📚 Medical Physics | 医疗物理考点精讲
Medical physics applies the principles of physics to the diagnosis and treatment of disease. It encompasses imaging techniques, radiation therapy, and radiation safety, forming a core part of the IB and WJEC Physics specifications. A solid understanding of how waves, particles, and fields interact with biological tissue is essential for success in this topic.
医疗物理将物理学原理应用于疾病的诊断与治疗。它涵盖了成像技术、放射治疗和辐射安全，是IB和WJEC物理大纲的核心部分。对于波、粒子和场如何与生物组织相互作用的扎实理解，是掌握本专题的关键。
1. Introduction to Medical Physics | 医疗物理简介
Medical physics bridges the gap between physical principles and clinical applications. It covers diagnostic imaging (X‑ray, ultrasound, MRI, nuclear medicine), radiation therapy, and radiation protection. The interdisciplinary nature of this field requires an ability to apply concepts from mechanics, waves, electromagnetism, and atomic physics to living systems.
医疗物理是物理原理与临床应用之间的桥梁。它涵盖诊断成像（X射线、超声、磁共振成像、核医学）、放射治疗和辐射防护。该领域的跨学科特性要求能够将力学、波、电磁学和原子物理的概念应用于生命系统。
Key quantities include absorbed dose, equivalent dose, effective dose, and half‑life. The biological effects of ionising radiation depend on the type of radiation, the absorbed energy per unit mass, and the sensitivity of the exposed tissue. Understanding these quantities is crucial for minimising risk while maximising diagnostic or therapeutic benefit.
关键量包括吸收剂量、当量剂量、有效剂量和半衰期。电离辐射的生物效应取决于辐射类型、单位质量吸收的能量以及受照组织的敏感性。理解这些量对于在最大化诊断或治疗收益的同时最小化风险至关重要。
2. X‑ray Production and Imaging | X射线的产生与成像
X‑rays are produced when high‑speed electrons are decelerated upon striking a metal target. In an X‑ray tube, a heated filament emits electrons via thermionic emission. These electrons are accelerated across a high potential difference (typically 50–150 kV) and hit a rotating tungsten anode. The sudden deceleration produces X‑rays via bremsstrahlung (braking radiation), while the ejection of inner‑shell electrons from the target atoms leads to characteristic X‑ray lines.
X射线是在高速电子撞击金属靶并减速时产生的。在X射线管中，加热灯丝通过热电子发射释放电子。这些电子在高电势差（通常为50–150 kV）上加速，并撞击旋转的钨阳极。突然减速通过轫致辐射产生X射线，而靶原子内层电子的激发则导致特征X射线。
The intensity of the X‑ray beam depends on the tube current (mA) and the accelerating voltage (kV). A higher kV increases the maximum photon energy and beam penetrability, while a higher mA increases the number of photons. The X‑ray spectrum consists of a continuous bremsstrahlung background superimposed with sharp peaks at characteristic energies.
X射线束的强度取决于管电流（mA）和加速电压（kV）。更高的kV增加最大光子能量和穿透力，而更高的mA增加光子数量。X射线谱由连续的轫致辐射背景和叠加在特征能量处的尖锐峰组成。
For imaging, a patient is placed between the X‑ray source and a detector. Tissues with a higher atomic number and density, such as bone, absorb more radiation and appear brighter on the image. Soft tissues show less contrast. Contrast media, such as barium or iodine, can be introduced to enhance visibility of certain structures.
成像时，患者置于X射线源和探测器之间。原子序数高、密度大的组织（如骨骼）吸收更多辐射，在影像上显得更亮。软组织对比度较低。可引入造影剂（如钡或碘）以增强某些结构的可见性。
3. X‑ray Attenuation and CT Scans | X射线衰减与CT扫描
The attenuation of an X‑ray beam passing through a material follows an exponential law. The transmitted intensity I after passing through a thickness x is given by:
穿过物质的X射线束衰减遵循指数规律。穿过厚度x后的透射强度I由下式给出：
I = I0 e–μx
Here I0 is the incident intensity and μ is the linear attenuation coefficient, which depends on the material’s density and atomic number as well as the photon energy. The half‑value thickness (HVT) is the thickness required to reduce the intensity by half: HVT = ln(2) / μ.
其中I0为入射强度，μ为线性衰减系数，它取决于材料的密度、原子序数以及光子能量。半值厚度（HVT）是将强度减半所需的厚度：HVT = ln(2)/μ。
Computed Tomography (CT) takes X‑ray imaging to three dimensions. An X‑ray tube rotates around the patient, and a large number of projections are recorded. A computer reconstructs cross‑sectional slices using filtered back‑projection. The result is a high‑resolution 3D image with excellent soft tissue contrast, far superior to conventional radiography.
计算机断层扫描（CT）将X射线成像提升到三维。X射线管围绕患者旋转，记录下大量投影。计算机利用滤波反投影算法重建横断面切片。结果得到高分辨率的三维图像，具有极好的软组织对比度，远超传统X光摄影。
CT scans deliver a higher radiation dose than a single radiograph. Therefore, the justification of the procedure must balance the clinical benefit against the radiation risk.
CT扫描提供的辐射剂量高于单次X光片。因此，检查的正当性必须平衡临床收益与辐射风险。
4. Ultrasound Imaging | 超声波成像
Ultrasound uses high‑frequency sound waves (typically 1–15 MHz) to produce images of the body’s interior. A piezoelectric transducer emits short pulses of ultrasound and detects echoes reflected from boundaries between tissues of different acoustic impedance.
超声波使用高频声波（通常为1–15 MHz）来产生人体内部图像。压电换能器发射短脉冲超声波，并检测从不同声阻抗组织之间界面反射的回波。
The acoustic impedance Z of a material is defined as the product of its density ρ and the speed of sound c in that material: Z = ρc. When ultrasound encounters a boundary, the fraction of intensity reflected depends on the impedance mismatch:
材料的声阻抗Z定义为其密度ρ与声音在该材料中的速度c的乘积：Z = ρc。当超声波遇到界面时，反射的强度比例取决于阻抗失配：
Reflected intensity / Incident intensity = ((Z2 – Z1) / (Z2 + Z1))2
Large differences in acoustic impedance, such as between soft tissue and bone or air, produce strong reflections that limit imaging depth. A coupling gel is used to eliminate the air gap between the transducer and the skin, reducing the impedance mismatch.
声阻抗的较大差异（如软组织与骨骼或空气之间）会产生强反射，限制成像深度。使用耦合凝胶消除换能器与皮肤之间的空气间隙，以减少阻抗失配。
The depth of a reflecting interface is calculated using the time delay t between pulse emission and echo reception: depth = c t / 2, where the factor 1/2 accounts for the round trip of the pulse. By scanning the beam across the body, a real‑time 2D image (B‑scan) is built up.
反射界面的深度利用脉冲发射与回波接收之间的时间延迟t计算：深度 = c t / 2，其中1/2因子考虑了脉冲的往返传播。通过在身体上扫描波束，可建立实时二维图像（B扫描）。
5. Doppler Effect in Ultrasound | 超声波中的多普勒效应
The Doppler effect in ultrasound allows measurement of blood flow velocity. When ultrasound is scattered by moving red blood cells, the frequency of the returning echoes is shifted. For a reflector moving with velocity v at an angle θ to the ultrasound beam, the observed frequency shift Δf is:
超声中的多普勒效应可测量血流速度。当超声波被移动的红细胞散射时，返回回波的频率发生偏移。对于以速度v沿与超声波束成角度θ运动的反射体，观测到的频移Δf为：
Δf = (2 f0 v cosθ) / c
where f0 is the transmitted frequency and c is the speed of sound in blood. The factor 2 arises because the ultrasound undergoes a Doppler shift twice: once on reception by the moving cell and again on re‑emission back to the transducer.
其中f0是发射频率，c是血液中的声速。因子2的出现是因为超声波经历了两次多普勒频移：一次在运动细胞接收时，另一次在向换能器再发射时。
Colour Doppler overlays flow information onto an anatomical B‑mode image, showing direction and relative speed of blood flow. This is invaluable in diagnosing vascular diseases and monitoring fetal circulation.
彩色多普勒将血流信息叠加到解剖B模式图像上，显示血流的方向和相对速度。这对于诊断血管疾病和监测胎儿循环具有极其重要的价值。
6. Nuclear Medicine and Gamma Camera | 核医学与伽马相机
Nuclear medicine uses radioactive tracers to obtain functional images of the body. A radiopharmaceutical, consisting of a gamma‑emitting radioisotope bound to a biologically active molecule, is introduced into the patient. The tracer accumulates in the organ or tissue of interest and emits gamma photons that are detected externally.
核医学使用放射性示踪剂获取人体的功能图像。由释放伽马射线的放射性同位素与生物活性分子结合的放射性药物被引入患者体内。示踪剂积聚在目标器官或组织中，并在体外被探测到的伽马光子中释放。
The gamma camera detects the emitted photons. A collimator (usually a lead plate with parallel holes) ensures that only gamma rays travelling in the correct direction reach the scintillator crystal, which converts each gamma photon into a flash of visible light. Photomultiplier tubes amplify the light signals, and a computer reconstructs the position of each scintillation event to form a 2D image of tracer distribution.
伽马相机探测发射的光子。准直器（通常为带平行孔的铅板）确保只有沿正确方向传播的伽马射线到达闪烁晶体，该晶体将每个伽马光子转换为可见光闪光。光电倍增管放大光信号，计算机重建每个闪烁事件的位置，形成示踪剂分布的二维图像。
Common isotopes include technetium‑99m (half‑life 6 hours, gamma energy 140 keV), used in bone, heart, and thyroid scans. The short half‑life minimises radiation dose while providing sufficient counts for imaging.
常见的同位素包括锝‑99m（半衰期6小时，伽马能量140 keV），用于骨骼、心脏和甲状腺扫描。其短半衰期在提供足够计数进行成像的同时，最小化了辐射剂量。
7. PET Scans | PET扫描
Positron Emission Tomography (PET) detects the annihilation of positrons emitted by a tracer to create three‑dimensional functional images. The most common radiotracer is fluorodeoxyglucose (FDG) labelled with fluorine‑18, a positron emitter with a half‑life of 110 minutes.
正电子发射断层扫描（PET）探测由示踪剂发射的正电子湮灭，以创建三维功能图像。最常用的放射性示踪剂是氟代脱氧葡萄糖（FDG），以氟‑18标记，这是一种半衰期为110分钟的正电子发射体。
When a positron encounters an electron, both are annihilated, producing two 511 keV gamma photons travelling in opposite directions. A ring of detectors surrounding the patient records coincident events. The line of response between two detectors identifies the line along which the annihilation occurred. By collecting millions of such coincidences, a tomographic reconstruction reveals regions of high metabolic activity, such as tumours or brain activity.
当正电子遇到电子时，两者湮灭，产生两个向相反方向移动的511 keV伽马光子。围绕患者的环形探测器记录符合事件。两个探测器之间的响应线确定了湮灭发生的线路。通过收集数百万个这样的符合事件，断层重建揭示了高代谢活动区域，例如肿瘤或脑活动。
PET is frequently combined with CT (PET‑CT) to provide both functional and anatomical information, improving diagnostic accuracy.
PET常与CT组合（PET‑CT），以提供功能和解剖信息，提高诊断准确性。
8. Magnetic Resonance Imaging (MRI) | 磁共振成像
MRI exploits the magnetic properties of hydrogen nuclei (protons) in the body. The patient is placed in a strong static magnetic field, typically 1.5–3 T, which aligns a small excess of proton spins parallel to the field. A radio‑frequency (RF) pulse at the Larmor frequency tilts these spins into the transverse plane. When the RF pulse is turned off, the protons relax back to equilibrium, emitting RF signals that are received by coils to form an image.
MRI利用体内氢原子核（质子）的磁性。患者被置于强静磁场中，通常为1.5–3 T，使少量过量的质子自旋平行于磁场排列。以拉莫尔频率发射的射频脉冲将这些自旋翻转至横向平面。当射频脉冲关闭后，质子弛豫回到平衡态，发射由线圈接收的射频信号，用于形成图像。
Contrast in MRI depends on proton density and two relaxation times: T1 (spin‑lattice) and T2 (spin‑spin). Different tissues have distinct T1 and T2 values, allowing exquisite soft tissue differentiation without using ionising radiation. Gradient coils create spatial variations in the magnetic field to encode position information.
MRI的对比度取决于质子密度和两个弛豫时间：T1（自旋‑晶格）和T2（自旋‑自旋）。不同组织具有不同的T1和T2值，无需使用电离辐射即可实现卓越的软组织区分。梯度线圈在磁场中产生空间变化以编码位置信息。
Safety considerations: The strong static field requires rigorous screening for ferromagnetic materials or implants. The RF pulses can cause tissue heating (SAR — specific absorption rate), which must be monitored.
安全注意事项：强静磁场要求严格筛查铁磁材料或植入物。射频脉冲可能引起组织加热（SAR — 比吸收率），必须进行监测。
9. Radiotherapy | 放射治疗
Radiotherapy uses ionising radiation to destroy malignant cells while minimising damage to surrounding healthy tissue. The primary goal is to deliver a lethal dose to the tumour volume while keeping doses to critical organs within tolerance limits.
放射治疗使用电离辐射摧毁恶性细胞，同时最小化对周围健康组织的损伤。首要目标是在临界器官耐受限度内对肿瘤体积施以致死剂量，。
External beam radiation employs a linear accelerator (linac) to produce high‑energy X‑rays (megavoltage) or electron beams. Conformal techniques shape the radiation beam to match the tumour profile, and intensity‑modulated radiation therapy (IMRT) varies the beam intensity across the field to further spare normal tissue.
外照射放疗使用直线加速器（linac）产生高能X射线（兆伏级）或电子束。适形技术使辐射束与肿瘤轮廓相匹配，而调强放射治疗（IMRT）在照射野内改变束流强度，进一步保护正常组织。
Brachytherapy involves placing sealed radioactive sources directly into or near the tumour, delivering a high local dose while sparing distant tissue. The inverse‑square law underpins the rapid dose fall‑off with distance from the source.
近程治疗涉及将密封放射源直接置于肿瘤内或其附近，施以高局部剂量，同时保护远处组织。随着距离源的距离增加，剂量迅速下降，其基础为平方反比定律。
Treatment planning uses CT and MRI images to delineate the target volume and calculate dose distribution using algorithms that model photon and electron transport.
治疗计划使用CT和MRI图像勾画靶体积，并利用模拟光子和电子输运的算法计算剂量分布。
10. Radiation Safety and Dosimetry | 辐射安全与剂量学
Radiation dosimetry quantifies the energy deposited by ionising radiation. The fundamental quantity is the absorbed dose, measured in grays (Gy): 1 Gy = 1 J kg⁻¹. The biological effect depends not only on absorbed dose but also on the radiation type, accounted for by the equivalent dose:
辐射剂量学量化电离辐射沉积的能量。基本量是吸收剂量，以戈瑞（Gy）为单位：1 Gy = 1 J kg⁻¹。生物效应不仅取决于吸收剂量，还取决于辐射类型，这由当量剂量考虑：
Equivalent dose (Sv) = Absorbed dose (Gy) × Radiation weighting factor (wR)
X‑rays, gamma rays, and beta particles have wR = 1, while alpha particles have wR = 20. The effective dose further accounts for tissue‑specific sensitivities:
X射线、伽马射线和贝塔粒子的wR = 1，而阿尔法粒子的wR = 20。有效剂量进一步考虑了组织特定的敏感性：
Effective dose (Sv) = Σ (Equivalent dose × Tissue weighting factor wT)
The fundamental principles of radiation protection are justification, optimisation (ALARA — As Low As Reasonably Achievable), and dose limitation. Practical protective measures include time (minimising exposure duration), distance (maximising distance from source, following inverse‑square law), and shielding (lead aprons, concrete walls).
辐射防护的基本原则包括正当性、最优化（ALARA — 合理可达到的尽可能低）和剂量限值。实际防护措施包括时间（最小化曝露时间）、距离（最大化与源的距离，遵循平方反比定律）和屏蔽（铅围裙、混凝土墙）。
11. Comparison of Imaging Techniques | 成像技术比较
Each imaging modality has strengths and limitations, making it suitable for different clinical scenarios. The table below summarises key features.
每种成像模态都有优势和局限，使其适用于不同的临床场景。下表总结了关键特征。
| Technique | Radiation | Contrast | Primary use |
|---|---|---|---|
| X‑ray / CT | Ionising (high CT dose) | Density, atomic number | Bone, lung, trauma, cancer staging |
| Ultrasound | None | Acoustic impedance | Obstetrics, abdomen, heart |
| MRI | None (non‑ionising) | T1, T2, proton density | Brain, spine, joints, soft tissue |
| Nuclear medicine | Gamma (internal) | Functional uptake | Organ function, tumour detection |
| PET | Positron (internal) | Metabolic activity | Oncology, neurology, cardiology |
While X‑ray and CT provide excellent anatomical detail, they use ionising radiation. Ultrasound and MRI are safer for repeated examinations, particularly in children and during pregnancy. Nuclear medicine and PET show function and can detect diseases before structural changes are visible.
X射线和CT提供卓越的解剖细节，但使用电离辐射。超声和MRI对重复检查更安全，特别是对于儿童和孕期。核医学和PET显示功能，可在结构变化可见之前检测疾病。
12. Exam Tips and Key Formulas | 考试要点与核心公式
Medical physics questions in IB and WJEC exams often assess both qualitative explanations and quantitative problem‑solving. Memorise the exponential attenuation law and the relationship between half‑value thickness and linear attenuation coefficient. Practice calculating intensity after passing through multiple layers of different materials.
IB和WJEC考试中的医疗物理题目通常评估定性解释和定量问题解决。牢记指数衰减定律以及半值厚度与线性衰减系数之间的关系。练习计算穿过多个不同材料层后的强度。
For ultrasound, ensure you can derive the depth formula from time‑delay measurements and explain the importance of impedance matching. Doppler problems may require resolution of velocities along the beam direction. In radiation dosimetry, be precise with units: absorbed dose in Gy, equivalent and effective dose in Sv.
对于超声，确保能够从时间延迟测量推导深度公式，并解释阻抗匹配的重要性。多普勒问题可能需要沿波束方向分解速度。在辐射剂量学中，单位要精确：吸收剂量用Gy，当量剂量和有效剂量用Sv。
Understand the principles of the gamma camera, PET coincidence detection, MRI relaxation times, and the production of X‑rays. Use comparison tables to structure your answers for imaging modalities. Always connect physical principles to clinical benefits and safety considerations, as these demonstrate higher‑level thinking rewarded in mark schemes.
理解伽马相机、PET符合探测、MRI弛豫时间以及X射线的产生等原理。使用对比表格来组织关于成像模态的答案。始终将物理原理与临床收益和安全考虑联系起来，因为这会体现高阶思维，在评分方案中受到奖励。
Key formulas to remember:
需记住的关键公式：
I = I0 e–μx
HVT = ln2 / μ
Z = ρ c
depth = c t / 2
Δf = (2 f0 v cosθ) / c
Equivalent dose = absorbed dose × wR
Revision of these concepts alongside past‑paper questions will build the confidence and fluency required to excel in medical physics.
结合历年真题梳理这些概念，将建立起在医疗物理中取得优异成绩所需的信心和熟练度。
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