Exact Parameter Determination for Parkinson's Disease Diagnosis with PET Using an Algebraic Approach
Exact Parameter Determination for Parkinson's Disease Diagnosis with PET Using an Algebraic Approach
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DOI：
10.1007/978-3-540-73433-8_9
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发表时间：
2007-07
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影响因子：
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通讯作者：
H. Yoshida;Koji Nakagawa;H. Anai;K. Horimoto
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文献类型：
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作者：
H. Yoshida;Koji Nakagawa;H. Anai;K. Horimoto
帕金森病的发病机制可以通过放射性示踪剂在分子水平上进行研究。多巴胺在脑中的浓度可以通过使用放射性示踪剂6-[18F]氟多巴（FDOPA）和正电子发射断层扫描（PET）来观察，并且多巴胺动力学可以被描述为脑组织的隔室模型。FDOPA动力学模型的求解是显式的，但其解的形式比较复杂，包括时域上的几个卷积。由于解的复杂形式，在过去的几十年中，图形分析如Logan或Patlak分析已被用作常规方法。由于帕金森氏病的一些动力学常数是在各种假设下获得的直线斜率或截距的图形分析中估计的，因此仅近似估计了有限的一组参数。我们分析了房室模型，通过使用微分方程的拉普拉斯变换和代数计算的帮助下，Gröbner基地建设。在拉普拉斯域上得到了动力学常数的严格解。在这里，我们首先推导出一个严格的解决方案的参数，连同讨论的优点的推导。接下来，我们描述了一个程序，以确定所观察到的时间-放射性曲线的动力学常数。最后，我们讨论了我们的方法的可行性，特别是作为诊断帕金森病的标准。
The mechanism of Parkinson’s disease can be investigated at the molecular level by using radio-tracers. The concentration of dopamine in the brain can be observed by using a radio-tracer, 6-[18F]fluorodopa (FDOPA), with positron emission tomography (PET), and the dopamine kinetics can be described as compartmental models for tissues of the brain. The models for FDOPA kinetics are solved explicitly, but the solution shows a complicated form including several convolutions over time domain. Owing to the complicated form of the solution, graphical analyses such as Logan or Patlak analysis have been utilized as conventional methods over past decades. Because some kinetic constants for Parkinson’s disease are estimated in the graphical analyses with the slope or intercept of the line obtained under various assumptions, only a limited set of parameters have approximately been estimated. We have analysed the compartmental models by using the Laplace transformation of differential equations and by algebraic computation with the aid of Gröbner base constructions. We have obtained a rigorous solution with respect to the kinetic constants over the Laplace domain. Here, we first derive a rigorous solution for the parameters, together with a discussion about the merits of the derivation. Next, we describe a procedure to determine the kinetic constants with the observed time–radioactivity curves. Last, we discuss the feasibility of our method, especially as a criterion for diagnosing Parkinson’s disease.