EE 5340/7340, SMU Electrical Engineering Department, © Carlos E. Davila, Electrical Engineering Dept. Southern Methodist University slides can be viewed at: EE 5340/7340 Introduction to Biomedical Engineering Catheterization & Cardiac Output

EE 5340/7340, SMU Electrical Engineering Department, © Example of Catheters

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area Bernoulli’s Equation: P t : total fluid pressure P : local static fluid pressure ( this is the term we want to measure )  : fluid density g : acceleration of gravity h : height of fluid w.r.t. a given reference u: fluid velocity pressure due to potential energy pressure due to kinetic energy

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area (cont.) pressure sensors P2P2 P1P1 heart valve orifice c.s. area = A

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area (cont.) frictionless flow difference in heights at 2 sensor locations is zero (h 1 = h 2 ) velocity at location 1 is small compared to location 2 velocity (u 1 << u 2 ) Assumptions: Bernoulli’s equation at location 1: (1)

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area (cont.) Bernoulli’s equation at location 2: (2) subtract (2) from (1): or:

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area (cont.) flow at orifice: assumes velocity through orifice = velocity at location 2 orifice c.s. area:

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Heart Valve Surface Area (cont.) If friction is taken into account: c d : discharge coefficient semilunar valve: c d = 0.85 mitral valve: c d = 0.6

EE 5340/7340, SMU Electrical Engineering Department, © Phonocardiography: Measurement of Heart Sounds mm Hg aortic pressure left ventricular pressure aortic valve opens mitral valve opens ECG heart sounds (phonocardiogram) 4th 1st 2nd 3rd 4th mitral valve closes dicrotic notch P R T Q S

EE 5340/7340, SMU Electrical Engineering Department, © Heart Sound Generation n first: movement of blood during V. systole, closure of AV valves, turbulence at aortic and pulmonary valves. n second: deceleration and flow reversal of blood in aorta and pulmonary artery; closure of semilunar valves. n third: termination of rapid filling of ventricles from atria. n fourth: due to propulsion of blood into ventricles during atrial contraction. n heart murmurs: due to turbulence resulting from heart valve stenosis (impeded flow through valve) or regurgitation (backflow through valve after valve closure). heart sounds are due to vibrations produced by acceleration or deceleration of blood, some theories:

EE 5340/7340, SMU Electrical Engineering Department, © Heart Sound Measurement n Stethoscope: Transmit sounds from the chest wall to ears. n frequency response: many resonances: log f firmly applied chest piece attenuates low frequencies; skin serves as diaphragm, becomes taught.

EE 5340/7340, SMU Electrical Engineering Department, © Heart Sound Measurement (cont.) n Dynamic microphone: VoVo + _ diaphragm frequency response: Hz

EE 5340/7340, SMU Electrical Engineering Department, © Heart Sound Measurement (cont.) n crystal microphone + _ piezoelectric crystal frequency response: Hz chest

EE 5340/7340, SMU Electrical Engineering Department, © Measurement of Blood Flow n Indicator Dilution Methods: cardiac output n Fick Method n Rapid Injection Methods n Dye Dilution n Thermodilution n Electromagnetic Flowprobes n Ultrasound Flowprobes

EE 5340/7340, SMU Electrical Engineering Department, © Indicator Dilution Methods  consider a given volume of water: V,  add to it a given mass of indicator: m  resulting change in indicator concentration: indicators: oxygen dye heat or:

EE 5340/7340, SMU Electrical Engineering Department, © Indicator Dilution Methods (cont.) n Now suppose the volume of water is time-varying: V(t) In order to maintain the same  C, must make m time varying as well: n or: n take time derivative: or F = Flow = dV/dt

EE 5340/7340, SMU Electrical Engineering Department, © Fick Method Indicator is O 2 gas F = blood flow (l/min) dm/dt = O 2 consumption (l/min) C a = arterial O 2 concentration (l O2 /l blood ) C v = venous O 2 concentration (l O2 /l blood )

EE 5340/7340, SMU Electrical Engineering Department, © Fick Method (cont.) gas flowmeter soda-lime canister O2O2 PA sample venous blood: C v sample arterial blood: C a ( C v in peripheral veins varies widely) (absorbs excess CO 2 ) O 2 is supplied continuously nose plug

EE 5340/7340, SMU Electrical Engineering Department, © Indicator Dilution via Rapid Injection In indicator dilution, one continuously adds indicator to an expanding volume of water in order to maintain a constant  C: n If the ratio is not constant, we get: (1)

EE 5340/7340, SMU Electrical Engineering Department, © Rapid Injection n This is the case in the rapid injection method, a quantity of indicator is added over a short period of time. Equation (1) becomes: n take derivative: (2)

EE 5340/7340, SMU Electrical Engineering Department, © Rapid Injection (cont.) Assume that: (2) becomes: or: (3)

EE 5340/7340, SMU Electrical Engineering Department, © Rapid Injection (cont.) Now integrate both sides of (3): where we assumed F is constant. Solving for flow:

EE 5340/7340, SMU Electrical Engineering Department, © Typical  C(t) Curve t due to recirculation 0 t1t1 t 1 typically around 30 s

EE 5340/7340, SMU Electrical Engineering Department, © Indicators n Non-Toxic Dye: indocyanine green: injected in pulmonary artery,  C(t) measured from blood drawn from catheter placed in femoral or brachial artery (leg). n Heat: used in thermodilution

EE 5340/7340, SMU Electrical Engineering Department, © Thermodilution F = flow (m 3 /sec) Q = heat in injectate in Joules  b = density of blood (kg/m 3 ) (can be determined from hematocrit) c b = specific heat of blood (J/kg o K) (can be determined from hematocrit)  T b (t) = T b - T baseline ( o K)  i = density of injectate (kg/m 3 ) (known) c i = specific heat of injectate (J/kg o K) (known) inject 4 ml of cold saline

EE 5340/7340, SMU Electrical Engineering Department, © Swan Ganz Catheter balloon R. Atrium pulmonary artery thermistor TiTi TbTb t due to recirculation 0 t1t1 t 1 typically around 30 s T baseline exponential fit cold saline injected from syringe

EE 5340/7340, SMU Electrical Engineering Department, © Density and Specific Heat of Blood

EE 5340/7340, SMU Electrical Engineering Department, © Example of Swan Ganz Catheter

EE 5340/7340, SMU Electrical Engineering Department, © Example of Swan Ganz Catheter (cont.) A. Rounded, Tapered Tip B. Deflated Profile Flush with Catheter C. Polyurethane or Latex Balloon Option D. Polyurethane Catheter Material E. Large High-Flow Port Holes F. Vivid Depth Insertion Marks G. Triple Seal Extension Divided Junction (DJ) H. Transparent Extensions I. Color coded, Labelled Extensions J. Three Thread Winged, Connector Hub K. Easy Handling Stopcock L. Balloon Inflation/Deflation Indicator (I) M. Mushroom Shaped Lumens for Strength and Flow N. Rugged Computer Connector O. Thermoset, Industry Standard Thermistor P. Pressure Release Valve (PRV) (Available Upon Request) Q. Contamination Sheath (CMS)

EE 5340/7340, SMU Electrical Engineering Department, © Examples of Cardiac Output Computers Columbus World Medical