Series and Parallel Vascular Networks
For a series resistance network, the total resistance (RT) equals the sum of the individual resistances. Therefore, for the vessels depicted in the figure, the total resistance is equal to the sum of the small artery (RA), arterioles (Ra), capillaries (Rc), venules (Rv), and vein (RV) resistances.
RT = RA + Ra + Rc + Rv + RV
The resistance of each segment relative to the total resistance of all the segments determines how changing the resistance of one segment affects total resistance. To illustrate this principle, a relative resistance value can be assigned to each of the five resistance segments in this model. The relative resistances will be similar to what is observed in a typical vascular bed.
Assume, RA = 20, Ra = 50, Rc = 20, Rv = 6, RV = 4
Therefore, RT = 20 + 50 +20 +6 + 4 = 100
Using this empirical model, we can see that doubling RV from 4 to 8 increases RT from 100 to 104, a 4% increase. In contrast, doubling Ra from 50 to 100 increases RT from 100 to 150, a 50% increase. If this were done for each of the segment, we would find that the arteriolar segment with the highest relative resistance (arterioles) has the greatest effect on total resistance. As a group, changes in diameter (and therefore resistance) of small arteries and arterioles have the greatest effect on vascular resistance because these two vessel segments comprise about 70% of the total resistance in most organs.
The above analysis also explains why the radius of a large, distributing artery must be decreased by more than 50% to have a significant effect on organ blood flow. These large arteries comprise only about 1% of the total resistance. Therefore, unlike arterioles, small changes in their diameter have a relatively small effect on total resistance. They must undergo large reductions in diameter before resistance and flow are significantly reduced. This is referred to as a "critical" stenosis. This can be confusing because the Poiseuille's equation indicates that resistance to flow is inversely related to radius to the fourth power. Therefore, a 50% reduction in radius should increase resistance 16-fold (1500% increase); however, total resistance will only increase by about 15% because the large artery resistance is normally only about 1% of the total resistance.