King R B, Raymond G M, Bassingthwaighte J B
Center for Bioengineering, University of Washington, Seattle 98195-7962, USA.
Ann Biomed Eng. 1996 May-Jun;24(3):352-72. doi: 10.1007/BF02660885.
It has been known for some time that regional blood flows within an organ are not uniform. Useful measures of heterogeneity of regional blood flows are the standard deviation and coefficient of variation or relative dispersion of the probability density function (PDF) of regional flows obtained from the regional concentrations of tracers that are deposited in proportion to blood flow. When a mathematical model is used to analyze dilution curves after tracer solute administration, for many solutes it is important to account for flow heterogeneity and the wide range of transit times through multiple pathways in parallel. Failure to do so leads to bias in the estimates of volumes of distribution and membrane conductances. Since in practice the number of paths used should be relatively small, the analysis is sensitive to the choice of the individual elements used to approximate the distribution of flows or transit times. Presented here is a method for modeling heterogeneous flow through an organ using a scheme that covers both the high flow and long transit time extremes of the flow distribution. With this method, numerical experiments are performed to determine the errors made in estimating parameters when flow heterogeneity is ignored, in both the absence and presence of noise. The magnitude of the errors in the estimates depends upon the system parameters, the amount of flow heterogeneity present, and whether the shape of the input function is known. In some cases, some parameters may be estimated to within 10% when heterogeneity is ignored (homogeneous model), but errors of 15-20% may result, even when the level of heterogeneity is modest. In repeated trials in the presence of 5% noise, the mean of the estimates was always closer to the true value with the heterogeneous model than when heterogeneity was ignored, but the distributions of the estimates from the homogeneous and heterogeneous models overlapped for some parameters when outflow dilution curves were analyzed. The separation between the distributions was further reduced when tissue content curves were analyzed. It is concluded that multipath models accounting for flow heterogeneity are a vehicle for assessing the effects of flow heterogeneity under the conditions applicable to specific laboratory protocols, that efforts should be made to assess the actual level of flow heterogeneity in the organ being studied, and that the errors in parameter estimates are generally smaller when the input function is known rather than estimated by deconvolution.
一段时间以来，人们已经知道器官内的局部血流并不均匀。局部血流异质性的有用度量是从与血流成比例沉积的示踪剂的局部浓度获得的局部血流概率密度函数（PDF）的标准差、变异系数或相对离散度。当使用数学模型分析示踪剂溶质给药后的稀释曲线时，对于许多溶质而言，考虑血流异质性以及通过多条平行途径的广泛转运时间范围非常重要。不这样做会导致分布容积和膜电导估计值出现偏差。由于在实际应用中所使用的路径数量应该相对较少，因此该分析对用于近似血流或转运时间分布的各个元素的选择很敏感。本文介绍了一种通过一种方案对器官内的异质血流进行建模的方法，该方案涵盖了血流分布的高血流和长转运时间极端情况。使用这种方法，进行了数值实验，以确定在忽略血流异质性的情况下，在无噪声和有噪声的情况下估计参数时所产生的误差。估计误差的大小取决于系统参数、存在的血流异质性量以及输入函数的形状是否已知。在某些情况下，当忽略异质性（均匀模型）时，一些参数的估计误差可能在10%以内，但即使异质性水平适中，也可能导致15 - 20%的误差。在存在5%噪声的重复试验中，与忽略异质性时相比，异质模型估计值的均值总是更接近真实值，但在分析流出稀释曲线时，均匀模型和异质模型的估计值分布在某些参数上存在重叠。当分析组织含量曲线时，分布之间的分离进一步减小。结论是，考虑血流异质性的多路径模型是在适用于特定实验室方案的条件下评估血流异质性影响的一种手段，应该努力评估所研究器官中血流异质性的实际水平，并且当输入函数已知而不是通过反卷积估计时，参数估计中的误差通常较小。
