Download Cardiovascular Biomechanics

Cardiovascular Biomechanics
Instructor
n
n
n
n
n
n
Robin Shandas, Ph.D.
Associate Professor of Pediatric Cardiology and
Mechanical Engineering
[email protected]
(303) 837-2586 (MWF) / (303) 492-0553 (T,Th)
Office: ECME 265
Office Hours: T, Th 10-11 a.m. or by appointment
(Please give me ~1-2 days notice for
appointments).
Cardiovascular Biomechanics,
Spring 2004
1
Scope of the Course
Mechanics and fluid mechanics of the cardiovascular
system.
Why take this course ?
n
n
n
n
Bioengineering as applied to the cardiovascular area.
Focused examination on the systems level.
Understand challenges of some of the most severe health
problems.
Apply modeling and design principles.
Cardiovascular Biomechanics,
Spring 2004
2
Tentative outline
Anatomy and Physiology of the
Cardiovascular System
Basic concepts
n
n
Solid mechanics.
Fluid mechanics.
Blood rheology.
Blood flow through arteries.
Cardiac dynamics.
Microcirculation (if time permits).
Cardiovascular Biomechanics,
Spring 2004
3
Textbook and Grading
Required book:
n
Cardiovascular Physiology by Berne and Levy,
Mosby.
Homework Assignments (~ 10): 40%
n
n
Most homework assignments will require
independent research.
Several HW assignments will involve class
presentations.
Midterm (1): 25%
Final project and presentation: 35%
Cardiovascular Biomechanics,
Spring 2004
4
Plumber or Cardiologist ?
Fixes leaky pipes (arterial dissections & aneurysms).
Repairs valves in the main pump (valvular
regurgitation).
Expands blocked pipes (percutaneous transluminal
coronary angioplasty – PTCA, stents)
Replaces main pumping system (cardiac
transplantation).
Filters and purifies the water (dialysis).
Cardiovascular Biomechanics,
Spring 2004
5
Where does the engineer fit ?
Understand physics of cardiovascular
processes.
n
Models
w mathematical; experimental; animal.
n
n
Provide insight into how healthy systems work and
how unhealthy systems adapt.
New information on effect of treatment.
Design diagnostics and prosthetics.
n
n
Imaging and measurement.
Artificial hearts; pacemakers; prosthetic valves…
Cardiovascular Biomechanics,
Spring 2004
6
History of Cardiovascular Study
Galen (130-200 A.D.)
n Palpated the pulse and classified according to
strength, rate
n Wrote On the Uses of the Parts of the Body of
Man
n First to disprove that arteries carried air
William Harvey (1628)
n First to postulate importance of blood
circulation.
Cardiovascular Biomechanics,
Spring 2004
7
History - contd
Stephen Hales (1733)
n First to measure arterial pressure in an animal.
n Correlated loss of pressure to loss of blood volume.
n Likened arterial elasticity to “Windkessel” model.
J.P. Poiseuille (1840)
n Established relationship between flow, pressure gradient and diameter in tube
flow.
Moens (1878)
n Pressure pulse transmission in elastic arteries.
Osborne Reynolds (1883)
n Description of transition from laminar (ordered) to turbulent (chaotic) flow in a
tube.
Fick (1864)
n First use of a manometer to measure pressure.
Otto Frank (1903)
n Stipulated the relationship between ventricular filling and contraction.
John Womersley (1954)
n Mathematical relationship between pressure and flow.
Cardiovascular Biomechanics,
Spring 2004
8
Scope of the problem
Mechanics:
n
Heart
w 3 layered fiber-reinforced structure with multiple fiber orientations.
w Highly dynamic.
n
Arteries
w Multilayered thick walled structures with a combination of linear and non-
linear viscoelastic elements.
w Combination of passive and active elements.
n
Capillaries
w Thin walled dynamic structures with predominantly active elements.
n
Veins
w Mainly passive multilayered structures, easily collapsible.
Cardiovascular Biomechanics,
Spring 2004
9
Scope of the problem
Fluid Mechanics
n
n
Unsteady flow.
Large range of flow conditions.
w Reynolds number: <1 in capillaries ‡ >10,000 in turbulent jets
within the heart.
w Tube flow, suddenly started jets, fully and transitionally
turbulent pulsating jets, sheet flow, entrance flow, curved pipe
flow, boundary layer separation, etc.
n
n
Non-newtonian fluid (shear-thinning).
Complex fluid-structure interactions.
Cardiovascular Biomechanics,
Spring 2004
10
How to tackle this problem ?
Simplify, simplify, simplify…
Couple clinical/physiological need with modeling approach.
Newtonian fluid
n
Ok assumption for larger vessels
w High shear conditions.
From steady to oscillating to pulsatile flow.
n
Steady flow assumption ok for veins, capillaries.
Linear to quasi-linear mechanics.
n
Ok for certain arteries (pulmonary artery).
Simplify fluid-structure interactions.
n
No viscoelasticity, limited or no pressure pulse reflection interactions,
harmonic analysis.
Cardiovascular Biomechanics,
Spring 2004
11
The Cardiovascular system
One of 3 major systems.
n
Endocrine – Chemical
w Regulation of various body functions (long term).
n
Nervous – Electrical
w Communication & short-term regulation and control.
n
Cardiovascular – Mechanical
w Delivery of nutrients, removal of waste
w Thermal & pressure regulation.
w Efficient regulation of gas/nutrients.
Cardiovascular Biomechanics,
Spring 2004
12
The Cardiovascular system
Essentially a plumbing system to deliver nutrients to
tissue.
Components:
n
n
n
n
n
Pump (heart)
Major tubing (arteries)
Minor connections and branches (arterioles).
Nutrient transfer (capillaries)
Return tubing (venules and veins).
Capillary network is the focus of the plumbing since
this is where nutrient/waste transfer takes place.
Cardiovascular Biomechanics,
Spring 2004
13
Cardiovascular System
Heart: 2 Chambers in Series
Pulmonary circulation in between
right heart and left heart.
Systemic circulation refers to
remaining circulatory systems.
Left heart provides major component
of work to drive blood through the
systemic circulation.
Heart pulsation: Systole (Contraction)
and Diastole (Relaxation/Filling)
Cardiovascular Biomechanics,
Spring 2004
14
Flow through the heart
Superior
Vena Cava
RV
RA
O2 In + CO2
Out via
Diffusion
Right &
Left
Lungs
LA
LV
Valves
Inferior
Vena Cava
RA -- Right Atrium
RV -- Right Ventricle
Cardiovascular Biomechanics,
Spring 2004
LA -- Left Atrium
LV -- Left Ventricle
15
Anterior Surface of the Heart
Cardiovascular Biomechanics,
Spring 2004
16
Interior of the Left Ventricle
Cardiovascular Biomechanics,
Spring 2004
17
Mechanical Events in the Left (Right)
Ventricle
Relaxation or Diastole
•
Blood fills ventricle from atrium
-- mitral (tricuspid) valve opens.
Atrial Systole or Contraction
•
Atrium contracts to expel
remaining blood and “prime”
ventricular pump.
Contraction or Systole
•
Ventricle contracts, aortic
(pulmonic) valve opens, blood is
ejected into the aorta.
Cardiovascular Biomechanics,
Spring 2004
18
Major Arteries and Veins
Arteries and Veins usually adjacent
to each other.
Large arteries and veins: 25 - 30
mm in diameter.
Many interventional procedures
(cardiac angiography,
catheterization) use the femoral
artery (left side) or femoral vein
(right heart) as the origin for
access to the heart.
Cardiovascular Biomechanics,
Spring 2004
19
Major Arteries and Veins
Original contraction is pulsatile. However, flow in capillaries and veins is
almost steady state, due to the elasticity of the large arteries.
Pulse Pressure = Systolic Pressure - Diastolic pressure
Cardiovascular Biomechanics,
Spring 2004
20
Pressure Drop in Cardiovascular
System
Small arteries produce the largest pressure drop
Cardiovascular Biomechanics,
Spring 2004
21
Functional Flow Area
Capillaries
contain
maximum crosssectional area
Cardiovascular Biomechanics,
Spring 2004
22
Organization of Skeletal/Cardiac
Muscle
Cardiovascular Biomechanics,
Spring 2004
23
Heart Muscle - Cardiomyocyte
Sarcomere = Fundamental
contractile apparatus;
Actin, Myosin - Proteins
Cardiovascular Biomechanics,
Spring 2004
24
Sliding Filaments - Key to Contraction
Cardiovascular Biomechanics,
Spring 2004
25
Properties of Skeletal & Cardiac
Muscle
Active -vs- Resting Tension
Cardiovascular Biomechanics,
Spring 2004
26
Differences Between Skeletal &
Cardiac Muscle
1 Many more structures present in cardiac muscle (more interconnections
among cells.
Cardiovascular Biomechanics,
Spring 2004
27
Differences Between Skeletal &
Cardiac Muscle
2. Many more mitochondria within cardiac muscle cells.
Foodstuff + O2 · CO2 + H2O + Energy (ATP)
Glucose is a common food
•
Energy for cellular processes provided by Adenosine TriPhospate (ATP)
•
Chemical (potential) energy stored in the covalent bonds between atoms
of a molecule.
•
ATP has much higher (≈ 2X) potential energy stored in its terminal bonds.
•
Release of one of the terminal phosphates releases ≈ 7300 calories / mole
(Compare to ≈ 3000 cal/mole for typical chemical bonds)
•
Mitochondria are part of the cellular apparatus responsible for providing
energy to the cell.
Cardiovascular Biomechanics,
Spring 2004
28
Differences Between Skeletal &
Cardiac Muscle
2. Many more mitochondria within cardiac muscle cells.
•
Skeletal muscle can build an “oxygen debt” by transforming
glucose into lactate - “Glycolysis.” -- Anaerobic (absence of
O2) activity.
•
However, cardiac muscle cannot withstand oxygen debt Constant aerobic activity.
•
Mitochondria in cardiac muscle cells function to constant
energy supply for cellular processes and muscular
contraction.
Cardiovascular Biomechanics,
Spring 2004
29
Differences Between Skeletal &
Cardiac Muscle
3. Many more capillaries feeding cardiac muscle cells.
•
Skeletal muscle: 1 capillary feeds ≈ 5 - 10 muscle fibers.
•
Cardiac muscle: 1 capillary per fiber (cardiomyocyte).
•
Constant aerobic activity requires constant input of O2 and
removal of CO2.
•
However, cardiac muscle cannot withstand oxygen debt Constant aerobic activity.
•
Mitochondria in cardiac muscle cells function to constant
energy supply for cellular processes and muscular
contraction.
Cardiovascular Biomechanics,
Spring 2004
30
The Heart Wall
Interior of ventricular chamber
(Endocardium)
Middle of ventricular wall
(Myocardium)
Exterior of wall (Epicardium)
Cardiovascular Biomechanics,
Spring 2004
31
Ventricular Contraction
A Normal
Contraction
B
Hyperdynamic,
via the use of a
positive inotropic
agent
C
Heart Failure
Inotrope - Affects cardiac
contraction
Chronotrope - Affects heart rate
Cardiovascular Biomechanics,
Spring 2004
32
The Frank-Starling Mechanism
Heart contraction is largely dependent
on loading.
Heart muscle expands to maximum
during filling.
Maximal length produces maximum
tension on the muscle, resulting in
forceful contraction.
Therefore, greater filling (more volume
entering the heart) produces greater
ejection (more volume leaving).
Cardiovascular Biomechanics,
Spring 2004
33
Starling’s Original Experiment
Venous
pressure
increased
Venous
pressure
back to
baseline
Control Period
Cardiovascular Biomechanics,
Spring 2004
34
The Frank-Starling Mechanism
Experimental Validation
Cardiovascular Biomechanics,
Spring 2004
35
The Frank-Starling Mechanism
Increase in preload
(more blood entering
ventricle during
diastole)
Extra amount entering
ventricle is ejected
(Balance is maintained)
End Diastolic Volume
(EDV) increases
Move further on the
length/tension curve of
cardiac muscle
T/Ao
Increased cardiac
contraction
L’/Lo
Cardiovascular Biomechanics,
Spring 2004
36
The Frank-Starling Mechanism
•
Compensation for increased preload or afterload via
increase in cardiac contraction so that cardiac output
matches venous return.
Preload
•
Left ventricular filling pressure (End Diastolic pressure
and/or volume in the ventricle).
Afterload
•
Peripheral resistance (Resistance in the arterial system
downstream of the left ventricle).
Why would preload and/or afterload increase ?
Cardiovascular Biomechanics,
Spring 2004
37
The Frank-Starling Mechanism
Cardiovascular Biomechanics,
Spring 2004
38
Pressure-Volume Loops
Cardiovascular Biomechanics,
Spring 2004
39
Effect of a Positive Inotrope on PV
Loop
Cardiovascular Biomechanics,
Spring 2004
40
Atrioventricular Valves: Tricsupid & Mitral
Semilunar Valves: Pulmonary & Aortic
Cardiovascular Biomechanics,
Spring 2004
41
Aortic Valve -- Longitudinal View
Cardiovascular Biomechanics,
Spring 2004
42
Mechanism of mitral valve closure
Henderson Y, Johnson FE: Two modes of closure of the heart valves, Heart, 4:69-82, 1912
Cardiovascular Biomechanics,
Spring 2004
.
43
Mechanism of mitral valve closure
Development of an adverse pressure gradient
Assume: No-viscous or
gravity effects, uniform
flow, no flow in C initially:
Momentum equation:
∂U + U ∂U = - 1 ∂P
r ∂x
∂t
∂x
No acceleration with x, So, according to continuity:
∂U/∂x = 0
During deceleration, ∂U/∂t < 0 ---> ∂P/∂x > 0 --> PB > PA
Cardiovascular Biomechanics,
Spring 2004
44
Flow downstream of the aortic valve
Cardiovascular Biomechanics,
Spring 2004
45
“Windkessel” Model for Aortic Flow
•
Aorta represented by an elastic chamber.
•
Peripheral blood vessels represented as a rigid tube with
constant resistance.
•
Ventricle pulses --> energy used to distend the aortic walls
and to drive flow downstream.
•
Energy used to extend the walls is subsequently used to
maintain forward flow during diastole.
•
In the elastic chamber, rate of change of volume is assumed to
be proportional to pressure.
•
Flow rate out is assumed to be proportional to pressure
gradient and resistance (electrical analog).
Cardiovascular Biomechanics,
Spring 2004
46
“Windkessel” Model for Aortic Flow
dp p
Q = K dt + R
Q = Flow rate; p = pressure; R = Resistance
Cardiovascular Biomechanics,
Spring 2004
47
Electrical Activity of the Heart
Action Potential: Cycle of changes in transmembrane electrical
potential that characterizes excitable tissue.
Cell
Voltage = 0
+
-
+
-
Cell
Voltage = -90 mV
Cardiovascular Biomechanics,
Spring 2004
48
Fast -vs- slow response cardiac fibers
Cardiovascular Biomechanics,
Spring 2004
49
Muscle twitch occurs after peak action potential is reached
Cardiovascular Biomechanics,
Spring 2004
50
Chemical and electrical gradients around a resting cardiac cell
Cardiovascular Biomechanics,
Spring 2004
51
Conduction system of the heart
Cardiovascular Biomechanics,
Spring 2004
52
The Electrocardiogram (EKG)
Cardiovascular Biomechanics,
Spring 2004
53
Action Potential
SA Node
Atrial Muscle
AV Node
HIS Bundle
Bundle Branches
Purkinje Fibers
Ventricular Muscle
Cardiovascular Biomechanics,
Spring 2004
54
Cardiovascular Biomechanics,
Spring 2004
55