📚 Using Ultrasound in Medicine | 医学中的超声波应用
Ultrasound has become an indispensable tool in modern medicine, enabling non-invasive visualisation of internal organs and blood flow. Unlike X-rays, ultrasound uses high-frequency sound waves, which are considered safer for repeated use and for imaging fetuses. This article explores the physics behind medical ultrasound, from the piezoelectric effect to pulse-echo imaging, A-scans, B-scans, and Doppler blood flow measurement, following the CIE A-Level Physics syllabus.
超声波已成为现代医学中不可或缺的工具，可实现内部器官和血流的无创可视化。与X射线不同，超声波使用高频声波，被认为对重复使用和胎儿成像更安全。本文遵循CIE A-Level物理大纲，探讨医学超声背后的物理学，从压电效应到脉冲回波成像、A型扫描、B型扫描和多普勒血流测量。
1. What is Ultrasound? | 什么是超声波？
Ultrasound refers to sound waves with frequencies above 20 kHz, which is beyond the upper limit of human hearing. In medical diagnostics, much higher frequencies are used, typically in the range of 1 MHz to 20 MHz. These high-frequency mechanical waves travel through soft tissues and undergo partial reflection at boundaries between different tissue types. By analysing the reflected echoes, detailed cross-sectional images of organs, blood vessels, and even a developing fetus can be constructed without using ionising radiation.
超声波是指频率高于20 kHz、超出人类听觉上限的声波。在医学诊断中，通常使用频率高得多的声波，范围约为1 MHz至20 MHz。这些高频机械波在软组织中传播，并在不同组织类型之间的界面处发生部分反射。通过分析反射回波，无需使用电离辐射即可构建器官、血管甚至发育中胎儿的详细截面图像。
2. Producing Ultrasound: The Piezoelectric Effect | 超声波的产生：压电效应
Medical ultrasound transducers rely on the piezoelectric effect. A piezoelectric crystal, such as lead zirconate titanate (PZT), deforms when a varying potential difference is applied across it, producing vibrations that generate ultrasound waves. Conversely, when the returning echo strikes the crystal, it induces an alternating voltage across the crystal. The same transducer therefore acts as both a transmitter and a receiver of ultrasound pulses. The crystal is cut to a thickness equal to half the wavelength of the desired ultrasound frequency to achieve resonance, maximising the efficiency of wave generation.
医学超声换能器依赖于压电效应。当在压电晶体（如锆钛酸铅，PZT）两端施加交变电压时，晶体会产生形变并振动，从而产生超声波。相反，当反射回波撞击晶体时，会在晶体两端感应出交变电压。因此，同一个换能器既充当超声脉冲的发射器又充当接收器。晶片被切割成厚度等于所需超声波波长的一半，以达到共振，从而最大限度地提高波的产生效率。
3. Acoustic Impedance and Reflection at Boundaries | 声阻抗与界面反射
When an ultrasound wave encounters a boundary between two media with different acoustic impedances, part of the wave is reflected and part is transmitted. The acoustic impedance Z of a medium is defined as the product of its density ρ and the speed of sound c in that medium:
Z = ρc
The fraction of intensity reflected is given by the reflection coefficient R for normal incidence:
R = (Z₂ − Z₁)² / (Z₂ + Z₁)²
To maximise transmission of ultrasound into the body, a coupling gel is applied between the transducer and the skin. This gel eliminates air, which has a very low acoustic impedance compared to skin, and its impedance is matched more closely to that of soft tissue, thereby reducing the strong reflection that would otherwise occur at the air–skin interface.
当超声波遇到具有不同声阻抗的两种介质之间的界面时，一部分波被反射，一部分波被透射。介质的声阻抗Z定义为它的密度ρ与该介质中声速c的乘积。
Z = ρc
法向入射时反射的强度比例由反射系数R给出：
R = (Z₂ − Z₁)² / (Z₂ + Z₁)²
为了最大限度地提高超声波传入体内的效率，在换能器与皮肤之间涂抹耦合凝胶。这种凝胶排除了空气（其声阻抗与皮肤相比非常低），并且其阻抗更接近软组织，从而减少了原本会在空气-皮肤界面处发生的强烈反射。
4. The Pulse-Echo Principle | 脉冲回波原理
In diagnostic ultrasound, short pulses of sound are emitted by the transducer, and the time delay t between transmission and reception of the echo is measured. Since the pulse travels to the reflecting surface and back, the distance d from the transducer to the interface is given by
d = (c × t) / 2
where c is the average speed of sound in the tissue (approximately 1540 m s⁻¹ in soft tissue). By recording multiple echoes and knowing the speed, a depth profile of reflecting interfaces can be built up, which is the basis of both A-scan and B-scan techniques.
在诊断超声中，换能器发射短声脉冲，并测量从发射到接收回波之间的时间延迟t。由于脉冲传播到反射面并返回，从换能器到界面的距离d由下式给出：
d = (c × t) / 2
其中c是组织中的平均声速（软组织中约为1540 m s⁻¹）。通过记录多个回波并已知速度，可以建立反射界面的深度轮廓，这是A型扫描和B型扫描技术的基础。
5. A-scan: Amplitude Scan | A型扫描：振幅扫描
An A-scan (Amplitude scan) displays the amplitude of received echoes as a function of time on a simple oscilloscope-type display. The horizontal axis represents time (hence depth), and the vertical deflection represents the echo intensity. A-scans are used in ophthalmology to measure the axial length of the eye, detect retinal detachment, or locate a foreign body. The distinct peaks correspond to reflections from the cornea, lens, and retina. Because no lateral information is recorded, an A-scan gives a one-dimensional plot of tissue interfaces along a single line of sight.
A型扫描（振幅扫描）在简单的示波器式显示屏上将接收到的回波振幅显示为时间的函数。水平轴代表时间（因此也表示深度），而垂直偏转则表示回波强度。A型扫描在眼科中用于测量眼轴长度、检测视网膜脱离或定位异物。清晰的峰值对应于来自角膜、晶状体和视网膜的反射。由于没有记录横向信息，A型扫描给出的是沿单条视线方向上组织界面的一维图形。
6. B-scan: Brightness Scan for 2D Imaging | B型扫描：亮度扫描用于二维成像
A B-scan (Brightness scan) produces a two-dimensional cross-sectional image. The transducer is moved across the skin, and at each position an A-scan is performed. Instead of displaying amplitude as a trace, the echo amplitude is converted to a brightness level at the corresponding depth on a screen. Many such A-lines are combined side by side to build up a 2D greyscale image. B-scans are the most common form of medical ultrasound imaging, used extensively for abdominal scans, fetal monitoring, and cardiac assessments. Modern systems use electronic phased-array transducers that steer and focus the beam rapidly without mechanical movement.
B型扫描（亮度扫描）产生二维截面图像。换能器在皮肤上移动，在每个位置进行一次A型扫描。与以轨迹形式显示振幅不同，回波振幅被转换为屏幕上相应深度处的亮度水平。将许多这样的A线并排组合，就组成了一幅二维灰度图像。B型扫描是最常见的医学超声成像形式，广泛用于腹部扫描、胎儿监测和心脏评估。现代系统使用电子相控阵换能器，可在无需机械移动的情况下快速引导和聚焦波束。
7. Real-time B-scan and 3D Ultrasound | 实时B超与三维超声
In a real-time B-scan, multiple frames are acquired per second (typically 20–60 frames per second) by electronically steering the ultrasound beam across a region. This allows the operator to view moving structures such as heart valves or fetal movements in real time. Further processing of multiple closely spaced 2D images allows for 3D volume rendering, which is commonly used in obstetric imaging to show facial features of the fetus. 3D ultrasound adds depth perception but the underlying resolution is still governed by the same physical principles as 2D imaging.
在实时B型扫描中，通过电子方式沿一个区域操控超声波束，每秒可采集多帧图像（通常每秒20-60帧）。这使得操作者可以实时观察心脏瓣膜或胎动等运动结构。对多个紧密间隔的二维图像进行进一步处理后可实现三维容积渲染，这在产科成像中常用于显示胎儿的面部特征。三维超声增加了深度感知，但其基本分辨率仍受与二维成像相同的物理原理支配。
8. Doppler Ultrasound for Blood Flow Measurement | 多普勒超声测量血流
When ultrasound is scattered by moving red blood cells, the frequency of the echoed signal is shifted due to the Doppler effect. For a blood vessel inclined at an angle θ to the ultrasound beam, the Doppler frequency shift Δf is given by
Δf = 2 f₀ v cos θ / c
where f₀ is the transmitted frequency, v is the velocity of blood, and c is the speed of sound in tissue. The factor 2 arises because the wave undergoes a shift upon hitting the moving cells and again upon reflection back to the transducer. By measuring Δf, the blood flow velocity can be determined. Direction of flow is obtained from whether Δf is positive (towards the transducer) or negative (away). Colour Doppler overlays this information onto a B-scan image, typically showing flow towards the probe in red and away in blue.
当超声波被运动中的红细胞散射时，由于多普勒效应，回波信号的频率会发生偏移。对于与超声波束成角度θ的血管，多普勒频移Δf由下式给出：
Δf = 2 f₀ v cos θ / c
其中f₀是发射频率，v是血流速度，c是组织中的声速。系数2的出现是因为波在碰到运动细胞时发生一次频移，在反射回换能器时又发生一次。通过测量Δf，可以确定血流速度。流动方向由Δf的正（朝向换能器）或负（远离换能器）来判断。彩色多普勒将这些信息叠加在B型扫描图像上，通常以红色表示流向探头，蓝色表示流离探头。
9. Factors Affecting Image Resolution | 影响图像分辨率的因素
Axial resolution, the ability to distinguish two targets along the beam direction, depends on the pulse duration and wavelength. A shorter pulse (higher frequency) gives better axial resolution because ultrasonic pulses contain fewer cycles. The minimum resolvable axial distance is roughly half the spatial pulse length. Lateral resolution depends on the width of the ultrasound beam; a narrower beam improves the ability to separate adjacent points. However, attenuation of ultrasound in tissue increases approximately linearly with frequency, limiting the effective penetration depth. Typical diagnostic frequencies involve a compromise: 3–5 MHz for deeper abdominal organs and 7–15 MHz for superficial structures such as thyroid and breast.
轴向分辨率，即沿波束方向区分两个目标的能力，取决于脉冲持续时间和波长。更短的脉冲（更高频率）可提供更好的轴向分辨率，因为超声脉冲包含的周期数较少。可分辨的最小轴向距离大约为空间脉冲长度的一半。侧向分辨率取决于超声波束的宽度；更窄的波束可提高分离相邻点的能力。然而，超声波在组织中的衰减随频率大致呈线性增加，从而限制了有效穿透深度。典型的诊断频率需要折中：较深腹部脏器使用3-5 MHz，甲状腺、乳腺等浅表结构使用7-15 MHz。
10. Intensity, Attenuation and Safety | 强度、衰减与安全性
The intensity I of an ultrasound beam is the power per unit area (W m⁻²). As the beam traverses tissue, energy is absorbed and scattered, causing attenuation. Absorption leads to heating, while very high intensities can cause the formation and violent collapse of gas bubbles, a phenomenon known as cavitation. Diagnostic ultrasound operates at spatial-peak temporal-average intensities well below the thresholds that produce biological effects. The ALARA principle (As Low As Reasonably Achievable) is applied to keep exposure minimised. Higher intensities are used therapeutically in High-Intensity Focused Ultrasound (HIFU), which can destroy targeted tissue such as tumours by thermal coagulation.
超声波束的强度I是单位面积的功率（W m⁻²）。当波束穿过组织时，能量被吸收和散射，导致衰减。吸收引起加热，而非常高的强度可导致气泡的形成和剧烈坍塌，这种现象称为空化。诊断超声工作时的空间峰值时间平均强度远低于产生生物效应的阈值。遵循ALARA原则（合理可行尽量低）以将暴露降至最低。治疗中会使用更高强度的聚焦超声（HIFU），通过热凝固作用破坏肿瘤等靶组织。
11. Advantages and Limitations in Medicine | 医学中的优点与局限性
Advantages: Ultrasound imaging is non-invasive, portable, and relatively inexpensive compared to MRI or CT. It uses no ionising radiation, making it safe for obstetric imaging and repeated scans. It provides real-time images that allow assessment of motion, such as heart valve function and blood flow. Limitations: Ultrasound is strongly reflected by bone and gas, making it difficult to image the brain, lungs, and structures behind bones. Image quality is highly operator-dependent and can be poor in obese patients due to greater attenuation. The resolution is inherently limited by wavelength, so it cannot match the fine detail of MRI in many applications.
优点：超声成像无创、便携，且相对于MRI或CT价格低廉。它不使用电离辐射，因此可用于产科成像和重复扫描，十分安全。它提供实时图像，可以评估运动情况，如心瓣膜功能和血流。局限性：超声波会被骨骼和气体强烈反射，因此难以对脑、肺以及骨骼后方的结构成像。图像质量高度依赖操作者，且肥胖患者因衰减更高可能导致图像不佳。分辨力本质受波长限制，因此在许多应用中细节不如MRI。
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