Intracranial hypertension is an important obstruction to intracranial blood flow. At moderate intracranial pressure (ICP) elevation the pulsatility of the middle cerebral artery flow velocity increases. This is expressed in the pulsatility index or PI, but also in the difference between Sys1 and Sys2.

The PI has an important drawback: it varies with heart rate. Schaafsma (2012) has, therefore, advocated to use a diastolic flow velocity with a fixed time with respect to stroke onset. Somewhat arbitrarily the D560 was chosen: the average flow velocity calculated over an interval of 80 ms around 560 ms after stroke onset. This allowed D560 to be calculated down to a pulse interval of 600 ms, which equals a heart rate of 100 BPM. At higher heart rates the interval of 80 ms was shifted forward so that it was safely based upon diastolic flow.

Since Sys1 is based upon arterial acceleration (Schaafsma 2014) it is relatively resistant to an increase in ICP, whereas the ejected stroke volume (Sys2) and diastolic flow are negatively affected, the blood being forced into other parts of the circulation where output resistance is less. This explains why the difference of Sys1 minus Sys2 becomes larger, especially when compared to the systemic blood pressure by calculating the ratio pulsatile apparent resistance (or PaR). 

When ICP increases further to levels associated with uncal or tegmental herniation the middle cerebral artery flow becomes pendular: systolic inflow but diastolic back flow and, ultimately, so called systolic spikes may be observed (Schaafsma 2025). These systolic spikes can be demonstrated in Neuromons CardioVascularSimulationApp for macOS, in particular, in the recent extension demonstrating the interaction of arterial acceleration and EDRF.

The Nobel prize awarded discovery of endothelium derived relaxation factor or EDRF, with the chemical formula NO or nitric oxide, made it clear that within tissues micro-circulation  is controlled by local factors. The resistance to the blood stream causes shear stress in the endothelium of feeding arteries releasing EDRF to the more distal branches. In this way arteries open when high resistance is met and, presumably, constrict when peripheral resistance is low, for instance, when arterioles open as part of vascular metabolic coupling.

Neuromon's cardiovascular model was expanded with a simulation of the hypothetical combined effect of arterial acceleration and EDRF. It is emphasised that for this purpose the model's parameters were fine tuned in order to meet its desired result: providing graphical imaging to theoretical considerations. The model cannot be calibrated to experimental data, since data describing the relation between arterial acceleration and EDRF are so far unavailable. 

Keeping this in mind the video below shows how the pressure wave resulting from the addition of a given stroke volume to the aorta spreads along the branches of the arterial tree without arterial acceleration and without regulation by EDRF. The added volume to the aorta pushes the blood forward into the branches of the arterial tree, resulting in a pulsatile wave that dampens along its course. The viscoelastic properties of the arterial tree prevent the pulsatile energy provided by heart contraction to fully reach into the periphery. 

As we have seen, arterial acceleration may promote the pressure wave in reaching periphery, since the presumed shortlisting contraction within the smooth muscle layers of the arterial tree augments the pressure wave generated by heart contraction. Since arterial acceleration is thought to spread as a peristaltic wave along the branches of the arterial tree and distal arteries profit from tension already built up by proximal branches, its effect is expected to become greater towards periphery.

In the video below the effect of arterial acceleration is visible as an increase in pulsatility in the most distal branches. In addition, the steeper onset of the pressure wave is expected to promote the release of EDRF, symbolised by the colour yellow in this video. In the model the amount of EDRF release within a single arterial branch is arbitrarily calculated from the maximal change of pressure (dPdt) in the capacitance one step more proximal. The EDRF is released into the next capacitance leading to an increase in its concentration, but because EDRF has a short half life the colouring of a capacitance to yellow is only short lived. 

Local differences in metabolic activity may result in local differences in arteriolar resistance causing inhomogeneities in tissue perfusion. Likewise, the pressure within a tissue is often not evenly spread. This too may cause inhomogeneities in tissue perfusion. 

The model was expanded by allowing the inclusion of local tissue pressure. Capacitances can be selected one by one and the model includes the effect of local tissue pressure by adjusting a slider up to 100mmHg max. The effect of this increase in tissue pressure is shown in the video below.

Arterial acceleration may improve the penetration of the pressure wave into tissues with unfavourable conditions, but it does not guarantee adequate blood supply. This is where EDRF comes into play. With the branches of the arterial tree EDRF helps to adjust local arterial diameter to local experienced shear stress. 

In the simulation below every resistances adapts to the local EDRF concentration. If EDRF is high there is a pressure build up at stroke onset meaning that blood, despite arterial acceleration blood has difficulty flowing into the periphery. In the model a more distal resistance will be lowered allowing the blood to flow in more easily and reduce the build up of pressure in the more proximal capacitance. When there is little build up of pressure, EDRF will be low, and the model will increase the next resistance.

In the model the resistances are adjusted gradually, changing from one heart beat to another. Small bar graphs centred in each branch represent whether its resistance is higher or lower than its mean setpoint. Resistances are not adapted instantaneously but stepwise from one heart beat to another to avoid oscillations within the model. The bar plots can, therefore, be seen to rise (with their colour turning from green to red) symbolising an increase in resistance and be seen to lower (with their colour turning from red to green) symbolising a decrease in resistance. No bar plot is seen when the resistance is at its means setpoint.

Having seen how EDRF and arterial acceleration are likely to collaborate, another important aspect of EDRF must be emphasised: its intrinsic capacity to homogenise the blood flow within the branches of the arterial tree.

In the simulation below we show how EDRF adjusts resistances (that are not ideally preset) so that minimal pressure build up occurs at proximal branching nodes and blood is allowed to flow downstream with minimal interruption. 

In cases of fibrillation or cardiac arrest there is no cardiac output to the brain. At a physiological temperature and without sedation the brain integrity may be preserved for only a few minutes. When resuscitation is effective and leads to a timely recovery of circulation, brain ischemia does not necessarily lead to disability. However, resuscitation may not start straight away and a delay longer than on estimate 6 minutes may lead to permanent brain damage.   

Brain ischemia becomes so pronounced that it leads to anoxic depolarisation of neurones. Anoxic depolarization leads to the intracellular cascade of apoptosis and, thereby, neuronal death. Those neurones most active at the moment of circulatory arrest are most vulnerable to permanent damage: usually the hippocampus and cerebellum suffer most from prolonged brain ischemia.

The theory of arterial acceleration gives a new perspective on the aim and technique or resuscitation. When properly executed, cardiac massage triggers the myogenic response in the arterial system, which helps to bring blood into motion in all the body's capillary systems, including the brain. The pressure on the chest wall may additionally result in blood volume being moved to the aorta, but when cardiac preload is low (due to a massive vaso-dilatation resulting from a loss of sympathetic tone) only a limited amount of blood volume may effectively be brought into motion. 

Theoretically, cardiac massage should aim to trigger the myogenic response and, therefore, be executed rapidly and in a high frequency. Backflow to the heart may be promoted by lifting the legs or positioning the patient in Trendelenburg, whenever feasible. Artificial breathing only contributes when there is at least some form of blood circulation established.

In the cardiovascular simulation model, cardiac arrest can be simulated by playing off the scenario. Heart massage can be performed by placing the mouse over the heart and making repetitive mouse (or trackpad) compressions at high frequency. When properly executed the arterial Sys1 component can be shown to recur in the signal.

Investigators have recently shown that the Systolic 1 based pulsatile apparent resistance (S1-PaR) is more sensitive to an increase in intracranial pressure than a simple pulsatility index (PI) based upon middle cerebral artery flow velocity (MCAFV) alone. S1-PaR is a so-called blood pressure (BP) corrected PI. It is designed to detect a difference between middle cerebral artery PI and arterial blood pressure PI.

The apparent resistance is defined by aR = BP / MCAFV similar to Ohm's law: R = I / V: resistance is current divided by voltage (difference).

Central to the work of Neuromon B.V. is the theory of arterial acceleration. This theory proposes that the pressure wave of the heart is amplified by a shortlasting contraction in the conducting vessels of the arterial tree: Sys1. The second phase of systole (Sys2) is the result of the stroke volume being ejected into the aorta. The propagation of the Sys1 is presumably faster than of Sys2, since the first is based upon a rapidly spreading depolarization within the smooth muscle cells of the arterial wall via the abundant presence of gap junctions. The propagation of the Sys2 wave is slower since it is dampened by the visco-elastic properties of the arterial tree. 

Arterial acceleration increases the penetration force of the Sys1 component, whereas Sys2 and diastolic flow velocity will be more sensitive to intracranial pressure elevation. This is typically the case when systolic spikes are seen in the MCAFV signal: only allowing flow during Sys1 and none during Sys2 and the diastolic phase.

Therefore, the relation between arterial blood pressure and MCAFV will be different during Sys1 compared to diastole. This leads to the definition of the PaR:

S1-PaR = (ED_aR - Sys1_aR) / TAVM_aR (with TAVM as abbreviation for time averaged mean).

The working of this parameter can be demonstrated in Neuromon's cardiovascular simulation. Let's start with simple settings of the model: no reflex activity but with arterial acceleration active.

In the simulation (red curve is arterial blood pressure (ABP) and blue curve is right middle cerebral artery flow velocity (MCAFV)):

This gives us the following results:

And the following waveforms (red curve is arterial blood pressure (ABP) and blue curve is right middle cerebral artery flow velocity (MCAFV)):

After normalization (dividing both signals by their time averaged means) and swapping the x- and y-axis:

Under these circumstances the relation between ABP and MCAFV (aR: symbolized by the angle of the lines with the x-axis) is similar during systole and diastole. Deviations from the ideal curve are partly due to a time lag between MCAFV-Sys2 in relation to ABP-Sys2. (Note that the pulsatility index (PI) is the width of the graph projected along the x-axis.)

What happens during elevated ICP? In the model ICP is assumed constant and adds up to normal venous pressure lowering the arterio-venous pressure difference that drives the blood flow.. During diastole, the relative effect of elevated ICP is larger than during systole and it may even lead to the cessation of flow at the so called critical closing pressure (CCP). Settings of the model (note: intracranial pressure):

The simulation (red curve is arterial blood pressure (ABP) and blue curve is right middle cerebral artery flow velocity (MCAFV)):

Leading to the following results:

And the following waveforms (red curve is arterial blood pressure (ABP) and blue curve is right middle cerebral artery flow velocity (MCAFV)):

After normalization (dividing both signals by their time averaged means) and swapping the x- and y-axis:

The increase in ICP brings the MCAFV closer to zero and under these circumstances the relation between ABP and MCAFV (aR: symbolized by the angle of the lines with the x-axis) is quite different during systole and diastole resulting in an increased value of S1-PaR. (Note that the PI is the width of the graph projected to the x-axis.)

S1-PaR = (ED_ABP/TAVM_ABP) / (ED_MCAFV/TAVM_MCAFV) - (S1_ABP/TAVM_ABP) / (S1_MCAFV/TAVM_MCAFV)

Comparing different parameters for a range of ICP values:

S1-PaR and PI rapidly increase when the end diastolic flow velocity becomes zero (at ICP > 30 mmHg). The CrCP increases more steadily since it is calculated over the full beat to beat average and the effect of the diastolic flow velocity becoming zero is more gradual.