📚 IB/AQA Physics: Medical Physics Key Concepts | IB/AQA 物理：医疗物理考点精讲
Medical physics applies fundamental principles of physics to clinical diagnosis and therapy. In both the IB (Option C: Imaging) and AQA A-level (Medical Physics) specifications, you are expected to understand the underlying physics of X-ray imaging, ultrasound, endoscopy, nuclear medicine, and MRI. This article distils the essential concepts, emphasising the key points most likely to appear in examinations, with paired English–Chinese explanations for clarity.
医疗物理将物理学基本原理应用于临床诊断与治疗。无论是 IB（选修C：成像）还是 AQA A-level（医学物理）大纲，都要求学生掌握 X 射线成像、超声、内窥镜、核医学和 MRI 的底层物理。本文浓缩核心概念，突出考试中最常见的关键点，并以中英对照的方式帮助理解。
1. X-ray Production | X 射线产生
X-rays are produced in an evacuated X-ray tube when high-speed electrons strike a metal target. A heated tungsten filament provides electrons via thermionic emission; these are then accelerated through a high potential difference (typically 50–150 kV) towards a rotating tungsten anode. The sudden deceleration of electrons in the anode material produces X-ray photons through two mechanisms: Bremsstrahlung (braking radiation) gives a continuous spectrum, while the ejection of inner-shell electrons followed by outer-shell transitions yields characteristic X-ray lines. Most of the electron kinetic energy is converted to thermal energy, so the anode must rotate rapidly and be cooled by circulating oil.
X 射线在真空 X 射线管中由高速电子撞击金属靶产生。加热的钨灯丝通过热离子发射提供电子，随后电子被高电压（通常 50–150 kV）加速，飞向旋转钨阳极。电子在阳极材料中急速减速，通过两种机制产生 X 射线光子：轫致辐射给出连续谱，而内壳层电子被轰出后外壳层电子跃迁填充空位产生特征 X 射线。电子的大部分动能转化为热能，因此阳极须高速旋转并用循环油冷却。
Photon energy range: 0 < Ephoton ≤ e·Vtube
Maximum frequency: fmax = eVtube / h
2. X-ray Attenuation and Half-Value Thickness | X 射线衰减与半价层
nds on the photon energy and the atomic number of the material. For monochromatic radiation, the Beer–Lambert law applies: I = I0 e–μx. The half-value thickness (HVT or x½) is the thickness that reduces the intensity by half; it relates to μ via x½ very different attenuation coefficients, which is the foundation of X-ray image contrast.
平行 X 射线束穿过厚度为 x 的材料时，其强度 I 呈指数衰减。衰减系数 μ 取决于光子能量和材料的原子序数。对于单色辐射，比尔–朗伯定律适用：I = I0 e–μx。半价层（HVT 或 x½）是指强度降至一半所需的厚度，与 μ 的关系为 x½ = ln 2 / μ。软组织和骨骼的衰减系数差异很大，这是 X 射线图像对比度的基础。
I = I0 e–μx , x½ = ln 2 / μ
3. X-ray Imaging and Image Contrast | X 射线成像与图像对比度
Traditional radiography places the patient between an X-ray source and a photographic film or digital detector. X-rays that pass through less attenuating tissue (e.g., lungs) darken the film more, while denser structures (e.g., bones) appear lighter. To enhance visibility of soft tissues, high-atomic-number contrast media such as barium sulfate (for gastrointestinal imaging) or iodine-based compounds (for blood vessels) are introduced. These materials strongly absorb X-rays, providing clear outlines of organs. Scattered radiation degrades contrast, so anti-scatter grids and collimators are used to improve image quality.
传统 X 射线摄影将患者置于 X 射线源和感光胶片或数字探测器之间。穿过衰减较少组织（如肺部）的 X 射线使胶片更黑，而致密结构（如骨骼）显得更白。为增强软组织可见度，会使用高原子序数造影剂，如硫酸钡（用于胃肠道成像）或含碘化合物（用于血管）。这些物质强烈吸收 X 射线，提供清晰的器官轮廓。散射辐射会降低对比度，因此使用防散射滤线栅和准直器来提高图像质量。
4. Computed Tomography (CT) Scanning | 计算机断层扫描 (CT)
A CT scanner consists of an X-ray tube that rotates around the patient together with a ring of detectors on the opposite side. A thin, fan-shaped beam passes through a cross-sectional slice of the body. Detectors measure attenuation at many angles, and a computer reconstructs a two‑dimensional map of attenuation coefficients displayed as Hounsfield units. Compared to a planar X-ray, CT provides vastly superior soft‑tissue contrast and three‑dimensional information, but with a significantly higher radiation dose. Modern spiral CT allows continuous table movement and faster scanning, reducing motion artefacts.
CT 扫描仪由绕患者旋转的 X 射线管与对面环状探测器阵列组成。细薄的扇形射束穿过身体的横断面层面。探测器从多个角度测量衰减，计算机据此重建以亨氏单位显示的衰减系数二维图。与传统平片相比，CT 提供了优越得多的软组织对比度和三维信息，但辐射剂量也显著增大。现代螺旋 CT 可连续移动检查床并实现更快扫描，减少运动伪影。
5. Ultrasound Imaging | 超声成像
Ultrasound uses high-frequency sound waves (1– t tissue interfaces, part of the wave is reflected back due to differences in acoustic impedance Z = ρc (ρ = density, c = speed of sound). The same transducer detects returning echoes, and the time delay is used to calculate the depth of the reflecting interface. A coupling gel is essential to eliminate air gaps, which would otherwise cause almost total reflection. The intensity reflection coefficient for normal incidence is R = (Z2 – Z1)² / (Z2 + Z1)².
超声使用由压电换能器产生的高频声波（1–20 MHz）。电脉冲使晶体振动，向体内发射短促超声脉冲。在组织界面处，因声阻抗 Z = ρc（ρ 为密度，c 为声速）的差异，部分波被反射回来。同一换能器探测返回的回声，并根据时间延迟计算反射界面的深度。耦合凝胶必不可少，它能消除空气间隙，否则空气间隙会导致近乎全反射。垂直入射时的强度反射系数为 R = (Z2 – Z1)² / (Z2 + Z1)²。
Z = ρc , R = (Z2 – Z1)² / (Z2 + Z1)²
6. Fibre Optics and Endoscopy | 光纤与内窥镜
Medical endoscopes exploit the principle of total internal reflection. A flexible bundle of optical fibres guides light into the body and carries an image back. Each fibre consists of a high‑refractive‑index core surrounded by a low‑index cladding. As long as the angle of incidence at the core–cladding boundary exceeds the critical angle θc = sin–1(nclad/ncore), light is confined to the core with minimal loss. Coherent fibre bundles (where the relative positions of fibres are maintained) transmit a pixelated image; non‑coherent bundles are used only for illumination. Endoscopes can also incorporate channels for surgical instruments or biopsy.
医用内窥镜利用全内反射原理。一束柔性光纤将光导入体内并将图像传导出来。每根光纤由高折射率纤芯和低折射率包层组成。只要纤芯–包层界面的入射角大于临界角 θc = sin–1(nclad/ncore)，光便被束缚在纤芯内，损耗极小。相干光纤束（维持各光纤相对位置）传输像素化图像；非相干光纤束仅用于照明。内窥镜还可集成手术器械通道或活检通道。
7. Radioactive Tracers and Gamma Camera | 放射性示踪剂与伽马相机
Nuclear medicine techniques involve introducing a radioisotope-labelled pharmaceutical into the body; the tracer concentrates in the organ of interest and emits gamma photons. A gamma camera detects these photons to form a functional image. The camera head contains a parallel‑hole lead collimator that allows only photons travelling perpendicular to the crystal to pass through. A large thallium‑doped sodium iodide NaI(Tl) scintillator converts each gamma photon into a flash of visible light, which is detected by an array of photomultiplier tubes (PMTs). The position of the scintillation event is calculated by comparing the signals from the PMTs. Technetium‑99m (γ energy 140 keV, half‑life 6 hours) is the most widely used isotope because of its ideal photon energy and short half‑life.
核医学技术将放射性同位素标记的药物引入体内；示踪剂富集于目标器官并发射伽马光子。伽马相机探测这些光子以形成功能性图像。相机探头包含平行孔铅准直器，只允许垂直于晶体方向的光子通过。大型铊掺杂碘化钠 NaI(Tl) 闪烁体将每个伽马光子转化为可见光闪光，由光电倍增管（PMT）阵列探测。闪烁事件的位置通过比较各 PMT 的信号计算得到。锝‑99m（γ 能量 140 keV，半衰期 6 小时）因其理想的光子能量和较短半衰期而成为使用最广泛的同位素。
8. Positron Emission Tomography (PET) | 正电子发射断层扫描 (PET)
PET uses tracers labelled with positron‑emitting isotopes, such as fluorine‑18. The emitted positron travels a short distance before annihilating with an electron, producing two back‑to‑back 511 keV gamma photons. A ring of detectors surrounding the patient registers these photons in coincidence – only events where two detectors are triggered within a narrow time window are accepted. Because the annihilation point lies along the line connecting the two detectors, a computer can reconstruct the spatial distribution of the tracer. PET is often combined with CT (PET‑CT) to provide both metabolic and anatomical information.
PET 使用发射正电子的同位素标记的示踪剂，如氟‑18。发射出的正电子行进很短距离后与电子湮灭，产生两个背对背的 511 keV 伽马光子。环绕患者的环状探测器在符合模式下记录这些光子——只有两个探测器在极窄时间窗内同时被触发的事件才被接受。由于湮灭点位于连接两个探测器的直线上，计算机可以重建示踪剂的空间分布。PET 常与 CT 融合（PET‑CT），同时提供代谢和解剖信息。
9. Magnetic Resonance Imaging (MRI) Fundamentals | 磁共振成像基础
MRI exploits the magnetic properties of hydrogen nuclei (protons) in water and fat molecules. When placed in a strong static magnetic field B0, protons precess about the field axis at the Larmor frequency f = γB0 / (2π), where γ is the gyromagnetic ratio. A short radiofrequency (RF) pulse at this Larmor frequency tips the net magnetisation away from B0. After the RF pulse, the magnetisation relaxes back to its equilibrium orientation, emitting a weak signal that is detected by receiver coils. Spatial localisation is achieved by applying magnetic field gradients, which make the Larmor frequency position‑dependent. Different tissues exhibit characteristic relaxation times T1 and T2, giving exquisite soft‑tissue contrast without ionising radiation.
MRI 利用水分子和脂肪分子中氢核（质子）的磁性。置于强静态磁场 B0 中时，质子以拉莫尔频率 f = γB0 / (2π)（其中 γ 为旋磁比）绕磁场轴进动。在此拉莫尔频率下的短射频脉冲将净磁化矢量从 B0 方向翻转。射频脉冲关闭后，磁化矢量弛豫返回平衡方向，发出微弱信号被接收线圈探测。通过施加磁场梯度使拉莫尔频率随位置变化，实现空间定位。不同组织表现出特征性的弛豫时间 T1 和 T2，从而在无电离辐射的情况下提供优良的软组织对比度。
fLarmor = γ B0 / (2π)
10. Radiation Dose and Safety | 辐射剂量与安全
The biological effect of ionising radiation is quantified by the equivalent dose H = D × wR, where D is the absorbed dose in gray (Gy) and wR is a radiation weighting factor (1 for X‑rays, gamma, and electrons; ~20 for alpha particles). For different tissues, the effective dose E = Σ (wT × H) gives a whole‑ d staff exposure. Protection methods include time limitation, distance (inverse square law), shielding (lead aprons, concrete walls), and monitoring with dosimeters. Ultrasound and MRI, by contrast, involve no ionising radiation and are considered safer for repeated or paediatric use.
电离辐射的生物效应用量当量 H = D × wR 量化，其中 D 是以戈瑞 (Gy) 为单位的吸收剂量，wR 是辐射权重因子（X 射线、伽马射线、电子为 1；α 粒子约 20）。对不同组织，有效剂量 E = Σ (wT × H) 给出以希沃特 (Sv) 为单位的全身风险度量。医疗物理师必须遵循 ALARA 原则（尽可能合理降低），尽量减少患者和工作人员的辐射暴露。防护方法包括限制时间、利用距离（平方反比定律）、屏蔽（铅围裙、混凝土墙）和使用剂量计进行监测。相比之下，超声和 MRI 不涉及电离辐射，用于重复检查或儿科检查时被认为更安全。
H = D × wR , E = Σ (wT × H)
Published by TutorHao | Medical Physics Revision Series | aleveler.com
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