内反射，sin θ_c = n_cladding / n_core。这使得光沿弯曲路径传播，对于通过自然开口或小切口进入内脏至关重要。相干束保留空间信息用于成像，而非相干束用于照明。
7. Gamma Camera and SPECT | 伽马相机与SPECT
A gamma camera detects gamma photons emitted from a radiopharmaceutical administered to the patient, usually technetium-99m (Tc-99m) which emits 140 keV gamma rays. The camera head contains a large sodium iodide (NaI) scintillation crystal, an array of photomultiplier tubes (PMTs), and a collimator (typically lead with parallel holes) to determine the direction of incoming photons.
伽马相机探测注入患者体内的放射性药物发出的伽马光子，通常使用锝-99m (Tc-99m)，发出 140 keV 伽马射线。探头包含一块大型碘化钠 (NaI) 闪烁晶体、光电倍增管 (PMT) 阵列以及一个准直器（通常为带平行孔的铅板），用于确定入射光子方向。
When a gamma photon strikes the NaI crystal, it produces a flash of visible light. PMTs detect the light and, via a position logic circuit, calculate the location of each scintillation event based on the relative signals. This builds a planar image showing the distribution of the tracer in the body.
伽马光子击中 NaI 晶体时产生可见光闪烁。PMT 探测该光，并通过位置逻辑电路根据相对信号计算每个闪烁事件的位置。由此生成平面图像，显示示踪剂在体内的分布。
Single Photon Emission Computed Tomography (SPECT) rotates one or more gamma camera heads around the patient and reconstructs 3D images, providing improved contrast and localisation compared to planar scintigraphy. Tc-99m is ideal due to its short half-life of 6 hours and suitable gamma energy, allowing effective detection with low patient dose.
单光子发射计算机断层扫描 (SPECT) 将一个或多个伽马相机探头绕患者旋转并重建三维图像，与平面闪烁扫描相比可提高对比度和定位精度。Tc-99m 半衰期 6 小时短，伽马能量合适，探测效率高且患者剂量低。
8. Positron Emission Tomography (PET) | 正电子发射断层扫描(PET)
PET imaging relies on the detection of two coincident 511 keV gamma photons produced when a positron (β⁺) annihilates with an electron. A positron-emitting radionuclide, such as fluorine-18 (F-18) in FDG, is administered to the patient. The positron travels a short range before annihilating, producing two gamma photons emitted almost exactly back-to-back (180° apart).
PET 成像依赖于探测正电子 (β⁺) 与电子湮灭产生的两个同时的 511 keV 伽马光子。将发射正电子的放射性核素（如氟-18 标记的 FDG）注入患者体内。正电子行进一小段距离后发生湮灭，产生两个几乎严格背对背（呈 180°）发射的伽马光子。
A ring of detectors surrounding the patient records coincidence events within a narrow time window (a few nanoseconds). A line of response (LOR) is defined between the two detectors that fired. Using tomographic reconstruction, a 3D map of tracer concentration is obtained, revealing metabolic activity because FDG accumulates in cells with high glucose uptake, such as cancer cells.
围绕患者的探测器环记录在狭窄时间窗（几纳秒）内的符合事件。在两个触发的探测器之间定义响应线 (LOR)。通过断层重建获得示踪剂浓度的三维分布图，揭示代谢活动，因为 FDG 聚集在葡萄糖摄取量高的细胞（如癌细胞）中。
PET provides functional information with high sensitivity, and when combined with CT (PET-CT), anatomical and metabolic images are fused for precise localisation. Common PET isotopes include carbon-11, nitrogen-13, and oxygen-15, all short-lived and requiring an on-site cyclotron.
PET 提供高灵敏度的功能信息，与 CT 结合 (PET-CT) 可将解剖与代谢图像融合，实现精确定位。常见 PET 同位素有碳-11、氮-13 和氧-15，均寿命短，需现场回旋加速器生产。
9. Radiotherapy and Medical Tracers | 放疗与医用示踪剂
Radiotherapy uses ionising radiation to destroy malignant cells, aiming to maximise dose to the tumour while sparing surrounding healthy tissue. External beam radiotherapy (EBRT) employs a linear accelerator (linac) to produce high-energy X-ray beams (MV range). The beam is shaped with multi-leaf collimators and wedge filters to conform to the tumour shape, and multiple beams from different angles intersect at the tumour to concentrate dose.
放疗使用电离辐射杀死恶性细胞，目标是最大化肿瘤剂量同时保护周围健康组织。外照射放疗 (EBRT) 使用直线加速器产生高能 X 射线束（兆伏级）。束流通过多叶准直器和楔形滤板塑形以适形肿瘤，并从不同角度交叉投照以集中剂量。
Brachytherapy involves placing sealed radioactive sources (e.g., iridium-192, iodine-125) directly into or near the tumour, delivering a highly localised dose. Proton beam therapy exploits the Bragg peak, where protons deposit maximum energy at a specific depth, reducing exit dose compared to photons.
近距离放疗将密封放射源（如铱-192、碘-125）直接置入肿瘤内部或附近，提供高度局部的剂量。质子束治疗利用布拉格峰，质子在特定深度沉积最大能量，与光子相比减少了出口剂量。
Medical tracers are radioactive substances that, when introduced into the body, trace specific physiological pathways. The ideal tracer emits pure gamma rays (for diagnostic imaging) and has a short half-life to limit patient dose. Tc-99m is the workhorse for nuclear medicine; for PET, F-18 FDG is widely used for oncology. The effective dose must be kept as low as reasonably achievable (ALARA principle).
医用示踪剂是引入体内的放射性物质，示踪特定生理通路。理想示踪剂发射纯伽马射线（用于诊断成像），短半衰期以限制患者剂量。Tc-99m 是核医学的主力；PET 中广泛使用 F-18 FDG 进行肿瘤学成像。有效剂量必须遵循可合理达到的最低原则 (ALARA)。
10. Radiation Protection and Safety | 辐射防护与安全
The fundamental principles of radiation protection are justification, optimisation, and limitation. Any exposure must be justified by a net benefit. Optimisation means keeping doses as low as reasonably achievable (ALARA). Dose limits apply to occupational workers and the public.
辐射防护的基本原则是正当化、最优化和剂量限值。任何照射必须带来的净利益方能进行。最优化意为将剂量保持在可合理达到的最低水平 (ALARA)。剂量限值适用于职业工作者和公众。
The three practical protective measures are: time (minimise duration near sources), distance (increase separation; intensity obeys the inverse square law I ∝ 1/r²), and shielding (use materials that attenuate radiation effectively; lead for X-rays and gamma rays, thick concrete or water for neutrons). In medical settings, lead aprons, thyroid shields, and lead glass screens protect staff during fluoroscopy and interventional radiology.
三项实用防护措施为：时间（缩短在源附近的时间）、距离（增大距离；强度遵循平方反比定律 I ∝ 1/r²）和屏蔽（使用有效衰减辐射的材料；X 射线和伽马射线用铅，中子用重混凝土或水）。在医疗环境中，铅围裙、甲状腺防护套和铅玻璃屏在荧光透视和介入放射学中保护工作人员。
Absorbed dose D (Gy) is the energy absorbed per unit mass. Equivalent dose H (Sv) = D × w_R, where w_R is the radiation weighting factor (1 for X/gamma/beta, up to 20 for alpha). Effective dose accounts for tissue sensitivities. Monitoring devices such as film badges, thermoluminescent dosimeters (TLDs), and optically stimulated luminescence (OSL) dosimeters are worn by radiation workers.
吸收剂量 D (Gy) 是单位质量吸收的能量。当量剂量 H (Sv) = D × w_R，其中 w_R 为辐射权重因子（X/γ/β 为 1，α 可达 20）。有效剂量考虑了组织敏感性。放射工作人员佩戴监测装置，如胶片剂量计、热释光剂量计 (TLD) 及光释光 (OSL) 剂量计。
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