标题： 基于基本原理的圆柱形PET系统径向灵敏度分析模型 显示英文标题

标题： Analytic Model of Radial Sensitivity in Cylindrical PET Systems Based on First Principles

摘要： 在圆柱形正电子发射断层扫描（PET）系统中，通常假设视野（FOV）的中心具有最高的系统灵敏度。 这一假设是标准化协议如NEMA NU 2-2018的基础，该协议规定在中心视野（CFOV）进行测量，并影响系统的表征和比较方式。 然而，实验研究报道了不同的径向灵敏度趋势，一些显示中心以外区域具有可比或更高的灵敏度，而另一些则揭示了更复杂、非单调的模式。 尽管有这些观察结果，但尚未明确建立描述径向平面灵敏度的第一性原理理论模型。 在本工作中，我们基于理想扫描仪几何结构和基本探测物理，推导出圆柱形PET系统中径向灵敏度分布的解析模型。 据我们所知，这是首个此类闭式理论公式，提供了在理想化条件下径向灵敏度变化的基础描述。 该模型排除了系统特定因素，如探测器效率或晶体形状，因此为概念理解和实际参考提供了一个可推广的基准。 为了评估该模型在现实系统中的相关性，我们使用代表性PET系统进行了蒙特卡洛模拟和物理实验。 测量和模拟的灵敏度剖面与理论预测良好一致，偏差归因于系统特定因素。 除了作为解释经验不一致性的参考外，这项工作还提供了基本的见解，可能支持系统设计、定量建模以及PET仪器的教学材料。 显示英文摘要

摘要： In cylindrical positron emission tomography (PET) systems, the center of the field of view (FOV) is typically assumed to have the highest system sensitivity. This assumption underlies standardized protocols such as NEMA NU 2-2018, which specify measurements at the CFOV, and influences how systems are characterized and compared. However, experimental studies report varying radial sensitivity trends, some showing comparable or higher sensitivity off center, while others reveal more complex, non-monotonic patterns. Despite these observations, a first-principles theoretical model describing radial plane sensitivity has not been clearly established. In this work, we derive an analytic model for the radial sensitivity distribution in a cylindrical PET system, based solely on ideal scanner geometry and basic detection physics. To our knowledge, this is the first closed-form theoretical formulation of its kind, offering a foundational description of radial sensitivity variation under idealized conditions. The model excludes system-specific factors such as detector efficiency or crystal shape, and thus provides a generalizable baseline for conceptual understanding and practical reference. To evaluate the model's relevance in real-world systems, we perform both Monte Carlo simulations and physical experiments using a representative PET system. The measured and simulated sensitivity profiles align well with theoretical predictions, with deviations attributable to system-specific factors. Beyond serving as a reference for interpreting empirical inconsistencies, this work contributes fundamental insight that may support system design, quantitative modeling, and educational materials on PET instrumentation.