Mathematical modelling in nuclear medicine.
Mathematical modelling in nuclear medicine.
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核医学中的数学建模。
DOI：
10.1007/bf02285464
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Feinendegen,LE
中科院分区：
文献类型：
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作者：
Kuikka,JT;Bassingthwaighte,JB;Henrich,MM;Feinendegen,LE
现代成像技术可以提供一系列图像，这些图像给出的信号与3D空间中可识别位置处的组织区域中的示踪剂（通过发射断层扫描）、X射线吸收对比材料（快速CT或可能的NMR对比）或天然化学物质（NMR）的浓度成比例。现在可以使用描述生理过程和适当解剖结构的数学模型分析浓度-时间曲线的方法来定量描述结构和功能：这就是代谢或功能成像的方法。一个人首先通过定义它应该代表什么来制定一个模型：这就是假设。当转化为一组自洽的微分方程时，模型就变成了一个数学模型，一个假设的定量版本。这就是人们想要用数据来测试的。然而，下一步是将数学模型简化为可计算的形式;解剖学和生理学上真实的模型考虑了血液组织交换单位内浓度的空间梯度，而房室模型通过使用平均浓度简化了方程。前者称为分布式模型，后者称为集总房室或混合室模型。由于两者都来自相同的思想，所以参数通常是相同的;它们的差异在于它们正确地、定量地表示假设的能力，有时还在于它们的可计算性。在这篇文章中，我们回顾了哲学和实践方面的建模分析，将图像序列转化为生理术语。
Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms.