Cardiovascular Biomechanics

Transcription

1 Cardiovascular Biomechanics Instructor Robin Shandas, Ph.D. Associate Professor of Pediatric Cardiology and Mechanical Engineering (303) (MWF) / (303) (T,Th) Office: ECME 265 Office Hours: T, Th a.m. or by appointment (Please give me ~1-2 days notice for appointments). Spring

2 Scope of the Course Mechanics and fluid mechanics of the cardiovascular system. Why take this course? 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. Spring

3 Tentative outline Anatomy and Physiology of the Cardiovascular System Basic concepts Solid mechanics. Fluid mechanics. Blood rheology. Blood flow through arteries. Cardiac dynamics. Microcirculation (if time permits). Spring

4 Textbook and Grading Required book: Cardiovascular Physiology by Berne and Levy, Mosby. Homework Assignments (~ 10): 40% Most homework assignments will require independent research. Several HW assignments will involve class presentations. Midterm (1): 25% Final project and presentation: 35% Spring

5 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). Spring

6 Where does the engineer fit? Understand physics of cardiovascular processes. Models mathematical; experimental; animal. Provide insight into how healthy systems work and how unhealthy systems adapt. New information on effect of treatment. Design diagnostics and prosthetics. Imaging and measurement. Artificial hearts; pacemakers; prosthetic valves Spring

7 History of Cardiovascular Study Galen ( A.D.) Palpated the pulse and classified according to strength, rate Wrote On the Uses of the Parts of the Body of Man First to disprove that arteries carried air William Harvey (1628) First to postulate importance of blood circulation. Spring

8 History - contd Stephen Hales (1733) First to measure arterial pressure in an animal. Correlated loss of pressure to loss of blood volume. Likened arterial elasticity to Windkessel model. J.P. Poiseuille (1840) Established relationship between flow, pressure gradient and diameter in tube flow. Moens (1878) Pressure pulse transmission in elastic arteries. Osborne Reynolds (1883) Description of transition from laminar (ordered) to turbulent (chaotic) flow in a tube. Fick (1864) First use of a manometer to measure pressure. Otto Frank (1903) Stipulated the relationship between ventricular filling and contraction. John Womersley (1954) Mathematical relationship between pressure and flow. Spring

9 Scope of the problem Mechanics: Heart 3 layered fiber-reinforced structure with multiple fiber orientations. Highly dynamic. Arteries Multilayered thick walled structures with a combination of linear and nonlinear viscoelastic elements. Combination of passive and active elements. Capillaries Thin walled dynamic structures with predominantly active elements. Veins Mainly passive multilayered structures, easily collapsible. Spring

10 Scope of the problem Fluid Mechanics Unsteady flow. Large range of flow conditions. Reynolds number: <1 in capillaries >10,000 in turbulent jets within the heart. Tube flow, suddenly started jets, fully and transitionally turbulent pulsating jets, sheet flow, entrance flow, curved pipe flow, boundary layer separation, etc. Non-newtonian fluid (shear-thinning). Complex fluid-structure interactions. Spring

11 How to tackle this problem? Simplify, simplify, simplify Couple clinical/physiological need with modeling approach. Newtonian fluid Ok assumption for larger vessels High shear conditions. From steady to oscillating to pulsatile flow. Steady flow assumption ok for veins, capillaries. Linear to quasi-linear mechanics. Ok for certain arteries (pulmonary artery). Simplify fluid-structure interactions. No viscoelasticity, limited or no pressure pulse reflection interactions, harmonic analysis. Spring

12 The Cardiovascular system One of 3 major systems. Endocrine Chemical Regulation of various body functions (long term). Nervous Electrical Communication & short-term regulation and control. Cardiovascular Mechanical Delivery of nutrients, removal of waste Thermal & pressure regulation. Efficient regulation of gas/nutrients. Spring

13 The Cardiovascular system Essentially a plumbing system to deliver nutrients to tissue. Components: 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. Spring

14 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) Spring

15 Flow through the heart Superior Vena Cava O 2 In + CO 2 Out via Diffusion RA RV Right & Left Lungs LA LV Valves Inferior Vena Cava RA -- Right Atrium RV -- Right Ventricle LA -- Left Atrium LV -- Left Ventricle Spring

16 Anterior Surface of the Heart Spring

17 Interior of the Left Ventricle Spring

18 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. Spring

19 Major Arteries and Veins Arteries and Veins usually adjacent to each other. Large arteries and veins: 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. Spring

20 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 Spring

21 Pressure Drop in Cardiovascular System Small arteries produce the largest pressure drop Spring

22 Functional Flow Area Capillaries contain maximum crosssectional area Spring

23 Organization of Skeletal/Cardiac Muscle Spring

24 Heart Muscle - Cardiomyocyte Sarcomere = Fundamental contractile apparatus; Actin, Myosin - Proteins Spring

25 Sliding Filaments - Key to Contraction Spring

26 Properties of Skeletal & Cardiac Muscle Active -vs- Resting Tension Spring

27 Differences Between Skeletal & Cardiac Muscle 1 Many more structures present in cardiac muscle (more interconnections among cells. Spring

28 Differences Between Skeletal & Cardiac Muscle 2. Many more mitochondria within cardiac muscle cells. Foodstuff + O 2 CO 2 + H 2 O + 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. Spring

29 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 O 2 ) 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. Spring

30 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 O 2 and removal of CO 2. 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. Spring

31 The Heart Wall Interior of ventricular chamber (Endocardium) Middle of ventricular wall (Myocardium) Exterior of wall (Epicardium) Spring

32 Ventricular Contraction A B C Normal Contraction Hyperdynamic, via the use of a positive inotropic agent Heart Failure Inotrope - Affects cardiac contraction Chronotrope - Affects heart rate Spring

33 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). Spring

34 Starling s Original Experiment Venous pressure increased Venous pressure back to baseline Control Period Spring

35 The Frank-Starling Mechanism Experimental Validation Spring

36 The Frank-Starling Mechanism Increase in preload (more blood entering ventricle during diastole) End Diastolic Volume (EDV) increases Extra amount entering ventricle is ejected (Balance is maintained) Move further on the length/tension curve of cardiac muscle Increased cardiac contraction T/Ao L /Lo Spring

37 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? Spring

38 The Frank-Starling Mechanism Spring

39 Pressure-Volume Loops Spring

40 Effect of a Positive Inotrope on PV Loop Spring

41 Atrioventricular Valves: Tricsupid & Mitral Semilunar Valves: Pulmonary & Aortic Spring

42 Aortic Valve -- Longitudinal View Spring

43 Mechanism of mitral valve closure Henderson Y, Johnson FE: Two modes of closure of the heart valves, Heart, 4:69-82, Spring

44 Mechanism of mitral valve closure Development of an adverse pressure gradient U t Assume: No-viscous or gravity effects, uniform flow, no flow in C initially: Momentum equation: + U U x = - 1 r P x No acceleration with x, So, according to continuity: U/ x = 0 During deceleration, U/ t < 0 ---> P/ x > 0 --> P B > P A Spring

45 Flow downstream of the aortic valve Spring

46 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). Spring

47 Windkessel Model for Aortic Flow Q = K dp dt + p R Q = Flow rate; p = pressure; R = Resistance Spring

48 Electrical Activity of the Heart Action Potential: Cycle of changes in transmembrane electrical potential that characterizes excitable tissue. Cell + - Cell + - Voltage = 0 Voltage = -90 mv Spring

49 Fast -vs- slow response cardiac fibers Spring

50 Muscle twitch occurs after peak action potential is reached Spring

51 Chemical and electrical gradients around a resting cardiac cell Spring

52 Conduction system of the heart Spring

53 The Electrocardiogram (EKG) Spring

54 SA Node Action Potential Atrial Muscle AV Node HIS Bundle Bundle Branches Purkinje Fibers Ventricular Muscle Spring

55 Spring