📚 Medical Physics for CCEA A-Level Physics | CCEA A-Level 物理：医疗物理考点精讲
Medical physics applies the principles of physics to the diagnosis and treatment of disease. From X-ray imaging to MRI, ultrasound to nuclear medicine, these techniques rely on a deep understanding of waves, electromagnetism, atomic structure and quantum phenomena. For CCEA A-Level Physics candidates, mastering the core imaging modalities, their physical principles and their clinical applications is essential.
医疗物理将物理学原理应用于疾病的诊断和治疗。从 X 射线成像到磁共振成像（MRI），从超声到核医学，这些技术都依赖于对波、电磁学、原子结构和量子现象的深入理解。对 CCEA A-Level 物理考生而言，掌握主要的成像模式、其物理原理及临床应用至关重要。
1. Introduction to Medical Imaging | 医学成像导论
Medical imaging techniques fall into two broad categories: non‑ionising and ionising. Non‑ionising methods include ultrasound and MRI, which do not damage cells directly. Ionising methods, such as X‑rays, CT and nuclear medicine, use high‑energy photons or particles that can ionise atoms and potentially cause biological harm. A key theme throughout this topic is balancing diagnostic benefits against risks.
医学成像技术可分为两大类：非电离型和电离型。非电离型包括超声和磁共振成像（MRI），它们不会直接损伤细胞。电离型方法，如 X 射线、CT 和核医学，使用高能光子或粒子，能使原子电离并可能造成生物损害。贯穿本主题的一个核心思想是在诊断获益与风险之间取得平衡。
The choice of imaging modality depends on the clinical question, the required resolution, the need for soft‑tissue contrast, and safety considerations. Key parameters such as spatial resolution, contrast, signal‑to‑noise ratio, and patient exposure are used to compare techniques.
成像模式的选择取决于临床问题、所需分辨率、软组织对比度的需求以及安全考量。空间分辨率、对比度、信噪比和患者暴露等关键参数常用于比较不同技术。
2. Production of X‑rays | X 射线的产生
X‑rays are produced in a rotating‑anode X‑ray tube. A heated filament (cathode) emits electrons by thermionic emission. These electrons are accelerated towards a tungsten target (anode) by a high potential difference, typically 50–150 kV. The accelerated electrons have kinetic energy Ek = eV, where e is the elementary charge and V the tube voltage.
X 射线在旋转阳极 X 射线管中产生。加热的灯丝（阴极）通过热电子发射释放电子。这些电子在 50–150 kV 的高电势差下被加速并撞击钨靶（阳极）。加速电子的动能 Ek = eV，其中 e 为元电荷，V 为管电压。
When high‑speed electrons strike the anode, most of their energy is converted into heat. About 1% produces X‑rays via two mechanisms: Bremsstrahlung (braking radiation) and characteristic radiation. Bremsstrahlung occurs when electrons are decelerated in the electric field of a tungsten nucleus, emitting X‑ray photons with a continuous spectrum. The minimum wavelength (maximum photon energy) is given by λmin = hc / eV.
当高速电子撞击阳极时，大部分能量转化为热量，约 1% 通过两种机制产生 X 射线：轫致辐射（制动辐射）和特征辐射。轫致辐射是电子在钨核电场中减速时发射出连续光谱的 X 射线光子。由 λmin = hc / eV 可得出最短波长（最大光子能量）。
Characteristic radiation occurs when an incoming electron ejects an inner‑shell electron from a tungsten atom. When an outer electron fills the vacancy, an X‑ray photon of a precise energy (characteristic of the element) is emitted. These sharp peaks appear on the X‑ray spectrum superimposed on the continuous Bremsstrahlung background.
特征辐射发生在入射电子将钨原子内壳层电子击出时。当外层电子填补空位时，会发射出具有确定能量（为元素所特有）的 X 射线光子。这些尖锐的峰出现在轫致辐射连续谱背景之上。
3. Interaction of X‑rays with Matter | X 射线与物质的相互作用
As X‑rays pass through tissue, their intensity decreases exponentially according to I = I₀ e−μx, where I₀ is the incident intensity, x the thickness of material, and μ the linear attenuation coefficient. The half‑value thickness (HVT) is x½ = ln 2 / μ.
当 X 射线穿过组织时，其强度按 I = I₀ e−μx 呈指数衰减，其中 I₀ 为入射强度，x 为材料厚度，μ 为线性衰减系数。半值层厚度为 x½ = ln 2 / μ。
Two dominant interaction processes occur in the diagnostic energy range: the photoelectric effect and Compton scattering. In the photoelectric effect, an X‑ray photon is completely absorbed, ejecting an inner‑shell electron. This effect depends strongly on atomic number Z (∝ Z³) and on photon energy (∝ 1/E³). It provides excellent contrast between bone (Z ≈ 13) and soft tissue (Z ≈ 7).
在诊断能量范围内，两种主要的相互作用过程为光电效应和康普顿散射。光电效应中，X 射线光子被完全吸收，击出内层电子。该效应强烈依赖于原子序数 Z（∝ Z³）和光子能量（∝ 1/E³）。它在骨骼（Z ≈ 13）和软组织（Z ≈ 7）之间提供极好的对比度。
Compton scattering is the inelastic scattering of a photon by an outer electron. Only part of the photon energy is transferred; the scattered photon has a longer wavelength. Compton scattering reduces image contrast and can contribute to patient dose and staff exposure. It is dominant at the higher energies used in radiotherapy and CT.
康普顿散射是光子与外层电子发生的非弹性散射，只有部分光子能量被传递，散射光子波长变长。康普顿散射会降低图像对比度，并可能增加患者剂量和工作人员暴露。在放疗和 CT 所用的较高能量范围内，它占主导地位。
4. Diagnostic X‑ray Imaging | 诊断性 X 射线成像
A conventional X‑ray image is a 2‑D projection of a 3‑D anatomy. Different tissues attenuate X‑rays to varying degrees, creating a shadowgram on a detector. Structures with high attenuation (bone) appear white; low attenuation (air‑filled lungs) appear dark. The use of contrast agents such as barium or iodine, which have high Z, artificially enhances the visibility of soft‑tissue structures like the gastrointestinal tract or blood vessels.
常规 X 射线图像是三维解剖结构的二维投影。不同组织对 X 射线的衰减程度不同，从而在探测器上形成阴影图。高衰减结构（骨骼）呈白色，低衰减结构（充气的肺）呈黑色。钡剂或碘剂等高原子序数对比剂的使用，可人为增强胃肠道或血管等软组织结构可见度。
Key factors affecting image quality include quantum mottle (noise from photon statistics), scattered radiation, geometric unsharpness, and the modulation transfer function of the detector. The radiation dose is quantified by the effective dose (measured in sieverts, Sv), which accounts for the radiosensitivity of different tissues.
影响图像质量的关键因素包括量子噪声（光子统计噪声）、散射辐射、几何模糊以及探测器的调制传递函数。辐射剂量由有效剂量（单位希沃特，Sv）量化，该剂量考虑了不同组织的放射敏感性。
5. Computed Tomography (CT) | 计算机断层扫描 (CT)
CT overcomes the superposition problem of planar X‑ray by acquiring many projections at different angles around the patient. A thin, fan‑shaped beam of X‑rays passes through a transverse slice of the body. Detectors on the opposite side measure the transmitted intensity. Using filtered back‑projection or iterative reconstruction algorithms, a cross‑sectional image representing the linear attenuation coefficients μ of each voxel is computed.
CT 通过围绕患者获取不同角度的多幅投影图像，克服了平面 X 射线的重叠问题。一束薄的扇形 X 射线穿过身体的横断面，对面的探测器测量透射强度。利用滤波反投影或迭代重建算法，可计算得到代表每个体素线性衰减系数 μ 的横断面图像。
CT numbers are expressed in Hounsfield Units (HU): HU = (μtissue − μwater) / μwater × 1000. Water has HU = 0, air HU ≈ −1000, and cortical bone HU ≈ +1000 to +3000. The ability to window level and window width allows clinicians to emphasise specific tissue types.
CT 值以亨斯菲尔德单位（HU）表示：HU = (μ组织 − μ水) / μ水 × 1000。水的 HU 为 0，空气 HU ≈ −1000，骨皮质 HU ≈ +1000 至 +3000。通过调整窗位和窗宽，临床医生可以突出显示特定的组织类型。
Modern multi‑slice CT scanners use helical acquisition where the X‑ray tube rotates continuously as the patient table moves. This reduces scan time and allows 3‑D volume reconstruction. However, CT delivers a significantly higher radiation dose than conventional radiography, so justification and optimisation are paramount.
现代多层螺旋 CT 扫描仪采用螺旋采集，即患者检查床移动时 X 射线球管连续旋转。这缩短了扫描时间并实现三维容积重建。然而，CT 的辐射剂量远高于常规 X 射线摄影，因此正当性和最优化至关重要。
6. Ultrasound Principles | 超声波原理
Ultrasound imaging uses high‑frequency sound waves (typically 2–20 MHz) generated and detected by a piezoelectric transducer. The piezoelectric effect converts electrical oscillations into mechanical vibrations and vice versa. When a voltage pulse is applied, the crystal vibrates, emitting an ultrasound pulse into the body. Returning echoes cause the crystal to vibrate, producing an electrical signal.
超声成像使用由压电换能器产生和检测的高频声波（通常 2–20 MHz）。压电效应将电振荡转换为机械振动，反之亦然。施加电压脉冲时，晶体振动，向体内发射超声脉冲。返回的回声使晶体振动，产生电信号。
At tissue interfaces, part of the ultrasound wave is reflected due to differences in acoustic impedance Z = ρc, where ρ is tissue density and c is speed of sound. The reflection coefficient R = [(Z₂ − Z₁) / (Z₂ + Z₁)]². A large impedance mismatch – for example at a soft‑tissue / bone or tissue / air interface – results in a strong echo and poor penetration. A coupling gel is used to eliminate air between the transducer and skin, matching impedances and maximising transmitted intensity.
在组织界面处，部分超声波因声阻抗 Z = ρc 的差异而被反射，其中 ρ 为组织密度，c 为声速。反射系数 R = [(Z₂ − Z₁) / (Z₂ + Z₁)]²。较大的声阻抗失配——例如软组织/骨骼或组织/空气界面——会产生强回声并导致穿透不良。使用耦合凝胶可消除探头与皮肤之间的空气，实现阻抗匹配并最大限度地提高透射强度。
7. Ultrasound Imaging and the Doppler Effect | 超声成像与多普勒效应
A‑mode (amplitude mode) and B‑mode (brightness mode) are the fundamental display modes. In B‑mode, the brightness of each dot corresponds to the echo amplitude, building a real‑time 2‑D grayscale image. The pulse‑echo technique measures the depth of a reflecting interface using d = cΔt / 2, where Δt is the round‑trip time.
A 型（幅度调制型）和 B 型（亮度调制型）是基本的显示模式。在 B 型中，每个像素点的亮度对应回声幅度，从而构建实时二维灰度图像。脉冲回波技术利用 d = cΔt / 2 测量反射界面的深度，其中 Δt 为往返时间。
Doppler ultrasound exploits the frequency shift that occurs when ultrasound is reflected from moving blood cells. The Doppler shift Δf ≈ (2f₀v cosθ) / c, where f₀ is the transmitted frequency, v the blood velocity, θ the angle between the beam and the flow, and c the speed of sound. This allows assessment of blood flow direction and velocity, crucial in vascular studies and cardiac imaging.
多普勒超声利用超声波从运动血细胞反射时发生的频率偏移。多普勒频移 Δf ≈ (2f₀v cosθ) / c，其中 f₀ 为发射频率，v 为血流速度，θ 为声束与血流方向的夹角，c 为声速。据此可以评估血流方向和速度，在血管研究和心脏成像中至关重要。
8. Radioactive Tracers and Gamma Imaging | 放射性示踪剂与伽马成像
Nuclear medicine imaging involves administering a radiopharmaceutical – a molecule labelled with a gamma‑emitting radioisotope – which accumulates in the target organ. The most common isotope is technetium‑99m (99mTc), produced from a molybdenum‑99 generator. It emits gamma photons of 140 keV, ideal for detection with a gamma camera, and has a half‑life of 6 hours, minimising patient dose.
核医学成像需给予放射性药物（一种标记了 γ 放射性同位素的分子），该药物在靶器官中聚集。最常用的同位素是锝‑99m（99mTc），由钼‑99 发生器生产。它发射能量为 140 keV 的 γ 光子，非常适于用伽马相机探测，且半衰期为 6 小时，可最大限度地减少患者剂量。
A gamma camera consists of a collimator (typically lead with parallel holes), a large‑area NaI(Tl) scintillation crystal, an array of photomultiplier tubes (PMTs), and electronics for position and energy calculation. The collimator ensures only gamma rays travelling perpendicularly strike the crystal, forming a 2‑D projection of tracer distribution. Anger logic determines the position of each scintillation event.
伽马相机由准直器（通常为带有平行孔的铅制品）、大面积 NaI(Tl) 闪烁晶体、光电倍增管阵列以及用于计算位置和能量的电子电路组成。准直器确保只有沿垂直方向行进的 γ 射线击中晶体，从而形成示踪剂分布的二维投影。安格逻辑确定每个闪烁事件的位置。
9. Positron Emission Tomography (PET) | 正电子发射断层扫描 (PET)
PET uses positron‑emitting isotopes such as fluorine‑18 (18F) labelled to a glucose analogue (FDG). The emitted positron travels a short distance (<1 mm) before annihilating with an electron, producing two 511 keV annihilation photons emitted back‑to‑back. A ring of detectors registers coincident photon pairs, allowing the line‑of‑response to be determined. PET thus provides functional images of metabolic activity, invaluable in oncology, neurology, and cardiology.
PET 使用正电子发射同位素，如用氟‑18（18F）标记的葡萄糖类似物（FDG）。发射出的正电子在行进很短距离（<1 mm）后与电子发生湮灭，产生两个背向发射的 511 keV 湮灭光子。一圈探测器记录符合光子对，从而确定响应线。因此 PET 提供代谢活动的功能图像，在肿瘤学、神经学和心脏病学中极具价值。
The main advantage of PET over SPECT is its higher spatial resolution and the ability to quantify tracer uptake. Modern scanners combine PET with CT (PET‑CT) to overlay functional data on anatomical detail, improving diagnostic accuracy.
与 SPECT 相比，PET 的主要优势在于更高的空间分辨率和定量示踪剂摄取值的能力。现代扫描仪将 PET 与 CT 结合（PET‑CT），将功能数据叠加到解剖细节上，提高诊断准确性。
10. Magnetic Resonance Imaging (MRI) | 磁共振成像 (MRI)
MRI exploits the magnetic properties of hydrogen nuclei (protons) abundant in water and fat. The patient is placed in a strong, uniform magnetic field B₀ (typically 1.5–3 T). Protons align with the field, producing a net macroscopic magnetisation. Their precession frequency is the Larmor frequency: f = γB₀ / 2π, where γ is the gyromagnetic ratio (42.6 MHz/T for protons).
MRI 利用了水和脂肪中大量存在的氢核（质子）的磁特性。患者被置于强而均匀的静磁场 B₀（通常 1.5–3 T）中。质子与外磁场对齐，产生净宏观磁化。质子的进动频率为拉莫尔频率：f = γB₀ / 2π，其中 γ 为旋磁比（质子为 42.6 MHz/T）。
A radiofrequency (RF) pulse at the Larmor frequency tips the magnetisation into the transverse plane. After the pulse ends, the nuclei relax back to equilibrium, emitting RF signals that are detected by receiver coils. Two relaxation times are crucial: T₁ (spin‑lattice relaxation) describes recovery of longitudinal magnetisation, and T₂ (spin‑spin relaxation) describes decay of transverse magnetisation. Image contrast can be weighted towards T₁, T₂, or proton density by adjusting pulse sequence parameters.
以拉莫尔频率施加射频（RF）脉冲将磁化矢量偏转至横向平面。脉冲结束后，核自旋弛豫回平衡态，发射可被接收线圈检测的射频信号。两个弛豫时间至关重要：T₁（自旋‑晶格弛豫）描述纵向磁化恢复，T₂（自旋‑自旋弛豫）描述横向磁化衰减。通过调整脉冲序列参数，可以使图像对比度加权重于 T₁、T₂ 或质子密度。
Spatial encoding is achieved through magnetic field gradients. Slice selection, phase encoding, and frequency encoding localise the signal in three dimensions. MRI provides exceptional soft‑tissue contrast without ionising radiation, though it is contraindicated for patients with certain metallic implants.
空间编码通过磁场梯度实现。层面选择、相位编码和频率编码将信号在三维空间中定位。MRI 在不使用电离辐射的情况下提供了出色的软组织对比度，但某些金属植入物的患者禁用。
11. Endoscopy and Fibre Optics | 内窥镜与光纤
Endoscopy enables direct visualisation of internal cavities using a flexible bundle of optical fibres. Each fibre consists of a high‑refractive‑index core surrounded by a lower‑index cladding. Light rays entering the core at an angle greater than the critical angle undergo total internal reflection, making them travel long distances along the fibre with minimal loss.
内窥镜使用柔性光纤束直接观察内部腔体。每根光纤由高折射率纤芯和低折射率包层构成。以大于临界角的角度进入纤芯的光线发生全内反射，可沿光纤长距离传输且损耗极小。
Coherent bundles preserve the spatial relationship between fibres, allowing an image to be transmitted. Incoherent bundles are used purely for illumination. Additional channels in the endoscope allow passage of air, water, suction, and surgical instruments. Today, video endoscopes replace fibre bundles with a miniature CCD sensor at the distal tip, providing higher resolution images.
相干光纤束保持纤维之间的空间关系，可传输图像。非相干光纤束仅用于照明。内窥镜中附加的通道可导入空气、水、抽吸或手术器械。现今，视频内窥镜用远端的微型 CCD 传感器取代了光纤束，提供更高分辨率的图像。
12. Comparison of Imaging Techniques | 成像技术比较
Selecting the appropriate imaging modality requires consideration of resolution, contrast mechanism, safety, availability, and cost. X‑ray and CT offer high spatial resolution but involve ionising radiation. Ultrasound is real‑time, portable, and safe, but limited by bone and gas. MRI provides excellent soft‑tissue contrast, while nuclear medicine offers functional and metabolic information. No single technique is superior for all clinical scenarios; they are complementary tools in modern medicine.
选择适当的成像模式需考虑分辨率、对比机制、安全性、可及性和成本。X 射线与 CT 提供高空间分辨率，但涉及电离辐射。超声为实时、便携、安全的检查，但受骨骼和气体限制。MRI 提供出色的软组织对比度，而核医学提供功能与代谢信息。没有哪一种技术在所有的临床场景中都占优，它们是现代医学中互补的工具。
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