Cardiovascular Fluid Mechanics
National Biomechanics Day
What is a fluid?
Fluid:
A material that continuously deforms under applied shear stress
Fluid mechanics is the study of fluids in…
motion (fluid dynamics)
at rest (fluid statics)
Why do we study fluid dynamics?
Why do we care about fluids in our body?
=
But… these equations are very difficult to solve for complex problems!
We use the Navier-Stokes Equations* to describe the behavior of any fluid
*One of the seven Millennium Prize Problems:
https://www.claymath.org/millennium-problems/navier–stokes-equation
However, we can solve these equations for some simple problems!
Simple example 1: Poiseuille flow
Simple example 1: Poiseuille flow
Using Navier-Stokes, we can predict that…
What does the velocity change throughout the pipe
How much pressure do we need to push this water?
R
L
Q: Flow rate [ml/s]
Velocity u(r)
r
p1
p2
[Pa]
[m/s]
Simple example 2: Mass conservation
Q1 [m3/s]
Q2
The flow rate does not change, but velocity does!
A1
A2
V1 [m/s]
V2
Simple example 3: Bernoulli’s Principle
Bernoulli’s Principle tells us how energy (velocity, pressure) changes throughout the fluid
Region 1
Region 2
V1
V2
p1
p2
Going from simple fluid dynamics problems to complex ones
In complex blood vessels, we cannot :(
In a straight pipe, we can find a simple equation!
What do we do for complex problems, like the human body?
We have to solve these equations with computational fluid dynamics!
Coronary artery disease
p1
p1
p2
p1
p2
p2
Aortic valve stenosis
Aortic valve stenosis
Measuring pressure inside someone’s heart is hard!
p1
p2
p1
p2
Application of Bernoulli’s Principle
Echocardiography uses sound waves to create images of our heart and to measure blood velocity (Doppler effect)
We can measure v1,v2 !
P1
P2