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首页> 外文会议>International Conference on Algebraic Biology(AB 2007); 20070702-04; Castle of Hagenberg(AT) >Exact Parameter Determination for Parkinson's Disease Diagnosis with PET Using an Algebraic Approach
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Exact Parameter Determination for Parkinson's Disease Diagnosis with PET Using an Algebraic Approach

机译：用代数方法确定PET诊断帕金森氏病的精确参数

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摘要

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-[~(18)F]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 Groebner 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.
机译：可以使用放射示踪剂在分子水平上研究帕金森氏病的机制。可以通过使用放射性示踪剂6- [〜（（18）F]氟多巴（FDOPA）和正电子发射断层扫描（PET）观察大脑中的多巴胺浓度，并且多巴胺动力学可以描述为脑组织。明确解决了FDOPA动力学模型，但该解决方案显示了一个复杂形式，包括在时域上的多个卷积。由于该解决方案的复杂形式，在过去的几十年中，诸如Logan或Patlak分析之类的图形分析已被用作常规方法。因为在图形分析中估计了帕金森氏病的一些动力学常数，并且曲线的斜率或截距是在各种假设下获得的，所以只能大致估计有限的一组参数。我们通过使用微分方程式的Laplace变换和借助于Groebner基构造的代数计算来分析隔室模型。对于拉普拉斯域上的动力学常数，我们已经获得了严格的解决方案。在这里，我们首先导出参数的严格解，并讨论有关推导的优缺点。接下来，我们用观察到的时间放射性曲线描述确定动力学常数的程序。最后，我们讨论了我们方法的可行性，特别是作为诊断帕金森氏病的标准。

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