Earliest effects of sudden occlusions on pressure profiles in selected locations of the human systemic arterial system

We have developed a numerical simulation method for predicting the time dependence (wave form) of pressure at any location in the systemic arterial system in humans. The method uses the matlab-Simulink environment. The input data include explicitly the geometry of the arterial tree, treated up to an arbitrary bifurcation level, and the elastic properties of arteries as well as rheological parameters of blood. Thus, the impact of anatomic details of an individual subject can be studied. The method is applied here to reveal the earliest stages of mechanical reaction of the pressure profiles to sudden local blockages (thromboses or embolisms) of selected arteries. The results obtained with a purely passive model provide reference data indispensable for studies of longer-term effects due to neural and humoral mechanisms. The reliability of the results has been checked by comparison of two available sets of anatomic, elastic, and rheological data involving (i) 55 and (ii) 138 arterial segments. The remaining arteries have been replaced with the appropriate resistive elements. Both models are efficient in predicting an overall shift of pressure, whereas the accuracy of the 55-segment model in reproducing the detailed wave forms and stabilization times turns out dependent on the location of the blockage and the observation point.

Figure 1

The arterial tree of the human body. First form left: the topology of model with 55 segments available in Ref. [11]; first form right: the topology of model with 138 segments available in Ref. [12]; in the middle: real topology.

Figure 2

Reflection coefficient of embolism $R_{\mathrm{emb}}$ as a function of time [40].

Figure 3

The pressure wave form (a) in ascending aorta, (b) in left brachial artery, and (c) in anterior communicating artery during 20 cycles of the heart at an embolism in the left common carotid artery. The inset in (a) represents the ventricular pressure wave form. Solid line: results from model with 55 segments; dotted line: results from model with 138 segments. The onset of the embolism takes place after first ten cycles of heart.

Figure 4

The pressure wave form in ascending aorta in (a) model of 55 segments and in (b) model of 138 segments, and in left brachial artery in (c) model of 55 segments and in (d) model of 138 segments, during 20 cycles of the heart at an embolism in the right brachial artery (solid black line) and left brachial artery (dotted grey line). After first ten cycles of heart the embolism of right brachial artery and of left brachial artery occurs.

Figure 5

The pressure wave form in ascending aorta (a) in model of 55 segments and (b) in model of 138 segments, and in left brachial artery (c) in model of 55 segments and (d) in model of 138 segments, during 20 cycles of the heart at an embolism in the right femoral artery (solid black line) and left femoral artery (dotted grey line). After first ten cycles of heart the embolism of right femoral artery and of left femoral artery occurs.

Figure 6

The pressure wave form (a) in ascending aorta and (b) in left brachial artery during 20 cycles of the heart at an embolism in the left common carotid artery. Solid line: results from model with 55 segments; dotted line: results from model with 138 segments; dashed line: results from 138-segment model reduced to 55 segments. The onset of the embolism takes place after first ten cycles of heart.

Figure 7

The pressure wave form (a) in ascending aorta and (b) in left brachial artery during 20 cycles of the heart at an embolism in the right brachial artery, and the pressure wave form (c) in ascending aorta and (d) in left brachial artery during 20 cycles of the heart at an embolism in the left brachial artery. Solid line: results from model with 55 segments; dotted line: results from model with 138 segments; dashed line: results from 138-segment model reduced to 55 segments. The onset of the embolism takes place after first ten cycles of heart.

Figure 8

The pressure wave form (a) in ascending aorta and (b) in left brachial artery during 20 cycles of the heart at an embolism in the right and/or left femoral artery. Solid line: results from model with 55 segments; dotted line: results from model with 138 segments; dashed line: results from 138-segment model reduced to 55 segments. The onset of the embolism takes place after first ten cycles of heart.

Figure 9

A small part (beginning) of the schema of the 55-segment main human arterial system.

Figure 10

The inner schema of the artery block “art3” representing segment 3 (brachiocephalic artery).