Scientific background

In a new extension of the Cardiovascular model we have explored the possible collaboration of arterial acceleration on the one hand and the release and spread of endothelium derived relaxing factor (EDRF) on blood circulation within a confined tree of branching arteries. These arteries have been modeled by capacitances connected with resistances. The first simulation demonstrates how the pulsatile signal of heart contraction in the more proximal branches is transformed to a continuous flow in the most distal branches.

The explanation for this is that any volume of blood driven into the capacitance on the left has three options: 1. remain in this capacitance, 2. flow over a resistance into the next capacitance up right or 3. flow over a resistance into the next capacitance down right. During systole blood is temporarily stored in the capacitance and is released during diastole. Since in a steady state total blood flow at the left (systole plus diastole) equals the summed capillary outflow at the far left, the temporary storage of volume during systole followed by its gradual release during diastole causes dampening of the outflow over each additional node of the arterial tree.

The second simulation shows that an increase in tissue pressure is an important obstacle for the non-pulsatile flow at the level of the capillaries. Blood flow will chose the path of least resistance and can easily bypass segments of the arterial tree under less favourable conditions. In version 2.3 of Neuromon's CardioVascularSimulation app we have added the effect of gravity, which also adds inhomogeneity in blood flow over the different branches of the arterial tree.

The third simulation shows how arterial acceleration enhances pulsatility of capillary outflow. In the model arterial acceleration is simulated by a temporary and shortlasting decrease in capacitance at stroke onset, causing all capacitances to resist expansion for a brief moment in time. In the model the triggering of arterial acceleration is synchronous for all capacitances from left to right, preventing temporary storage of blood volume and, thereby, forcing blood out of all end arterioles during the first 100-150 ms of each heart beat.

Thereby, arterial acceleration augments the change in blood flow (dF/dt) at stroke onset (upstroke), causing an increase in 'intimal rub' and, thereby, an increased release of endothelin derived relaxation factor (EDRF). In the simulation more EDRF is indicated by a more intense yellow colour. After turning the arterial acceleration on, its effect on blood flow and on the production of EDRF is shown by a systolic peak during early systole and a pulsatile colouring of the arterial branches. EDRF is a free radical (with chemical formula NO or nitric oxide) that is rapidly inactivated. In the model the tau of exponential decay is set to 3 s, meaning that the concentration is reduced to a factor 1/e within 3 s. Therefore, EDRF has little chance to build up within the capacitances and its concentration modulates synchronously to the beating heart.

Arterial acceleration has more penetration power, meaning that it is more likely to persist when tissue pressure increases. In the model, an increase in tissue pressure can be simulated by selecting nodes in the arterial tree (turning to orange), turning tissue pressure 'on' and gradually shifting the slider mid below to the right. As explained elsewhere on these pages, the increase in tissue pressure makes the flow velocity signal more Sys1 (= arterial acceleration) dominant.

With arterial acceleration active, the flow velocity waveform changes from Sys2 exclusive at the far left, via Sys2 dominant, Sys12 balanced, Sys1 dominant to Sys1 exclusive in the nodes with increased tissue pressure at the far right.

In the case of increased tissue pressure arterial acceleration may still overcome the resistance to blood flow. However, when nothing further happens, tissue perfusion remains fully dependent on arterial acceleration. This is where EDRF comes in: tissues at elevated tissue pressures will still receive the Sys1 pulse of arterial acceleration. The abrupt change in flow (from almost naught to the flow generated by arterial acceleration) results in a large dF/dt and, consequently, to more EDRF released and transported into the next capacitance with its more distal branches. Arterial acceleration can in a way be seen as a probing pulse testing tissue conditions. The release of EDRF instigates dilatation of more distal arterial branches, allowing distal branches to open up and increasingly allow blood flow during late systole and diastole also. This is demonstrated in the next simulation.

In the simulation the release of EDRF from a connecting resistance is modeled as function of the steepness of flow increase at beat onset (dF/dt). The release of EDRF is indicated by the color yellow adding to the EDRF concentration already present in the feeding capacitance. This colours both arterial branches from blue to yellow but most so for the branch meeting the highest resistance to flow. The peak concentration of EDRF attained within a branch is taken as input for changing its resistance, with high values of EDRF lowering the resistance (green arrows pointing down) and low values of EDRF increasing resistance (red arrows pointing up). When, for instance, there are high tissue pressures in capillary outflow, diastolic flow will decrease, but Sys1 flow is preserved by arterial acceleration and results in an increase in dF/dt at stroke onset. By the increase in EDRF production, the outflow resistances gradually decrease allowing more blood to push through during late systole (Sys2) and diastole. This mechanism works its way up from distal to proximal branches in the arterial tree. That is one of the emergent properties of the model: rules imposed on subcomponents lead to complex behaviour of the arterial tree as a whole.

Since EDRF release is closely linked with the strength of arterial acceleration any increase will automatically result in more EDRF released and thus a better penetration of the pressure pulse into more distal branches. A decrease in the strength of arterial acceleration causes less penetration of the pressure wave. This is demonstrated by the simulation below.

On a larger scale this explains how the combination of arterial acceleration and EDRF work together to make blood flow within the arterial branches more homogenous: when a large resistance to blood flow is met, more EDRF is produced and transported into the more distal branches by the wave of arterial acceleration, whereas a low vascular resistance causes less production of EDRF and allows more distal branches to increase their resistance. This is simulated below. Different nodes have been selected with an increase in tissue pressure. It shows how the release of EDRF opens up some and closes down other distal branches of the tree.

From version 2.3 onwards the same can be demonstrated for tissues at low hydrostatic pressures causing a collapse of distal capacitances at a low pressure, resulting in a larger dF/dt during acceleration. In these tissues the release of EDRF is greater and leads to vasodilatation. Tissues at high hydrostatic pressures have a lower dF/dt, since arterial acceleration adds less to the flow already generated by gravity. In these tissues the release of EDRF will be less and results in vasoconstriction. In this way the arterial tree adapts to the pressure gradient resulting from gravity.

In summary, it is not arterial acceleration alone but it is arterial acceleration combined with EDRF production that truly allows blood to reach into all the bodies capillary systems.

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.

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.