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.不同器官的血液供应评估，需使用合适的示踪剂（tracer）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，相关脉冲响应函数（impulse response functions）的处理均采用经验性方法，未纳入器官血管形态学的关联关系。本研究首次针对该关联关系展开系统性探讨。我们证明，在血管分叉处血液充分混合的近似条件下，整支动脉树的响应函数形式可简化为单个血管段的响应函数形式。当纳入血管树的几何缩放特性时，所得表达式可进一步显著简化。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路径。然而，正如针对大脑大动脉的实测动脉自旋标记（arterial spin labeling）示例所展现的，该问题属于不适定逆问题（ill-posed inverse problem）。我们还对单个血管段内的物质转运进行了分析，证实血管段内可实验测得的示踪剂浓度取决于所采用的测量原理。针对动脉树主干中段——该段内单个血管段的血流可视为层流——我们推导得到了响应函数的显式表达式。将该理论应用于区域脑血流量（regional cerebral blood flow）分析时，在通过颈动脉（carotid arteries）评估必要动脉输入的场景下，现有理论的预测结果约低估20%，这与近期发表的实验数据相一致。