Course Syllabus

Week 1 Course Rules

Course Objectives

Doppler Ultrasound

I. The Doppler Effect (Jones, Morse and Ingard, Halliday and Resnik)

A. Source stationary, receiver moving

B. Source moving, receiver stationary

C. Approximation for c << v.

II. Continuous Wave Ultrasound (Jones)

A. Basic instrument schematic.

B. Transmitted and received waveforms, time domain.

C. Transmitted and received waveforms, frequency domain.

III. Pulsed Doppler Ultrasound (Jones)

A. Concept of range gating

B. Instrumentation schematic

C. Signals in the time and frequency domain.

1. gate function

2. transmitted pulse

3. received Doppler shifted signal

4. receiver pulse

5. downmixed signal

6. ambiguity

(a) wrap around of the downmixed signal.

(b) broadening of the Doppler spectrum.

D. Shape of the downmixed signal.

IV. Scattering (Morse and Ingard)

V. Attenuation

Week 2 Laser Doppler Anemometry (Adrian)

I. The fringe model and signal processing

a) Calculation of fringe spacing.

b) Doppler ambiguity from the fringe model.

c) Optimal seeding of the fluid.

d) The Doppler pedistal.

II. The Doppler model

a) Doppler equation

b) Optical heterodyning

c) Relationship between the fringe model and the Doppler model

III. Demonstration of Doppler signals from the flow rig.

a) Laser and laser optics

1. Bragg cell switch

2. Changes of laser beam appearance with seeding concentration

3. Adjustment of beam crossing

4. Adjustment of plane of the beam intersection

b) PM tube

1. PM tube supply voltage

2. Alignment and focusing

3. Output signal

4. Change in signal intensity with position of receiver

c) 40 MHz oscillator and downmixer.

d) Amplifier/Band Pass Filter.

e) Data rate

1. Effect of amplitude setting and thresholding level.

2. Effect of flow velocity.

f) Fringe count

g) Zero crossing counter

h) Coincidence mode

i) A/D converter

j) Computer interface

1. Data formats

2. Parallel interface

IV. Practical Considerations

a) Signal averaging and low pass filtering

b) Index of refraction

1. Motion in air vs. motion in the model.

i. Snell’s law

ii. The trigonometric relationships

iii. Simplification for small angles

2. Deflection of the beams.

3. Fluid medium for index of refraction matching.

4. Dependence of refractive index on glycerol-water ratio.

c) Dependence of viscosity on glycerol-water ratio.

d) Model construction

V. Comparison of Laser and Ultrasound Doppler

a) Doppler shift equation

b) Downmixing method

c) Frequency of transmitted signal

d) Transit time effects

e) Spatial resolution, temporal resolution and noise

f) Invasiveness

Week 3 Hot film anemometry (Holman)

I. Heat transfer model for hot film anemometry, calibration.

a) Heat transfer from a cylinder.

b) Energy dissipation in a metallic resistor.

c) Concept of constant temperature anemometry.

d) Bridge Circuit

1. Show that if the op amp is not saturated then the R_probe = R_reference

2. Show that a disturbance sends op amp in the right direction.

e) Relationship between current and velocity for constant temperature anemometry.

f) Limits of zero velocity and high velocity.

II. Limitations

a) Cannot distinguish forward and reverse flow.

b) Non-linear relationship between current and velocity.

c) Inherently invasive.

d) Requires physical access.

e) Calibration can drift over time (accumulation of sludge).

III. Advantages

a) High frequency response.

b) High spatial resolution.

IV. Hot film anemometry and turbulent flow.

V. Comparison of hot film anemometry with LDA and Doppler ultrasound.

Week 4 Flow Meters and Viscometry (Holman)

I. Electromagnetic Flow Meters

A. Induced EMF

II. Transit Time Flow Meters

III. Calibration of flow meters

A. Gravity fed system.

B. Pump driven system.

1. Weirs

2. Overflow

C. Rotameters

1. Why it is not stokes flow

2. Flow in an annulus

D. Venturi meters.

E. Viscometry methods

1. Non Newtonian behavior of blood

a. Apparent viscosity vs strain rate

b. In Poiseuelle flow

c. In Dean flow

d. In post stenotic flow

e. Comparison of Newtonian and non-Newtonian numerical simulations.

f. Comparison of blood to cornstarch in water

2. Cone and plate viscometer

a. Viscosity as a function of torque, r, y, W.

b. Show that the velocity profile is linear with y.

i. Navier Stokes Equations in Cylindrical Coordinates

ii. Show that r and z momentum give v_r = 0 and v_z = 0

iii. Show that continuity gives ¶v_q/¶q = 0.

iv. Reduce equations

v. Substitute V = z tanj so solution will be separable

vi. Apply separation of variables.

(a) Get equidimensional equation in r.

(b) Get sinusoid in z.

vii. Apply no shear at r = R.

viii. Separation constant goes to zero.

ix. Both r and zeta equations are liner

c. Show that the shear rate is constant throughout the device.

d. Demonstrate the use of the cone-plate viscometer.

3. Viscometry by poiseuille flow

a. Viscosity as a function of DP, Q, R.

b. Show that you can calculate R accurately if the other parameters are known.

c. Show that shear rate is not constant with r.

d. Deduce that this is not a good way to get m for non-Newtonian fluids.

e. Consider the effects of entrance effects.

4. Couette flow viscometer

Week 5 MRI/Exam 1

1) Fundamentals of MRI.

A. Proton frequency proportional to magnetic field.

B. Can set up z gradient to select a slice.

C. Can set up x gradient on reception of radio signal to select a strip.

D. Can set up y gradients and do inverse Radon transforms to get voxels.

2) Phase contrast MRI.

3) Exam 1

Week 6 Particle tracking/Particle image velocimetry

1) Particle tracking techniques.

2) Particle image velocimetry (cross-correlation methods).

3) Comparison of PIV with LDA.

Week 7 Data acquisition (Digit Program Handout)

1) A/D and D/A conversion, parameter selection.

A. Include files

B. Lock process, memory swapping, thrashing.

C. Concept of a structure, typedef.

D. Data formats (byte, short, ushort, etc.).

E. Sample and hold, multiplexor.

F. Burst and frame clocks.

G. Circuit to generate tone burst to sync A/D and parallel Interface.

i. How to create an oscillator w/ 1 inverter and a low pass filter.

ii. Use of a Mosfet as a switch.

iii. Summing circuit

H. Circuit to drive a flow valve with a sound card

i. Problems with sound card

a. Only two channels.

b. Need high data rate (high memory)

c. Cannot send out signals outside of the audio range

ii. Use of am modulation to get very low frequencies.

a. Diode bridge

b. Low pass filter

c. Amplifier

2) Parallel interfaces

A. Handshaking for a parallel interface

i. TSI Data format

ii. Translating data format to floating point

iii. Handshaking signals

iv. Pinout for interface

v. DACQ call and program

B. Circuit to generate acquisition bursts from a frame and burst clock.

i. Monostable circuit.

a. Nand gates, nor gates and inverters.

b. Stable and unstable states of the monostable.

c. Changing pulse duration with an RC circuit.

d. Use of input B to turn monostable on and off.

ii. Power supply construction.

3) IEEE interface bus, clocks.

4) Flow control valves

A. Georgia Tech couette valve

B. UHDC pump system

C. Target Rock valve

D. ASCO control valve

E. How to do reverse flow

i. Change from having reverse flow before op to none after

ii. Models for inductance, capacitance and resistance

iii. Use of recirculation for reverse flow.

Week 8 Data analysis

1) Data interpolation, spectral analysis.

2) Ensemble averaging, phase shift averaging, filtering

A. White noise, colored noise, discrete noise, red noise

B. Threshold method to get waveform period

C. Systole time is relatively constant, diastole varies

D. Convolution theorem, pictorial explanation

E. Gibbs phenomenon

F. Need to double array size for cross-correlation

3) Calculation of flow rate, shear stress, etc.

Week 9 PET Imaging (Handout from the web)

1) Proton-heavy carbon emits positron

2) Annihlation with electron to get two 511 keV gamma rays.

3) Simultaneous gamma detection.

4) Use of inverse Radon transform to get an image.

5) Handout on Radon transform.

Single Photon Emission Computed Tomography (SPECT)

Thermal dilution

Computer Aided Tomography applied to cardiovascular measurements.

Week 10 Review/Final/Project due

Term Project: Each student will be required to collect a relatively complete set of velocity data on a particular cardiovascular-relevant flow geometry and to interpret these results in light of the expected flow patterns in that geometry. The techniques will most likely involve LDA or hot film, but are not limited these. Flow rates will need to be measured simultaneously, and appropriate signal analysis must be done.

Steven A. Jones

Cardiovascular Flow Measurement