Data from: Blood tracer kinetics in the arterial tree

Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.不同器官血液供应的评估，需借助合适的示踪剂对血液进行标记。示踪剂动力学呈线性特征：观测位点的示踪剂浓度，是动脉血流上游某处输入信号的线性响应。当前相关冲激响应函数的处理均采用经验方法，未结合器官的血管形态学关联关系。本研究首次针对这一关联展开探讨。我们证明，在血管分叉处血液充分混合的近似条件下，整个动脉树的响应函数形式可简化为单根血管段的响应函数形式。当考虑血管树的几何缩放特性时，所得表达式可进一步大幅简化，这为通过实验测定的响应函数在体获取血管形态学信息提供了全新途径。然而，正如针对大脑大动脉的实测动脉自旋标记（Arterial Spin Labeling）示例所展示的，该过程属于不适定逆问题。我们进一步分析了单根血管段内的物质输运过程，并证实血管段内可实验测得的示踪剂浓度取决于测量原理。针对动脉树主干部分——该部分血管内血流可视为层流，我们推导得到了冲激响应函数的显式表达式。将其应用于脑区域血流量测量分析时，现有理论在通过颈动脉评估得到必要的动脉输入信号后，预测结果会出现约20%的低估，这与近期的实验数据相符。