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 ...评估不同器官的血液供应，需借助合适的示踪剂（tracer）对血液进行标记。示踪剂动力学呈线性特征：观测位点处的示踪剂浓度，是动脉血流上游某一输入位点的线性响应。当前针对对应的脉冲响应函数（impulse response functions），多采用经验式处理，未将其与器官的血管形态学（vascular morphology）建立关联。本研究首次针对该关联展开探究。我们证实，在血管分叉（vessel bifurcations）处血液充分混合的近似假设下，整条动脉树（arterial tree）的响应函数形式可简化为单支血管段的响应函数形式。若纳入动脉树的几何缩放特征，所得表达式可进一步大幅简化。这为通过实验测得的响应函数实现体内（in vivo）血管形态学评估提供了全新路径。然而正如基于实测动脉自旋标记（arterial spin labeling）的示例所展示的那样，该问题属于不适定逆问题。