Fluid Dynamics: Orthostatic Blood Pressure Equation

[Umair Shariff]

Hi everyone, I have been hunting all over the Internet for an explanation to changes in the blood pressure when sitting, standing or lying down. I know the complex mechanisms that are involved but I need an equation for an ideal system with the heart in the middle and the pressure that needs to be generated to drive blood to the brain in various positions.

It has been a long time since I studied physics and fluid dynamics, but this equation, F=2gh, keeps popping up in my head. I'd appreciate if someone could either verify and confirm this or provide me with an alternate equation

Thank you

 

[jim mcnamara]

I can't give you a good answer. But you need to revisit some assumptions. I believe.
In mammals like giraffes there are special arterial valves to control BP in the head for example as it moves head up/down to browse on low shrubs. All mammals and people have ways to alter BP that involve hormones like vasodilators and valve structures in veins as well. So, you need to consider the "control" system as it were.

Correct me if you think I'm wrong here:
In other words there is a whole lot more going on than you seem to describe. Anything that simple would be interesting but unlikely to be usefully accurate.
http://www.merckmanuals.com/home/he...enous-disorders/overview-of-the-venous-system

Here is a link with a partial discussion( full doc behind a paywall, sorry, if useful hit the local college library):
http://link.springer.com/article/10.1007/s007910050030#page-1

 

[Umair Shariff]

Yes, I understand that the mechanisms involved to control blood pressure are varied including the means by which the body provides feedback on changes in pressure.

I am looking for a simple analogy to share with my friend so that he is better able to understand the difference in posture. This is by no means an academic venture and I need to be able to simply convey my meaning to him

I can't give you a good answer. But you need to revisit some assumptions. I believe.
In mammals like giraffes there are special arterial valves to control BP in the head for example as it moves head up/down to browse on low shrubs. All mammals and people have ways to alter BP that involve hormones like vasodilators and valve structures in veins as well. So, you need to consider the "control" system as it were.

Correct me if you think I'm wrong here:
In other words there is a whole lot more going on than you seem to describe. Anything that simple would be interesting but unlikely to be usefully accurate.
http://www.merckmanuals.com/home/he...enous-disorders/overview-of-the-venous-system

Here is a link with a partial discussion( full doc behind a paywall, sorry, if useful hit the local college library):
http://link.springer.com/article/10.1007/s007910050030#page-1

 

[Andy Resnick]

Hi everyone, I have been hunting all over the Internet for an explanation to changes in the blood pressure when sitting, standing or lying down. I know the complex mechanisms that are involved but I need an equation for an ideal system with the heart in the middle and the pressure that needs to be generated to drive blood to the brain in various positions.

It has been a long time since I studied physics and fluid dynamics, but this equation, F=2gh, keeps popping up in my head. I'd appreciate if someone could either verify and confirm this or provide me with an alternate equation

Thank you

The basic idea of orthostatic pressure comes simply from the hydrostatic pressure head ΔP = ρgh, where ρ is the fluid density and h the height above (or below) a reference. When standing, the pressure at your feet is higher than the pressure at your head, for example. When you are lying down, your heart does not have to overcome that much orthostatic pressure, and so when you stand up rapidly, the blood pressure in your head temporarily drops.

This simple model has been applied to orthostatic intolerance disorder and bone loss resulting from long-duration microgravity. The reality is more complex, and the corresponding models become more complex. A good source text is "Cardiovascular and Respiratory Systems: Modeling, Analysis and Control" (Batzel, Kappel, Schneditz and Tran).