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.
