Cardiovascular Biomechanics
Instructor
n Robin Shandas, Ph.D.
n Associate Professor of Pediatric Cardiology and
Mechanical Engineering
n Robin.shandas@colorado.edu
n (303) 837-2586 (MWF) / (303) 492-0553 (T,Th)
n Office: ECME 265
n Office Hours: T, Th 10-11 a.m. or by appointment
(Please give me ~1-2 days notice for appointments).
Scope of the Course
Mechanics and fluid mechanics of the cardiovascular system.
Why take this course ?
n Bioengineering as applied to the cardiovascular area. n Focused examination on the systems level.
n Understand challenges of some of the most severe health
problems.
Tentative outline
Anatomy and Physiology of the
Cardiovascular System
Basic concepts
n Solid mechanics.
n Fluid mechanics.
Blood rheology.
Blood flow through arteries.
Cardiac dynamics.
Textbook and Grading
Required book:
n Cardiovascular Physiology by Berne and Levy,
Mosby.
Homework Assignments (~ 10): 40%
n Most homework assignments will require
independent research.
n Several HW assignments will involve class
presentations.
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).
Where does the engineer fit ?
Understand physics of cardiovascular
processes.
n Models
w mathematical; experimental; animal.
n Provide insight into how healthy systems work and
how unhealthy systems adapt.
n New information on effect of treatment.
Design diagnostics and prosthetics.
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
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.
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
Scope of the problem
Fluid Mechanics
n Unsteady flow.
n 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 Non-newtonian fluid (shear-thinning). n Complex fluid-structure interactions.
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,
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.
The Cardiovascular system
Essentially a plumbing system to deliver nutrients to tissue.
Components:
n Pump (heart)
n Major tubing (arteries)
n Minor connections and branches (arterioles). n Nutrient transfer (capillaries)
n Return tubing (venules and veins).
Capillary network is the focus of the plumbing since this is where nutrient/waste transfer takes place.
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)
Flow through the heart
Superior Vena Cava Inferior Vena Cava RA RV Right & Left Lungs O2 In + CO2 Out via Diffusion LA LV Valves RA -- Right Atrium RV -- Right Ventricle LA -- Left Atrium LV -- Left VentricleMechanical 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
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.
Original contraction is pulsatile. However, flow in capillaries and veins is almost steady state, due to the elasticity of the large arteries.
Small arteries produce the largest pressure drop
Pressure Drop in Cardiovascular
System
Capillaries contain
maximum cross-sectional area
Organization of Skeletal/Cardiac
Muscle
Sarcomere = Fundamental
contractile apparatus;
Actin, Myosin - Proteins
Active -vs- Resting Tension
Properties of Skeletal & Cardiac
Muscle
1 Many more structures present in cardiac muscle (more interconnections among cells.
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)
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.
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
Differences Between Skeletal &
Cardiac Muscle
Interior of ventricular chamber (Endocardium)
Exterior of wall (Epicardium) Middle of ventricular wall
(Myocardium)
A Normal
Contraction
B Hyperdynamic, via the use of a positive inotropic agent
C Heart Failure
Inotrope - Affects cardiac
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).
Control Period Venous pressure increased Venous pressure back to baseline
The Frank-Starling Mechanism
Increase in preload (more blood entering ventricle during
diastole)
End Diastolic Volume (EDV) increases
Move further on the length/tension curve of cardiac muscle
T/Ao
Extra amount entering ventricle is ejected
(Balance is maintained)
• 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 ?
Effect of a Positive Inotrope on PV
Loop
Atrioventricular Valves: Tricsupid & Mitral Semilunar Valves: Pulmonary & Aortic
Mechanism of mitral valve closure
Mechanism of mitral valve closure
Development of an adverse pressure gradientAssume: No-viscous or gravity effects, uniform
flow, no flow in C initially: Momentum equation:
∂U
∂t
+ U ∂U
∂x
= - 1
r
∂P
∂x
No acceleration with x, So, according to continuity: ∂U/∂x = 0
“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.
“Windkessel” Model for Aortic Flow
Q = K
dp
dt +
R
p
Electrical Activity of the Heart
Action Potential: Cycle of changes in transmembrane electrical potential that characterizes excitable tissue.
Cell Cell
Voltage = 0
+ - +
SA Node Atrial Muscle AV Node HIS Bundle Bundle Branches Purkinje Fibers Ventricular Muscle Action Potential
