Validation of models of venous outflow from the cranial cavity in the supine and upright body positions

Introduction

The way through which blood flows out of the brain depends on body posture. The internal jugular vein (IJV), which is a paired blood vessel, constitutes the primary outflow route in the supine, prone, and lateral decubitus body postures. In the upright (sitting and standing) body positions the IJV collapses and a substantial part of outflow is shifted towards alternative pathways, primarily to the vertebral venous plexus, which is composed of the vertebral veins, the epidural veins, and other adjacent tiny veins situated next to the cervical spinal column [1–3]. Several studies have suggested that an impaired cerebral venous outflow can be associated with neurodegenerative and neuroinflammatory diseases [4–8]. Stenoses of the IJV seem to be main cause of such an impairment [9]. Therefore, understanding the physical background of the cerebral venous outflow is important. Normally, there are no strictures in the IJV, but some individuals present with stenoses either at the level of the jugular foramen (upper part of this vein) or at the level of the jugular valve, which is situated just above the junction of the IJV with the brachiocephalic vein. To comprehend the haemodynamic relevance of these strictures, it should be remembered that the IJV is always narrowed in the upright body position, and despite this fact the cerebral outflow is not disturbed. Yet, in this body position the venous outflow is facilitated by gravity, which – on the contrary – is of negligible importance in the supine and other horizontal positions [10–12]. Since the investigations on these phenomena in living subjects are difficult to perform, are invasive, and often not possible to conduct due to bioethical aspects, computational flow modelling (CFM) can provide a surrogate insight into the biomechanics of cerebral venous outflow. In our previous paper, based on the results of computational flow simulations, we suggested that the strictures located at the level of the jugular foramen are probably more clinically relevant than the pathological jugular valves [13, 14]. Yet, this study used the models of the IJVs only, without alternative outflow pathways. The current study is the continuation of that research, and it was primarily aimed at building reliable models comprising both jugular and vertebral outflow pathways. Such models could be useful in further research on understanding the influence of differently located and shaped stenoses in the IJV.

Material and methods

For this study CFM software (Flowsquare+, Nora Scientific, Japan), was used. All the computations were performed in an Intel BOXNUC8i7BEH2 mini PC (Intel, Santa Clara, CF, USA) equipped with an Intel® CoreTM i7 processor and an Intel® Iris® Plus Graphics 655 graphic card.
The 3-dimensional models were 180 mm long along the axis of flow, and 60 mm and 30 mm along other axes. The mesh size of the models in any direction was 0.25 mm, and it contained about 7 million active cells. It comprised the initial inflow field representing the cerebral circulation, which branched into 2 alternative outflow routes: the tube representing the IJV, and the irregular network representing the vertebral veins and the epidural venous plexus that in humans form the vertebral outflow route. Then these 2 alternative pathways re-joined to form the outflow field. To facilitate the simulations, we modelled only one side of the cerebral venous outflow: one IJV and one side of the vertebral venous pathway. The tubular-shaped model of the IJV was 125 mm long and at the outflow had cross-sectional diameters of 10 mm and 12 mm (cross-sectional area of 0.94 cm2). The model of the vertebral venous pathway had a similar length as the model of the internal jugular vein, and at the outflow it had a cross-sectional area of about 0.75 cm2, and still the main part of the vertebral pathway was divided into many thin irregular parallel channels. During simulations 10 probes measuring flow parameters were positioned inside the models: 2 probes in the inflow field, 2 probes in the middle part of the IJV, 3 probes in the terminal part of the IJV, just above the jugular valve, and 3 probes in the terminal part of the vertebral pathway (Fig. 1).
For this study 2 three-dimensional models of the cerebral venous outflows were constructed, with different status of the IJV (Figs. 2, 3):
1) Model with open IJV, representing the flow in the supine body position; this vein had cross-sectional diameters: 8.6 × 12.8 mm (cross-sectional area 0.87 cm2) and had no strictures or valves;
2) Model with collapsed IJV, representing the flow in the upright body position; this vein model of the IJV had cross-sectional diameters: 1.7 × 12.0 mm (cross-sectional area 0.16 cm2), also without additional strictures or valves.
In both models the vertebral route was the same, with a cross-sectional area of about 0.75 cm2. Two varieties were considered in the case of model 2:
a) with many thin irregular parallel channels, as in model 1;
b) with similar irregular but wider parallel channels.
The flow was simulated during 1200 consecutive steps, each of them lasting 0.28 ms, which in total was equivalent to 0.35 s of real-time flow. Pilot simulations revealed that after such a number of steps, the flow stabilized and there was no clear benefit from additional computational time. Using our computer set, depending on the model, it took around 20–40 hours of computational time for each case.
Parameters of the fluid were set up to be similar to those observed during blood flow in the IJV. Velocity component along the long axis of the model for the initial field, the area of which was 2.08 cm2, was set up at 8 cm/s, which enabled the inflow of fluid into the model at the level of approximately 400 ml/min, was equal to 50% of the physiological cerebral blood flow. Initial pressure was 750 Pa (equivalent to 7.65 cm H2O; a physiological pressure in the IJV in the supine body position). Dynamic viscosity of the fluid was 2.78 × 10–3 kg/m/s (which is the dynamic viscosity of whole blood at 37ºC). The density of the modelled fluid was constant at 1055 kg/m3, which is the density of blood at room temperature.
In the case of the model 2, with a collapsed IJV representing the flow in the upright body position, in order to understand how the pressure and flow velocity influence the outflow in the setting of increased flow resistance, we additionally used different flow parameters in the initial inflow field: flow velocity 16 cm/s and 20 cm/s, and pressure 1500 Pa. With the use of above-described probes we measured flow volumes in each of the alternative pathways and the total flow through our models.

Results

In model 1 the majority of blood flowed out through the IJV (Fig. 4). 84% of the total flow was via the IJV, and the remaining 16% utilized the vertebral pathway. This share of flow between these pathways is in line with the observations in living subjects. The total flow volume in the outflow field was 399 ml/min, which again was in line with observations in humans (total cerebral flow in humans is at the level of 750 ml/min) [10, 11].
Conversely, in model 2, which represented the upright body position, there was a substantial shift of flow toward the vertebral venous plexus (Fig. 5). When the initial velocity and pressure were the same as in model 1, only 36% of blood flew out through the IJV. Moreover, the total flow volume in the outflow field was only 136 ml/min.
Therefore, we looked at flow volumes in the model with a collapsed IJV using different initial velocity and pressure values. The results of these simulations are summarized in Table 1. We found that if Flowsquere+ CFM software was used, in order to achieve correct flow volumes, the velocity in the initial field had to be increased to 20 cm/s. An increase of initial pressure as well as widening of venous channels in the vertebral route had little influence on the desired total flow, which should be at the level of 300–400 ml/min to obtain reliable results of flow simulations in more complex models.

Discussion

This in silico research was aimed primarily at finding reliable models comprising both jugular and vertebral outflow pathways, which could be used to evaluate haemodynamic significance of stenoses of the IJV, which are differently located and shaped. Modelling of the flow in the supine body position was relatively simple, and the only problem was to find the correct value of flow velocity in the initial field. We found that the value of 8 cm/s enabled modelling of total flow, which was similar to physiological cerebral outflow in humans. Modelling of the flow in the upright body position was more difficult. Although Flowsquare+ software is user-friendly and does not require expensive computers, it is not possible to include gravitational effects in the simulations. Here, to get proper results, flow augmented by gravity should be modelled using changes of initial parameters. We found that the best method to mimic physiological cerebral outflow in the upright body position was to change the value of flow velocity in the initial field to 20 cm/s. By contrast, changing the pressure in the initial field or widening the channels in the vertebral pathway was not correct.

Conclusions

Models 1 and 4, presented in Table 1, seem to be optimal to investigate cerebral venous outflow in silico with the use of Flowsquare+ CFM software. The authors declare no conflict of interest.

References