Herholz K, Patlak C S
J Cereb Blood Flow Metab. 1987 Apr;7(2):214-29. doi: 10.1038/jcbfm.1987.47.
An analytical method based on Taylor expansions was developed to analyze errors caused by tissue heterogeneity in dynamic positron emission tomography (PET) measurements. Some general rules concerning the effect of parameter variances and covariances were derived. The method was further applied to various compartmental models currently used for measurement of blood flow, capillary permeability, glucose metabolism, and tracer binding. Blood flow and capillary permeability are shown to be generally underestimated in heterogeneous tissue, the underestimation being more severe for slowly decaying, constant or increasing input functions rather than for bolus input, and increasing with measurement time. Typical errors caused by the heterogeneity due to insufficient separation between gray and white matter by a PET scanner with full width at half-maximum (FWHM) = 5 to 10 mm resolution range between -0.9 and -6% in dynamic CBF measurements with intravenous (i.v.) bolus injection of 15O-water or inhalation of 18F-fluoromethane and total measurement times of 6 or 10 min, respectively. Binding or metabolic rates determined with tracers that are essentially trapped in tissue (e.g., FDG for measurement of cerebral glucose metabolism) are only slightly overestimated (0.5-3.0%) at typical measurement times and are essentially independent of the shape of the input function. The error increase considerably if tracer accumulation is very slow, however, or if short measurement times [less than 5/(k2 + k3)] are used. Some rate constants are also subject to larger errors.
开发了一种基于泰勒展开式的分析方法，以分析动态正电子发射断层扫描（PET）测量中组织异质性引起的误差。推导了一些关于参数方差和协方差影响的一般规则。该方法进一步应用于目前用于测量血流量、毛细血管通透性、葡萄糖代谢和示踪剂结合的各种房室模型。结果表明，在异质组织中，血流量和毛细血管通透性通常被低估，对于缓慢衰减、恒定或增加的输入函数，而不是团注输入，这种低估更为严重，并且随测量时间增加。在静脉注射15O-水或吸入18F-氟甲烷的动态脑血流量（CBF）测量中，当PET扫描仪半高宽（FWHM）=5至10mm分辨率，总测量时间分别为6或10分钟时，灰质和白质之间分离不足导致的异质性在动态CBF测量中引起的典型误差在-0.9%至-6%之间。用基本上被困在组织中的示踪剂（例如用于测量脑葡萄糖代谢的FDG）确定的结合或代谢率在典型测量时间仅略有高估（0.5-3.0%），并且基本上与输入函数的形状无关。然而，如果示踪剂积累非常缓慢，或者使用短测量时间[小于5/（k2 + k3）]，误差会显著增加。一些速率常数也会有较大误差。
