A method for parametric estimation of the number and size distribution of cell clusters from observations in a section plane
A method for parametric estimation of the number and size distribution of cell clusters from observations in a section plane
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DOI：
10.2307/2533999
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发表时间：
1998-03-01
期刊：
影响因子：
1.9
通讯作者：
Luebeck, EG
中科院分区：
文献类型：
--
作者：
de Gunst, MCM;Luebeck, EG
被认为是发现的数量和大小分布的细胞簇生长在一个器官或组织的数量和大小的横切面，这样的细胞簇在一个平面部分的观察的问题。这个问题与体视学中著名的微粒或威克塞尔问题密切相关，后者涉及球形物体的横切。然而，对于大多数生物学应用，假设细胞簇具有球形是不现实的，因为它们可以以各种方式生长。因此，我们提出了一种方法，允许更一般的空间配置的集群。假设一个参数的增长模型是可用于细胞簇的数量和大小，表达式得到的数量和大小的横切面中的集群在一个截面上的每个时间点的概率分布。这些表达式包含的系数是独立的参数生长模型和时间，但取决于模型选择的空间中的细胞簇的配置。这些结果使我们能够直接在数据上通过最大似然法来估计生长模型的参数，而不必处理基于二维数据的三维量估计的逆问题。对于构型模型的实际选择，将不可能获得系数的精确值，但是它们可以通过空间构型的计算机模拟而容易地近似。Monte Carlo模拟进行近似系数为两个特定的空间配置模型。对于这两个配置模型，所提出的方法被施加到癌前minifoci在大鼠肝脏的假设下的两个事件模型的致癌参数的增长模型的数据。
The problem of finding the number and size distribution of cell clusters that grow in an organ or tissue from observations of the number and sizes of transections of such cell clusters in a planar section is considered. This problem is closely related to the well-known corpuscle or Wicksell problem in stereology, which deals with transections of spherical objects. However, for most biological applications, it is unrealistic to assume that cell clusters have spherical shapes since they may grow in various ways. We therefore propose a method that allows for more general spatial configurations of the clusters. Under the assumption that a parametric growth model is available for the number and sizes of the cell clusters, expressions are obtained for the probability distributions of the number and sizes of transections of the clusters in a section plane for each point in time. These expressions contain coefficients that are independent of the parametric growth model and time but depend on which model is chosen for the configuration of the cell clusters in space. These results enable us to perform estimation of the parameters of the growth model by maximum likelihood directly on the data instead of having to deal with the inverse problem of estimation of three-dimensional quantities based on two-dimensional data. For realistic choices of the configuration model, it will not be possible to obtain the exact values of the coefficients, but they can easily be approximated by means of computer simulations of the spatial configuration. Monte Carlo simulations were performed to approximate the coefficients for two particular spatial configuration models. For these two configuration models, the proposed method is applied to data on preneoplastic minifoci in rat liver under the assumption of a two-event model of carcinogenesis as the parametric growth model.