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Define Resistance and Compliance. What are the primary and secondary parameters that are affected by the changes in both Resistance and Compliance? Explain how these combinations of changes have an effect on the arterial parameters and why? Use results from windksimrun. Observe and state the changes in trends and use the theory discussed in class to justify these changes. Refer back to Wind KesIndiv Results.

Resistance can quite simply be defined as the tendency of a particular item to oppose the blow flow going through or by it, and is usually dictated by the size and diameter of the different vessels. In other words, as the amount of resistance decreases, the amount of blow flow proportionally increases, regardless of the fact that the perfusion pressure goes down, since resistance is inversely related to the flow. It should always be remembered that blood ends up flowing through the cardiovascular system from areas of higher pressure to those of lower pressure. (Silverthorn, 473)

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When dealing with the resistance element, there are three main parameters to take a look at. First, the radius of the tube (r), as that can have a direct impact on the flow rate to begin with. Next, the length of the tube (L), as this also important in dictating the parameters of the flow rate. Finally, the viscosity of the substance going through the tube can also have a large impact as well (represented by eta). The French physician Jean Leonard Marie Poiseuille came up with the relationship between these factors, known as Poiseuille's law. R=8L*(eta)/(pi)*r4. That being said, since 8/(pi) is a constant, it can accordingly be removed from the equation, leaving us with the relationship stating that R is inversely proportional to L*(eta)/r4. In English, this means to us that the resistance increases as the tube length increases, that the resistance increases as the viscosity increases, and the resistance decreases as the radius increases (473-474).

In what can be considered to be an 'ideal' situation, where there are no external factors such as elasticity involved, with a flow and resistance that is constant, the model can be seen in the following equation: Q(t) = DP(t)/R. Q(t) is the flow at time t measured in units of L/s and ∆P(t) is the difference in pressures (pressure upstream - pressure downstream) in mmHg. However, it is relatively rare in life to encounter such 'ideal' situations, and in true biological systems, arteries will show properties of compliance. Compliance, which is a relationship between pressure and volume, can be defined as a measure of the tendency of a hollow vessel to stretch in response to changes in pressure.

Changes in resistance and compliance primarily affect the flow of the substance but also secondarily affect the pressure of the substance that is acting on the walls of the vessel. In summation, changes in resistance end up affecting the rate of flow of the substance and changes in compliance end up affecting the amount of volume that can be stored for a specific particular flow of a substance. Thus, the changed fluid flow rates can affect the severity of the compliance's effects on both pressure and volume.

The arterial parameters are defined as pressure, volume, and flow. Changes in the resistance and compliance will end up affecting them, as they are all inherently interlinked. Compliance dictates the amount of volume that can be stored in a particular vessel. On that token, if there is more volume that can be stored, the flow rate of the substance will go down, as will the pressure, and vice versa if there is less volume that can be stored in that vessel. As mentioned earlier, resistance can also affect substance flow.

Figure . In this figure, differently colored lines are representative of vessels with different resistances. The figure itself is showing the max flow, min flow, mean flow, and fractional flow in systole change with changes in the arterial compliance and the arterial resistance in a series of vessels that have fixed resistances, and gives the ability to visually see the relationships.

The top left sub-figure shows that as the compliance goes up, the max flow also increases at a constant resistance. In this simulation, the max flow models the blood flow during systole, and the max flow stays the same (constant) when the compliance is below the baseline, which is the compliance of a normal artery. This is consistent with what was expected, as less compliant leads it to behave like a lead pipe and store little to no volume. On the other hand, when the compliance goes above the baseline, the max flow goes down. This is not too surprising either, as it is known that the greater the compliance, the more the tendency of the vessel to expand in order to accommodate the increased volume, which results in a lower flow through output. In addition, it can be observed that when at a fixed compliance, higher resistance means a lower max flow, since resistance essentially controls the flow rate.

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The top right sub-figure is essentially the inverse of the first situation, and it is showing the effects of the aforementioned conditions (resistance and compliance) on the min flow situation. The min flow happens during diastole, when the heart is in a fully relaxed state, and is driven by the volume of substance that is stored in the artery during systole. This makes the min flow extremely close to zero until the baseline is reached, and when the compliance goes over the baseline, the min flow increases as well, since more volume is being stored, resulting in a higher min flow. Min flow can also be seen in this sub-figure to decrease as resistance increases in equally compliant vessels.

The bottom left sub-figure helps to analyze the situation further by showing the average of the min and max flows. As long as the compliance is below the baseline, the mean flow essentially behaves akin to the max flow. However, once the compliance goes past the baseline, it now models the min flow. The rationale here is that vessels that are more compliant have the ability to store more volume, which lowers the max flow (and resultantly increases the min flow) and vice versa.

Finally, the bottom right sub-figure shows the fractional flow during systole (max flow) while changing the resistance and compliance factors. As resistance increases, the fractional systolic flow decreases, since the resistance essentially regulates how much substance can flow during systole, and thus a higher resistance allows for less substance flow.

Figure .This figure displays the changing relationship between the pressure and volume as there are changes in the compliance and the resistance. When the resistance is fixed, the maximum pressure goes down as the compliance goes up, and when the compliance is fixed, the maximum pressure goes down as the resistance decreases. The differently colored lines represent different resistances.

The top left sub-figure shows max pressure against compliance, and it can be observed from this that as the compliance is increased, the max pressure decreases. That being noted, another observation from this graph is that with a higher resistance, there is accordingly a higher initial and final max pressure, which shows that there is a relationship that exists between the resistance and the max pressure. As would be expected, the max pressure happens during systole.

The top right sub-figure shows min pressure versus compliance, and shows that min pressure increases as compliance increases, and also that the greater the resistance, the greater the min pressure. As was the case with the min flow, the min pressure happens during diastole since the lowest pressure happens when the heart is in a relaxed state.

The bottom left sub-figure shows arterial volume versus time. The arterial volume can be described as a combination of the min and max volumes of increasing compliance. The dashed lines are representative of the max values, and likewise the solid lines of the min values. When looking at these two with relation to the other, the min values have a higher slope, and as the compliance goes up, so does the volume.

The bottom right graph is the change in volume against the compliance, and is done essentially to be able to visualize the arterial volume versus time graph in a way that makes it give more information. The distance between the max and min is taken for each of the points for each individual resistance, and is plotted in a new graph. For each resistance, there is a maximum change in volume. From this, it can be seen that when the resistance is lower, the larger the compliance when it reaches its maximum. Furthermore, lower resistance means a greater change in volume.

What physiological conditions cause such a change in resistance and compliance?

Of the quantities that vary in time (i.e., variables - as opposed to those that are fixed (called parameters), which quantities do we need to know to give a complete description of the state of the systems? Use results from SimpWind.mdl.