A2 Physics: Medical Physics Key Points | A2 物理：医疗物理 考点精讲

📚 A2 Physics: Medical Physics Key Points | A2 物理：医疗物理 考点精讲

Medical physics covers the physical principles behind major diagnostic and therapeutic tools, including X-rays, ultrasound, nuclear medicine and MRI. Understanding these concepts is essential for answering A2 exam questions on imaging, dosimetry and safety.

医疗物理涵盖了X射线、超声、核医学和磁共振等主要诊断与治疗工具背后的物理原理。学习这些概念对于解答A2考试中关于成像、剂量和安全性的问题至关重要。

1. X-ray Production and Spectrum | X射线的产生与光谱

X-rays are produced when high-energy electrons from a heated cathode are accelerated across a large potential difference and strike a rotating metal anode.

当热阴极发出的高能电子经过大电位差加速并撞击旋转的金属阳极时，就会产生X射线。

The X-ray spectrum consists of a continuous background (bremsstrahlung) due to electrons decelerating near nuclei, and sharp characteristic peaks caused by inner-shell electron transitions.

X射线光谱包含由电子在原子核附近减速产生的连续轫致辐射背景，以及由内壳层电子跃迁产生的尖锐特征峰。

λ_min = hc / eV

The minimum wavelength λ_min corresponds to the maximum photon energy, where all kinetic energy of an electron is converted into a single photon.

最短波长 λ_min 对应于最大光子能量，此时电子的全部动能转化为单个光子。

2. X-ray Attenuation Mechanisms | X射线的衰减机制

As an X-ray beam passes through matter, its intensity decreases due to photoelectric absorption, Compton scattering and pair production (the latter only above 1.02 MeV).

X射线束通过物质时，由于光电吸收、康普顿散射以及电子对效应（仅发生在1.02 MeV以上）强度会下降。

In diagnostic energy ranges (20–150 keV), the photoelectric effect is dominant in high-Z materials such as bone, giving excellent contrast, while Compton scattering dominates in soft tissue.

在诊断能量范围（20–150 keV）内，光电效应在骨骼等高Z值材料中占主导地位，提供良好对比度，而康普顿散射在软组织中占主导。

3. Attenuation Coefficient and Half-Value Thickness | 衰减系数与半价层

The exponential attenuation of a monoenergetic X-ray beam is described by:

单能X射线束的指数衰减规律如下：

I = I₀ e^(-μx)

where μ is the linear attenuation coefficient (unit: m^-1 or cm^-1).

其中 μ 为线性衰减系数（单位：m^-1 或 cm^-1）。

The half-value thickness (HVT) is the thickness required to reduce intensity to half its initial value:

半价层是将强度降低到初始值一半所需的厚度：

x₁/₂ = ln 2 / μ

Bone has a higher μ than soft tissue, so it attenuates X-rays more strongly and appears white on a radiograph.

骨骼的 μ 值比软组织高，因此对X射线的衰减更强，在X光片上呈现白色。

4. Image Contrast Enhancement | 图像对比度增强

Contrast can be enhanced by administering contrast media with high atomic numbers, such as barium sulfate (barium meal) or iodine compounds.

通过使用高原子序数的造影剂，如硫酸钡（钡餐）或碘化合物，可以增强对比度。

These substances fill soft-tissue cavities and absorb X-rays more effectively, allowing outlines of the digestive tract or blood vessels to become visible.

这些物质填充软组织腔体并更有效地吸收X射线，使消化道或血管的轮廓变得可见。

Exposure factors (kVp, mAs) and grid techniques are also used to reduce scattered radiation and improve image sharpness.

曝光参数（千伏峰值、毫安秒）和滤线栅技术也用于减少散射辐射并提高图像锐度。

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

A CT scanner rotates an X-ray tube and detector array around the patient, acquiring many projections from different angles to reconstruct cross-sectional images.

CT扫描仪旋转X射线管和探测器阵列围绕患者，从不同角度获取许多投影，重建出横截面图像。

The image is divided into voxels (volume elements), and each voxel is assigned a CT number (Hounsfield unit) based on its linear attenuation coefficient:

图像被划分为体素，每个体素根据其线性衰减系数分配一个CT值（亨氏单位）：

CT number = 1000 × (μ_tissue – μ_water) / μ_water

Windowing allows the radiologist to select a range of CT numbers for display, optimising contrast for different tissues (e.g., lung vs bone).

窗宽窗位技术使放射科医师能够选择CT值显示范围，针对不同组织（如肺与骨骼）优化对比度。

6. Ultrasound Imaging Principles | 超声成像原理

Ultrasound uses high-frequency sound waves (typically 2–18 MHz) generated by a piezoelectric transducer that converts electrical pulses into mechanical vibrations and vice versa.

超声使用高频声波（通常为2–18 MHz），由压电换能器产生，它将电脉冲转换为机械振动，反之亦然。

The pulse-echo technique measures the time delay and intensity of echoes reflected from tissue boundaries with different acoustic impedances Z = ρc.

脉冲回波技术测量从具有不同声阻抗 Z = ρc 的组织边界反射回来的回声的时间延迟和强度。

Coupling gel is essential to exclude air between the transducer and skin, since almost 100% of ultrasound is reflected at an air–tissue interface.

必须使用耦合凝胶排除换能器与皮肤之间的空气，因为在空气-组织界面几乎100%的超声波会被反射。

7. Doppler Effect in Ultrasound | 超声多普勒效应

When ultrasound is reflected from moving red blood cells, the frequency shift Δf is proportional to the velocity v of the blood flow:

当超声波从运动的红细胞反射时，频率偏移 Δf 与血流速度 v 成正比：

Δf = (2 f₀ v cos θ) / c

where f₀ is the transmitted frequency, θ is the angle between the ultrasound beam and blood flow, and c is the speed of sound in tissue (≈ 1540 m s^-1).

其中 f₀ 为发射频率，θ 为超声波束与血流方向之间的夹角，c 为组织中的声速（≈1540 m s^-1）。

Colour Doppler assigns a colour map (red towards, blue away) to visualise flow direction and detect stenosis or valve defects.

彩色多普勒将颜色映射（朝向探头红色，远离探头蓝色），以可视化血流方向并检测狭窄或瓣膜缺损。

8. Nuclear Medicine and PET Scanning | 核医学与PET扫描

In nuclear medicine, a radiopharmaceutical (such as technetium-99m) is introduced into the body; it accumulates in specific organs and emits gamma rays detected by a gamma camera.

在核医学中，放射性药物（如锝-99m）被引入体内，聚集在特定器官并发射伽马射线，由伽马相机探测。

Positron emission tomography (PET) uses β⁺-emitting isotopes (e.g., fluorine-18). The emitted positron annihilates with an electron, producing two 511 keV gamma photons travelling in opposite directions.

正电子发射断层扫描（PET）使用发射β⁺的同位素（如氟-18）。发射的正电子与电子湮灭，产生两个沿相反方向运动的511 keV伽马光子。

Coincidence detection along a line of response allows computer reconstruction of a 3D map of metabolic activity, essential for oncology and neurology.

沿响应线的符合探测技术可通过计算机重建代谢活动的三维图像，在肿瘤学和神经学中至关重要。

9. Magnetic Resonance Imaging (MRI) | 磁共振成像 (MRI)

MRI relies on the nuclear magnetic resonance of hydrogen nuclei (protons) in water and fat. In a strong static magnetic field B₀, protons align parallel or anti-parallel, creating a net magnetisation.

MRI依赖于水与脂肪中氢核（质子）的核磁共振。在强静磁场 B₀ 中，质子平行或反平行排列，产生净磁化强度。

A radiofrequency pulse at the Larmor frequency f = γ B₀ (where γ is the gyromagnetic ratio) flips the magnetisation; when the pulse stops, protons relax, emitting signals detected by RF coils.

在拉莫尔频率 f = γ B₀（其中γ为回磁比）的射频脉冲将磁化强度翻转；脉冲停止后质子弛豫，发射出由射频线圈检测的信号。

T₁ and T₂ relaxation times differ between tissues, providing excellent soft-tissue contrast without ionising radiation.

不同组织的 T₁ 和 T₂ 弛豫时间不同，无需电离辐射即可提供优良的软组织对比度。

10. Safety and Biological Effects | 安全与生物效应

Ionising radiation (X-rays, gamma rays) can break chemical bonds and damage DNA, leading to deterministic effects (e.g., skin burns at high dose) and stochastic effects (e.g., cancer induction).

电离辐射（X射线、伽马射线）可断裂化学键并损伤DNA，导致确定性效应（如高剂量下的皮肤灼伤）和随机效应（如诱发癌症）。

The absorbed dose D is measured in grays (Gy), but the effective dose in sieverts (Sv) accounts for radiation type (quality factor) and tissue sensitivity.

吸收剂量 D 以戈瑞（Gy）为单位，而有效剂量以希沃特（Sv）为单位，考虑了辐射类型（品质因数）和组织敏感性。

Ultrasound and MRI are considered non-ionising and generally safer, though heating (ultrasound) and RF deposition (MRI) must still be monitored.

超声和MRI被认为无电离，通常更安全，但仍需监测加热效应（超声）和射频能量沉积（MRI）。

The ALARA principle (As Low As Reasonably Achievable) guides all medical imaging protocols to minimise patient exposure while maintaining diagnostic quality.

ALARA原则（尽可能低剂量）指导所有医学成像流程，在保持诊断质量的同时最大限度减少患者暴露。

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Published by TutorHao | Physics Revision Series | aleveler.com

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