📚 The Principles of Computed Axial Tomography | 计算机轴向断层扫描原理
Computed axial tomography (CAT or CT) is an imaging technique that produces cross-sectional images of the body by measuring the transmission of X-rays through a thin slice and reconstructing the internal distribution of linear attenuation coefficients.
计算机轴向断层扫描（CAT或CT）是一种成像技术，通过测量X射线穿透人体某一薄层后的透射强度，重建出该薄层内线性衰减系数的空间分布，从而获得身体的断面图像。
1. From Plain X-rays to CT | 从普通X射线到CT
A conventional X-ray image is a shadow of all the tissues lying between the X-ray tube and the film or detector. Structures overlap in projection, and small differences in soft-tissue density are often impossible to distinguish.
普通X射线照片是位于X射线管与胶片或探测器之间所有组织的叠加阴影。各结构在投影中相互重叠，软组织之间轻微的密度差异往往难以分辨。
CT overcomes this problem by examining the body one thin slice at a time. The X-ray beam is confined to a narrow slice, and measurements are taken from many angles around that slice. A computer then reconstructs a two-dimensional cross-sectional image.
CT通过逐层检查身体来克服这一问题。X射线束被限制在一个薄层内，并围绕该层从多个角度测量透射强度，随后由计算机重建出二维断面图像。
The word ‘axial’ indicates that the slice is normally taken perpendicular to the long axis of the patient. The term ‘computed’ emphasises that the image is not a direct shadow but is calculated from numerical data.
“轴向”一词表示断层切面通常垂直于患者身体的长轴方向。“计算机”一词强调CT图像不是直接投影，而是根据数字数据计算出来的。
2. Exponential Attenuation of X-rays | X射线的指数衰减
When a narrow, monoenergetic X-ray beam passes through a uniform material, its intensity decays exponentially with thickness. If the linear attenuation coefficient is μ and the thickness is x, the transmitted intensity I is related to the initial intensity I₀ by:
当一束窄的、单能量的X射线穿过均匀物质时，其强度随厚度呈指数衰减。若线性衰减系数为μ，厚度为x，则透射强度I与初始强度I₀的关系为：
I = I₀ e−μx
The linear attenuation coefficient μ depends on the density of the material, its atomic number and the photon energy. Dense materials such as bone attenuate X-rays much more strongly than air or soft tissue.
线性衰减系数μ取决于材料的密度、原子序数以及光子能量。骨骼等致密材料对X射线的衰减远强于空气或软组织。
In the body, tissues are not uniform along a ray. The path can be divided into many small elements, each with its own coefficient μᵢ and thickness Δx. The total attenuation therefore involves the sum of μᵢΔx along the ray.
人体内组织沿射线路径并不均匀。可将路径划分为许多小单元，每个单元有各自的衰减系数μᵢ和厚度Δx。因此总衰减等于沿射线路径上所有μᵢΔx之和。
In mathematical terms, the transmitted intensity is an exponential of a line integral:
用数学语言来说，透射强度是某个线积分的指数函数：
I = I₀ exp(−∫ μ(x) dx)
This line integral is exactly what a CT scanner measures. Each X-ray ray path gives one ‘projection value’ related to the total attenuation along that line.
这个线积分正是CT扫描仪实际测量的物理量。每一条X射线路径都给出一个与沿线总衰减相关的“投影值”。
3. Main Components of a CT Scanner | CT扫描仪的主要部件
A CT scanner contains an X-ray tube, a patient table, a detector array, a high-voltage generator and a powerful computer. The X-ray tube and detectors are mounted on a ring-shaped gantry that can rotate around the patient.
CT扫描仪包含X射线管、患者检查床、探测器阵列、高压发生器和功能强大的计算机。X射线管和探测器安装在一个可绕患者旋转的环形机架（gantry）上。
Collimators in front of the tube limit the X-ray beam to a narrow fan. Detectors on the opposite side of the patient measure the transmitted intensity. The detectors must have a fast response, high sensitivity and a wide dynamic range.
X射线管前方的准直器将X射线束限制为窄扇形束。患者对侧的探测器测量透射强度。探测器必须响应快、灵敏度高并且具有宽的动态范围。
The patient lies on a table that moves stepwise through the gantry. After one slice has been scanned, the table advances by the slice thickness and the next slice is scanned. This step-and-shoot method was the original ‘axial’ scan mode.
患者躺在检查床上，床体逐步穿过机架。完成一个断层的扫描后，床体前进一个断层厚度的距离，再扫描下一层。这种“步进-曝光”方式就是最初“轴向”扫描模式。
The same fan-beam geometry can also be operated in a spiral or helical mode, where the X-ray tube rotates continuously while the table moves smoothly. Spiral CT allows faster scanning and is now the most common clinical mode.
同样的扇形束几何结构也可采用螺旋扫描模式，即X射线管连续旋转，同时床体平稳移动。螺旋CT扫描速度更快，是目前最常用的临床模式。
4. Axial Scanning and Data Collection | 轴向扫描与数据采集
During an axial CT scan, the X-ray tube rotates around the patient while detectors record transmitted radiation at many angular positions. At each angle, an entire fan of X-rays passes through the slice and is detected simultaneously.
在轴向CT扫描中，X射线管围绕患者旋转，探测器在多个角度记录透射辐射。在每个角度，整束扇形X射线穿过目标断层并被探测器同时接收。
The patient remains stationary during each rotation, so the image represents a single anatomical slice. Because the beam is narrow, most scattered photons are rejected, which improves the contrast and accuracy of the measured attenuation values.
在每次旋转期间患者保持静止，因此图像代表单一解剖断面。由于射线束很窄，大部分散射光子被排除，从而提高了测量衰减值的对比度和准确性。
For one slice, the scanner may collect several hundred to over a thousand projections. Each projection contains intensity measurements from hundreds of individual detector elements. The complete set is called a sinogram because a point inside the slice traces out a sinusoidal pattern in projection space.
对于一个断层，扫描仪可能采集几百甚至上千个角度投影。每个投影包含来自数百个独立探测器单元的强度数据。完整的数据集合称为正弦图（sinogram），因为断层内的一个点在投影空间中会描绘出正弦曲线轨迹。
5. From Intensity Measurements to Projections | 从强度测量到投影值
The raw detector readings must be converted into attenuation data. For each ray, the transmitted intensity I is compared with the incident intensity I₀, and the logarithmic quantity ln(I₀/I) is calculated.
探测器的原始读数必须转换为衰减数据。对每一条射线，将透射强度I与入射强度I₀比较，并计算对数量ln(I₀/I)。
This logarithm is proportional to the line integral of μ along the ray. A larger value means that the averaged tissue along the ray is denser or more attenuating. The set of all these line-integral values is called a projection.
这个对数值与沿射线的μ线积分成正比。数值越大，说明沿该射线路径的平均组织越致密或衰减能力越强。所有这些线积分值的集合称为一个投影。
In practice, corrections are needed for beam hardening, detector sensitivity variations and background noise. Modern scanners apply calibration tables and reconstruction algorithms to keep the final images quantitatively reliable.
实际操作中还需要对射束硬化、探测器灵敏度差异和背景噪声进行校正。现代扫描仪通过校准表与重建算法来保证最终图像的定量可靠性。
6. Image Reconstruction: Back Projection | 图像重建：反投影法
The aim of reconstruction is to determine the value of μ at every point in the slice. One simple method is back projection: each projection is ‘smeared’ back along the direction in which it was measured, and the smeared values are added together.
重建的目标是确定断层内每一点的μ值。一种简单的方法是反投影：将每个投影沿其原始测量方向“涂回”到图像区域，然后将所有方向的反投影叠加起来。
Simple back projection produces a reconstructed image, but it is blurred. Points of high attenuation create star-like streaks, and the resulting image does not accurately represent the true μ values. Radiologists would find the images unacceptable for diagnosis.
简单反投影可以产生重建图像，但图像是模糊的。高衰减点会产生星芒状伪影，最终图像并不能准确反映真实的μ值。这种图像在临床上无法满足诊断要求。
The mathematical solution is to filter each projection before back projection. This is called filtered back projection. The filter corrects for the blurring effect and sharpens edges, producing a diagnostically useful image.
数学上的解决办法是在反投影之前先对每个投影进行滤波处理。这称为滤波反投影法。滤波器修正了模糊效应并锐化边缘，从而生成可用于诊断的图像。
Modern scanners often use iterative reconstruction methods instead of filtered back projection. Iterative methods simulate the scan, compare the simulated projections with the measured data, and update the image step by step. They can reduce noise and allow lower radiation doses.
现代扫描仪常采用迭代重建算法代替滤波反投影。迭代方法先模拟扫描过程，将模拟投影与实测数据比较，然后逐步更新图像。这类方法可以降低噪声并允许使用更低的辐射剂量。
7. CT Numbers and the Hounsfield Scale | CT值与亨斯菲尔德标度
To display the reconstruction, each pixel in the image is assigned a CT number in Hounsfield units (HU). The CT number compares the linear attenuation coefficient of the voxel, μ, with that of water, μwater:
为了显示重建结果，图像中的每个像素被赋予一个以亨斯菲尔德单位（HU）表示的CT值。CT值将体素的线性衰减系数μ与水的线性衰减系数μwater进行比较：
HU = 1000 × (μ − μwater) / μwater
By this definition, water has a CT number of 0 HU. Air, which has a nearly zero linear attenuation coefficient, has a CT number of approximately −1000 HU. Dense cortical bone is typically above +1000 HU.
根据这一定义，水的CT值为0 HU。空气的线性衰减系数几乎为零，其CT值约为−1000 HU。致密皮质骨的CT值通常在+1000 HU以上。
| Tissue / Material | Approximate HU range |
| Air | −1000 |
| Lung | −900 to −500 |
| Fat | −100 to −50 |
| Water | 0 |
| Soft tissue | +40 to +80 |
| Bone | +400 to +3000 |
Because CT numbers are quantitative, two tissues that appear almost identical on a plain X-ray can be distinguished on CT if their Hounsfield values differ by only a few units. This gives CT outstanding low-contrast resolution.
由于CT值是定量的，在普通X光片上看起来几乎相同的两种软组织，如果两者的亨斯菲尔德值相差几个单位，就可以在CT上加以区分。这使CT具有极佳的低对比度分辨能力。
8. Windowing, Greyscale and Contrast | 窗宽窗位、灰阶与对比度
A typical CT scanner produces 12-bit data, giving more than 4000 different CT numbers between −1000 and +3000 HU. The human eye, however, can distinguish only a small number of grey shades on a monitor.
典型CT扫描仪产生12位数据，在−1000到+3000 HU之间可区分超过4000个CT值。然而，人眼在显示器上只能分辨有限数量的灰度级别。
Therefore, CT images are displayed using ‘windowing’. The radiologist chooses a window level and a window width. The window level is the centre CT number of the displayed range; the window width is the total range of CT numbers mapped from black to white.
因此，CT图像使用“窗”技术显示。放射科医生选择窗位（window level）和窗宽（window width）。窗位是显示范围的CT值中心；窗宽是从黑到白映射的CT值总范围。
A narrow window width increases contrast but clips tissues outside the range. For example, a narrow window centred at +50 HU can make a small difference between normal and abnormal soft tissue appear obvious. A wide window is used when bone and air must be shown in the same image.
窄窗宽可以增强对比度，但会把范围之外的组织显示为纯黑或纯白。例如，以+50 HU为中心的窄窗可以使正常与异常软组织之间的细微差异变得明显。当需要同时显示骨骼和空气时，则采用宽窗宽。
Windowing explains why a single CT dataset can generate many different-looking images: the underlying HU data do not change, but the display mapping can be adjusted to optimise visibility for each clinical question.
窗技术解释了为什么同一组CT数据可以产生许多外观不同的图像：底层HU数据不改变，但显示映射可根据临床问题调整，以优化可见性。
9. Advantages of CT over Plain Radiography | CT相对于普通X射线摄影的优势
The most important advantage of CT is the removal of anatomical superimposition. A CT image displays a true cross-section, so the exact location, size and shape of a lesion can be assessed in three dimensions by stacking contiguous slices.
CT最重要的优势是消除了解剖结构的重叠。CT图像显示真实断面，通过连续断层堆叠，可以从三维角度评估病灶的精确位置、大小和形状。
CT also provides quantitative attenuation information. The Hounsfield number helps identify whether a lesion is fluid, fat, calcified or blood, which is often impossible to determine from a plain film.
CT还提供定量的衰减信息。亨斯菲尔德值有助于判断病灶是液体、脂肪、钙化还是血液，而这在普通X光片上通常无法判断。
The main disadvantages are higher radiation dose, higher cost and lower spatial resolution than plain film for very fine detail. A CT scan can deliver an effective dose of several millisieverts, much greater than a single chest X-ray.
主要缺点是辐射剂量更高、费用更高，并且在非常细微的结构上空间分辨率低于普通X光片。一次CT扫描的有效剂量可达数毫希沃特，远高于一次胸部X光片。
10. Radiation Dose and Safety | 辐射剂量与安全
CT uses ionising radiation, and the risk depends on the patient’s age, the scanned region and the chosen scan protocol. Typical effective doses are about 1–2 mSv for a head CT and 5–10 mSv for an abdominal CT.
CT使用电离辐射，风险取决于患者年龄、扫描部位和所选扫描方案。头部CT的典型有效剂量约为1–2 mSv，腹部CT约为5–10 mSv。
The linear attenuation coefficient depends on photon energy, so the X-ray spectrum influences both image quality and dose. Modern systems use automatic exposure control, tube current modulation and iterative reconstruction to reduce dose while maintaining diagnostic image quality.
线性衰减系数取决于光子能量，因此X射线能谱同时影响图像质量和剂量。现代系统使用自动曝光控制、管电流调制和迭代重建，在保持诊断图像质量的同时降低剂量。
In medical physics, the principle of justification states that the benefit of a CT scan must outweigh its risk. Scans should not be requested without a clear clinical indication, and paediatric protocols should always be adapted to the smaller body size and higher radiosensitivity of children.
医学物理中的正当化原则要求CT扫描的获益必须大于风险。没有明确临床指征不应申请CT扫描；儿童扫描必须根据其较小的体型和更高的辐射敏感性调整扫描参数。
11. Clinical Applications and Modern Developments | 临床应用与现代发展
CT is widely used for imaging the brain, where it can quickly detect bleeding, stroke and tumours. It is also used for chest imaging, abdominal imaging, trauma assessment and CT angiography of blood vessels.
CT广泛用于脑部成像，可以快速发现出血、卒中和肿瘤。它也可用于胸部、腹部成像、创伤评估以及血管CT造影。
CT images are used in radiotherapy planning to map the position of a tumour relative to surrounding organs. The quantitative HU values can be converted into electron-density maps needed for dose calculations.
CT图像还用于放射治疗计划，以确定肿瘤相对于周围器官的位置。定量的HU值可转换为剂量计算所需的电子密度图。
Modern multidetector CT forms a three-dimensional volume in a single breath-hold. The computer can then generate multiplanar reformats, three-dimensional virtual endoscopy images and CT coronary angiograms.
现代多排探测器CT可在一次屏气时间内完成三维容积扫描。计算机随后可以生成任意平面的重建图像、三维虚拟内镜图像以及CT冠状动脉造影图像。
In the A-level physics course, CT illustrates the key principles of X-ray attenuation, logarithmic projection data, rotating source–detector geometry and mathematical image reconstruction. These ideas connect atomic physics, radiation physics and practical medicine.
在A-Level物理课程中，CT体现了X射线衰减、对数投影数据、旋转源-探测器几何以及数学图像重建等关键原理。这些概念将原子物理、辐射物理和临床医学紧密联系在一起。
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