8.5.2. Biomedical Applications

The heart blockage, you know it. This is very common in artery systems who have a heart blockage. That means if I have a blockage, okay, this is pipe flow. and the blockage. If it is a symmetry this blockage is a symmetry that means blockage what is happening in this side this side is same. So, if I draw the streamlines for this so you can understand it the middle streamline will go like this and other flow patterns will be change it like the first one will come like this come like this go like this.

come like this go like this if it is a symmetry we can draw the streamlines that is what.

In the context of fluid mechanics, when blood flow in arteries is obstructed, it creates a blockage. If this blockage is symmetrical, meaning it obstructs the artery evenly on both sides, the flow patterns will change predictably. The main streamline, or the path that the blood typically flows, will still attempt to follow a similar route, but the presence of the blockage causes alterations in velocity and pressure in surrounding blood flow. This symmetrical blockage leads to a certain distribution of streamlines around the blockage, allowing us to anticipate how the blood will flow.

Imagine a garden hose with a thumb partially pressing down on the opening. If you apply pressure evenly on both sides, the water still flows but in a different way, creating turbulent patterns that move around the blockage. Similarly, in the artery, blood will alter its path around the blockage, leading to a change in how blood pressure and velocity behave.

Now, if you look at these terms, if I look at this d v by d t, if I just expand it I will have a in vector forms. So, I will have these components is a local accelerations component which is with respect to time and I will have a components V dot grade. Please look at some of the vectors calculus part or vector relations in any of the engineering mathematics books. I am not going more details.

When examining blockages, it is crucial to understand the difference between symmetric and asymmetric blockages. A symmetric blockage will distribute the flow adjustments evenly, while an asymmetric blockage will create more turbulence and changes in velocity at one side than the other. This leads to complexity in predicting the flow pattern as forces are unevenly distributed, causing stress on the artery walls and affecting blood flow efficiency.

Consider a river that flows straight, representing symmetric flow where there is no obstruction. Now, if a large branch falls into one side of the river, it disrupts the flow and creates areas of faster and slower water movement around the obstruction. This is like an asymmetric blockage in an artery, which may require more medical intervention to resolve.

You will have the pressure diagrams that is what we will also change it and the velocity will change it the vortex formations will change it that is the fluid mechanics strength. It can apply for biomechanics, it can be applied for turbo machineries, it can apply for any civil engineering structures and all.

The flow of blood through arteries can be affected significantly by Reynolds numbers, which indicate whether the flow is laminar (smooth) or turbulent. Small changes in flow conditions can switch a flow from being predictable and smooth to chaotic, thus changing the patterns of pressure and velocity. In medical terms, this could lead to health risks such as increased heart strain or even a stroke.

Think about water flowing through a narrow straw versus a large pipe. In the straw (like a small artery), the flow is smooth and easy, but if you try to shove more water through it, the flow starts to swirl and become chaotic, representing how changing conditions can affect blood flow in our bodies.

--