📚 Medical Physics: Key Exam Topics for IB & OCR A-Level | 医科物理：IB与OCR考点精讲
Medical physics is a fascinating field that applies physics principles to diagnosis and treatment. This article covers essential exam topics for both IB Physics (Option B: Medical Physics) and OCR A-Level Physics (Module 6: Medical Imaging and Radiotherapy), including imaging techniques, radiation therapy, and safety considerations.
医学物理是一个将物理学原理应用于诊断和治疗的迷人领域。本文涵盖IB物理（选修B：医学物理）和OCR A-Level物理（模块6：医学成像与放射治疗）的核心考点，包括成像技术、放射治疗与安全考量。
1. Ultrasound Imaging and the Piezoelectric Effect | 超声成像与压电效应
Ultrasound imaging uses high-frequency sound waves (typically 1–15 MHz) to produce images of soft tissues. The transducer contains a piezoelectric crystal, such as lead zirconate titanate (PZT), which generates ultrasound pulses when a voltage is applied and also detects returning echoes by converting pressure variations back into voltage signals.
超声成像利用高频声波（通常1–15 MHz）生成软组织图像。探头内含压电晶体（如锆钛酸铅PZT），施加电压时产生超声脉冲，并接收返回的回声，将压力变化转换回电压信号。
The piezoelectric effect is the ability of certain materials to generate an electric charge in response to applied mechanical stress (direct effect) and to deform mechanically when an electric field is applied (inverse effect). Both are used in ultrasound: the inverse effect produces the sound pulse, and the direct effect detects the echo.
压电效应是指某些材料在受到机械应力时产生电荷（正效应），以及在施加电场时发生机械形变（逆效应）。超声中两者均利用：逆效应产生声脉冲，正效应探测回声。
The same transducer acts as both transmitter and receiver, pulsing in short bursts and then switching to listening mode.
同一探头兼作发射器和接收器，以短脉冲群发射，然后切换至接收模式。
2. A-scan, B-scan and Acoustic Impedance | A型扫描、B型扫描与声阻抗
An A-scan (amplitude scan) displays the echo amplitude as a function of time (depth) on an oscilloscope. It is used in ophthalmology to measure eye dimensions.
A型扫描（幅度扫描）在示波器上显示回声幅度随时间（深度）的变化曲线，常用于眼科测量眼轴长度。
B-scan (brightness scan) produces a two-dimensional image by converting echo amplitudes into brightness levels. Multiple scan lines form a cross-sectional image used for fetal imaging and abdominal scans.
B型扫描（亮度扫描）通过将回声幅度转换为亮度值生成二维图像。多条扫描线形成断层图像，用于胎儿和腹部检查。
Acoustic impedance Z = ρc (density × speed of sound). At boundaries between tissues with different impedances, ultrasound is reflected. The intensity reflection coefficient α = ((Z₂ – Z₁)/(Z₂ + Z₁))². To maximize transmission, a gel with impedance matching that of skin is used to reduce reflection at the probe-skin interface.
声阻抗 Z = ρc（密度 × 声速）。在阻抗不同的组织界面，超声发生反射。强度反射系数 α = ((Z₂ – Z₁)/(Z₂ + Z₁))²。为使透射最大，使用与皮肤阻抗匹配的耦合凝胶，以减少探头-皮肤界面的反射。
3. X-ray Production and Spectra | X射线的产生与能谱
X-rays are produced when high-speed electrons collide with a metal target (usually tungsten) in an X-ray tube. Thermionic emission from a heated filament provides electrons, which are accelerated by a high voltage (kVp) toward the anode.
X射线由高速电子撞击金属靶（通常为钨）产生。加热灯丝发射热电子，经高压（kVp）加速轰击阳极。
The X-ray spectrum consists of a continuous spectrum (bremsstrahlung) and characteristic X-ray peaks. Bremsstrahlung arises from deceleration of electrons by the target nuclei, producing all energies up to the electron kinetic energy. Characteristic X-rays are emitted when an inner-shell electron is knocked out and an outer electron fills the vacancy.
X射线谱包含连续谱（轫致辐射）和特征X射线峰。轫致辐射由电子被靶原子核减速产生，能量范围直至电子动能。特征X射线由内壳层电子被击出后，外壳层电子跃迁填补空穴时发射。
Key variables: increasing tube current (mA) increases the intensity at all energies; increasing tube voltage (kVp) shifts the spectrum to higher energies and increases intensity. The minimum wavelength is given by λmin = hc/eV.
关键变量：增加管电流（mA）提高所有能量下的强度；增加管电压（kVp）使能谱向高能方向移动并提高强度。最短波长 λmin = hc/eV。
4. Attenuation and Half-Value Thickness | 衰减与半值层
As X-rays pass through matter, their intensity I decreases exponentially: I = I₀ e–μx, where μ is the linear attenuation coefficient and x the thickness. The half-value thickness (HVT or x½) is the thickness that reduces intensity by half: x½ = ln2/μ.
X射线穿过物质时，强度I呈指数衰减：I = I₀ e–μx，其中μ为线性衰减系数，x为厚度。半值层 (x½) 是使强度减半的厚度：x½ = ln2/μ。
Attenuation depends on photon energy and tissue type; it is due mainly to photoelectric absorption at low energies and Compton scattering at higher diagnostic energies. Bone has a higher μ than soft tissue, enabling contrast in radiographs.
衰减取决于光子能量和组织类型；低能时主要由于光电吸收，诊断能量范围内以康普顿散射为主。骨骼的线性衰减系数高于软组织，使X光片产生对比度。
5. Computed Tomography (CT) Scanning | 计算机断层扫描（CT）
CT uses a rotating X-ray source and detectors opposite the source to obtain many projections at different angles. A computer reconstructs a cross-sectional image using back-projection and filtered back-projection algorithms.
CT利用旋转的X射线源和相对的探测器，在不同角度获取多个投影。计算机通过反投影和滤波反投影算法重建横截面图像。
Each voxel is assigned a CT number in Hounsfield Units (HU): HU = 1000 × (μtissue – μwater)/μwater. Air is –1000, water is 0, bone can be up to +1000 or more.
每个体素被赋予一个CT值，单位为亨氏（HU）：HU = 1000 × (μ组织 – μ水)/μ水。空气为–1000，水为0，骨骼可达+1000或更高。
Advantages of CT over conventional X-rays: high contrast resolution, 3D reconstructions, but higher patient dose.
CT相较于传统X光的优点：高对比度分辨率，可三维重建，但患者剂量更高。
6. Radioactive Tracers and Gamma Cameras | 放射性示踪剂与伽马相机
In nuclear medicine, a radiopharmaceutical containing a gamma-emitting isotope (e.g. technetium-99m, half-life 6 hours) is administered to the patient. It concentrates in specific organs, and emitted gamma rays are detected to assess function.
在核医学中，将含有伽马发射同位素（如锝-99m，半衰期6小时）的放射性药物注入患者体内。药物在特定器官中聚集，发射的伽马射线被探测以评估功能。
A gamma camera (Anger camera) consists of a collimator (usually lead with parallel holes) to select gamma photons travelling perpendicular to the detector, a scintillation crystal (NaI) that converts gamma rays into light flashes, photomultiplier tubes (PMTs) to convert light into electrical pulses, and electronics to determine the position based on pulse amplitudes.
伽马相机（Anger相机）包括准直器（通常为带平行孔的铅板）以选择垂直入射的伽马光子，闪烁晶体（NaI）将伽马射线转为可见光闪光，光电倍增管将光转为电脉冲，电子电路根据脉冲幅度确定位置。
7. PET Scans and Coincidence Detection | PET扫描与符合探测
Positron Emission Tomography (PET) uses a radiotracer that emits positrons (β⁺). When a positron annihilates with an electron, two gamma photons of 511 keV are emitted in opposite directions (180°).
正电子发射断层扫描（PET）使用发出正电子的放射性示踪剂。正电子与电子湮灭，产生两个能量511 keV、方向相反（180°）的伽马光子。
A ring of detectors records pairs of photons in coincidence (within a narrow time window, ~ns). The line of response along which the annihilation occurred is determined, and a 3D image of tracer concentration is reconstructed. PET provides functional metabolic information, often combined with CT (PET-CT) for anatomical reference.
一圈探测器以符合探测方式记录光子对（在狭窄时间窗内，约纳秒级）。由此确定湮灭发生的响应线，重建示踪剂浓度的三维图像。PET提供功能性代谢信息，常与CT结合（PET-CT）进行解剖定位。
8. Magnetic Resonance Imaging (MRI) Principles | 磁共振成像（MRI）原理
MRI exploits the magnetic properties of hydrogen nuclei (protons). In a strong static magnetic field B₀ (e.g. 1.5 T), proton spins align either parallel (low energy) or anti-parallel (high energy), creating a net magnetization.
MRI利用氢原子核（质子）的磁特性。在强静磁场B₀（如1.5 T）中，质子自旋平行（低能）或反平行（高能）排列，产生净磁化。
A radiofrequency (RF) pulse at the Larmor frequency (f = γ B₀ / 2π, where γ is the gyromagnetic ratio) tips the magnetization into the transverse plane. After the pulse, the transverse magnetization precesses, inducing a signal in receiver coils. Two relaxation times govern contrast: T₁ (spin-lattice) and T₂ (spin-spin). Tissues have different T₁ and T₂ values, enabling excellent soft-tissue contrast without ionizing radiation.
频率为拉莫尔频率（f = γ B₀ / 2π，γ为旋磁比）的射频脉冲将磁化矢量翻转至横向平面。脉冲停止后，横向磁化进动，在接收线圈中感应出信号。两个弛豫时间决定对比度：T₁（自旋-晶格）和T₂（自旋-自旋）。不同组织的T₁和T₂值各异，实现了优异的软组织对比度且无电离辐射。
9. Radiotherapy and Dosimetry | 放射治疗与剂量学
Radiotherapy uses ionizing radiation to damage cancer cells, mainly by causing DNA double-strand breaks. External beam radiotherapy often uses high-energy X-rays from a linear accelerator (linac), or gamma rays from cobalt-60. Internal radiotherapy (brachytherapy) places sealed sources near the tumour.
放射治疗使用电离辐射破坏癌细胞，主要通过引起DNA双链断裂。外照射放疗常用直线加速器产生的高能X射线，或钴-60的伽马射线。内照射放疗（近距离治疗）将密封源置于肿瘤附近。
Absorbed dose D = E/m, measured in gray (Gy) where 1 Gy = 1 J/kg. Equivalent dose H = D × wR (radiation weighting factor), measured in sievert (Sv). Effective dose accounts for tissue sensitivity: E = Σ (wT × H). These quantities are essential for treatment planning and radiation protection.
吸收剂量 D = E/m，单位为戈瑞（Gy），1 Gy = 1 J/kg。当量剂量 H = D × wR（辐射权重因子），单位为希沃特（Sv）。有效剂量考虑组织敏感性：E = Σ (w<
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