Medical Imaging: X-rays, Ultrasound, PET and MRI | 医学成像：X 射线、超声波、PET 与 MRI

📚 Medical Imaging: X-rays, Ultrasound, PET and MRI | 医学成像：X 射线、超声波、PET 与 MRI

Medical imaging uses different parts of the electromagnetic spectrum and sound waves to visualise internal body structures for diagnosis and treatment planning. This revision guide covers the core CIE A-Level Physics topics: X-ray production and attenuation, computed tomography, ultrasound, radionuclide imaging, PET and MRI, with the key physical principles and equations you need to know.

医学成像利用电磁波谱的不同部分和声波来显示体内结构，以辅助诊断和制定治疗方案。本复习指南涵盖 CIE A-Level 物理核心考点：X 射线产生与衰减、计算机断层扫描、超声波、放射性核素成像、PET 和 MRI，包括你需要掌握的关键物理原理和公式。

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1. X-ray Production and the X-ray Spectrum | X 射线产生与能谱

In an X-ray tube, a heated filament emits electrons by thermionic emission. A high potential difference accelerates these electrons across a vacuum towards a tungsten or molybdenum target.

在 X 射线管中，加热灯丝通过热电子发射释放电子。高电势差使这些电子在真空中加速，撞向钨或钼靶。

Most of the electron kinetic energy is converted to thermal energy, but a small fraction produces X-ray photons by two mechanisms: bremsstrahlung (braking radiation) and characteristic radiation. Bremsstrahlung gives a continuous spectrum, while characteristic lines arise from electron transitions between inner atomic shells.

大部分电子动能转化为热能，但一小部分通过两种机制产生 X 射线光子：轫致辐射（制动辐射）和特征辐射。轫致辐射产生连续能谱，而特征谱线来自原子内壳层之间的电子跃迁。

λ_min = hc/eV

The minimum wavelength λ_min occurs when all of an electron’s kinetic energy is converted into one photon. Increasing the tube voltage V raises the maximum photon energy and shifts λ_min to a shorter wavelength. Increasing the tube current raises the intensity of the beam without changing λ_min.

最小波长 λ_min 出现在电子全部动能转化为单个光子的情况。增大管电压 V 会提高最大光子能量，使 λ_min 向更短波长方向移动。增大管电流会提高射线束强度，但不会改变 λ_min。

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2. Attenuation of X-rays | X 射线衰减

When X-rays pass through matter, their intensity I decreases exponentially with thickness x according to the equation below, where μ is the linear attenuation coefficient of the material.

当 X 射线穿过物质时，其强度 I 随厚度 x 按以下公式指数衰减，其中 μ 为材料的线性衰减系数。

I = I₀ e^(−μx)

The half-value thickness x½ is the thickness that reduces the transmitted intensity to half its original value. It is related to μ by x½ = ln 2 / μ, and it is useful for comparing the penetrating ability of different materials.

半值厚度 x½ 是使透射强度降为原来一半的厚度。它与 μ 的关系为 x½ = ln 2 / μ，可用于比较不同材料的穿透能力。

Bone has a much larger μ than soft tissue at diagnostic X-ray energies because bone contains calcium with a higher effective atomic number. This difference produces strong contrast in an X-ray image.

在诊断用 X 射线能量下，骨的 μ 远大于软组织，因为骨含有有效原子序数更高的钙。这种差异会在 X 射线图像中产生强烈对比。

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3. Conventional X-ray Imaging and Contrast | 常规 X 射线成像与对比度

A conventional X-ray image is a two-dimensional projection of the attenuation along each ray path. Dense structures such as bone absorb more radiation and appear white, while air-filled lungs appear dark.

常规 X 射线图像是沿每条射线路径衰减的二维投影。骨等致密结构吸收更多辐射而呈现白色，而充满空气的肺呈现黑色。

Soft tissues have similar attenuation coefficients, so contrast can be enhanced by administering a contrast medium such as barium sulfate or iodine. The contrast medium absorbs X-rays strongly and outlines the organ of interest.

软组织的衰减系数相近，因此可以通过服用硫酸钡或碘等造影剂来增强对比度。造影剂强烈吸收 X 射线，从而勾勒出目标器官的轮廓。

Collimation and lead shielding are used to reduce patient dose and scattered radiation. Image intensifiers or flat-panel detectors improve image quality while allowing lower exposure times.

使用准直器和铅屏蔽来减少患者剂量和散射辐射。影像增强器或平板探测器可提高图像质量，同时缩短曝光时间。

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4. Computed Tomography (CT) Scanning | 计算机断层扫描（CT）

In CT, an X-ray tube and an array of detectors rotate around the patient. The attenuation of many thin beams is recorded at different angles as the patient moves slowly through the gantry.

在 CT 中，X 射线管和探测器阵列围绕患者旋转。随着患者缓慢移动通过机架，系统记录不同角度下许多细射线束的衰减。

A computer reconstructs a cross-sectional image of the slice using algorithms such as filtered back projection. Each pixel in the image represents the local linear attenuation coefficient of the tissue.

计算机利用滤波反投影等算法重建该层的横断面图像。图像中的每个像素代表组织的局部线性衰减系数。

CT gives much better soft-tissue contrast and three-dimensional information than a single projection radiograph, but the radiation dose is considerably higher. It is widely used for brain, chest and abdominal imaging.

CT 的软组织对比度和三维信息远优于单次投影 X 线摄影，但辐射剂量显著更高。它广泛用于脑、胸和腹部成像。

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5. Ultrasound and Piezoelectric Transducer | 超声波与压电换能器

Ultrasound refers to longitudinal sound waves with frequencies above the human hearing range, typically 1–15 MHz for medical scans. Higher frequencies give better resolution but poorer penetration.

超声波是指频率超过人耳听觉范围的纵波，医学扫描通常使用 1–15 MHz。频率越高，分辨率越好，但穿透力越差。

A piezoelectric crystal such as lead zirconate titanate (PZT) changes shape when a voltage is applied, producing ultrasound pulses. When an echo returns, the crystal is compressed and generates a small voltage, so the same transducer acts as both transmitter and receiver.

锆钛酸铅（PZT）等压电晶体在施加电压时会改变形状，从而产生超声脉冲。当回波返回时，晶体受到压缩并产生小电压，因此同一换能器既充当发射器又充当接收器。

A water-based gel is applied to the skin to eliminate air gaps, because air has an acoustic impedance very different from skin and would reflect almost all the ultrasound.

皮肤上涂抹水性耦合凝胶以消除空气间隙，因为空气的声阻抗与皮肤差异极大，几乎会反射所有超声波。

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6. Acoustic Impedance and Reflection at Boundaries | 声阻抗与界面反射

The acoustic impedance Z of a medium is defined as Z = ρc, where ρ is the density and c is the speed of sound. Its SI unit is kg m⁻² s⁻¹.

介质的声阻抗 Z 定义为 Z = ρc，其中 ρ 为密度，c 为声速。其 SI 单位是 kg m⁻² s⁻¹。

Z = ρc

At a boundary between two media, the fraction of ultrasound intensity reflected is given by R = (Z₂ − Z₁)² / (Z₂ + Z₁)². A large impedance mismatch causes a strong echo, while closely matched impedances allow most energy to be transmitted.

在两种介质的界面上，超声强度反射比由 R = (Z₂ − Z₁)² / (Z₂ + Z₁)² 给出。阻抗失配越大，回声越强；阻抗匹配越好，大部分能量越能透射。

R = (Z₂ − Z₁)² / (Z₂ + Z₁)²

For example, the impedance mismatch between air and skin is huge, so ultrasound cannot enter the body without coupling gel. Bone and gas bubbles also produce strong reflections that can shadow deeper tissue.

例如，空气与皮肤的阻抗失配极大，因此没有耦合凝胶时超声波无法进入人体。骨骼和气泡也会产生强反射，可能遮挡更深层组织。

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7. A-scan and B-scan Ultrasound | A 扫描与 B 扫描超声

In an A-scan, the transducer sends a short

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