Principles of Biomedical Systems & Devices

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WEEK 10: Flow & Volume of Blood

Measurement of Flow & Volume of Blood

A measurement of paramount importance: concentration of O2 and other nutrients in cells Very difficult to measure Second-class measurement: blood flow and changes in blood volume

correlate well with concentration Third-class measurement: blood pressure correlates well with blood

flow Fourth class measurement: ECG correlates adequately with blood

pressure How to make blood flow / volume measurements? Standard flow meters, such as turbine

flow meters, obviously cannot be used! Indicator-dilution method: cont./rapid injection, dye dilution,

thermodilution Electromagnetic flowmeters Ultrasonic flowmeters / Doppler flowmeters Plethysmography: Chamber / electric impedance / photoplethysmography

Indicator Dilution with Continuous Injection

Measures flow / cardiac output averaged over several heart beats

Fick’s technique: the amount of a substance (O2) taken up by an organ / whole body per unit time is equal to the arterial level of O2 minus the venous level of O2 times the blood flow

va CC

dtdmC

dtdm

dt

dVF

Blood flow, liters/min(cardiac output)

Consumption of O2 (mL/min)

Arterial and venousconcentration of O2 (mL/L of blood)

dtdV

dtdmC

Change in [] due to continuously added indicator m to volume V

Fick’s technique

How is dm/dt (O2 consumption) measured?

Where and how would we measure Ca and Cv? (Exercise)

minL/5mL/L140L/mL190

minmL/250

][O][O

min)(mL/O

22

2

va

nconsumptioOutputCardiac

Indicator Dilution with Rapid Injection

A known amount of a substance, such as a dye or radioactive isotope, is injected into the venous blood and the arterial concentration of the indicator is measured through a serious of measurements until the indicator has completely passed through given volume.

The cardiac output (blood flow) is amount of indicator injected, divided by average concentration in arterial blood.

t

dttC

mF

0

)(

Indicator – Dilution Curve

After the bolus is injected at time A, there is a transportation delay before the concentration begins rising at time B. After the peak is passed, the curve enters an exponential decay region between C and D, which would continue decaying alone the dotted curve to t1 if there were no recirculation. However, recirculation causes a second peak at E before the indicator becomes thoroughly mixed in the blood at F. The dashed curve indicates the rapid recirculation that occurs when there is a hole between the left and right sides of the heart.

An Example

Dye Dilution

In dye-dilution, a commonly used dye is indocyanine green (cardiogreen), which satisfies the following Inert Safe Measurable though spectrometry Economical Absorption peak is 805 nm, a wavelength at which

absorption of blood is independent of oxygenation 50%of the dye is excreted by the kidneys in 10 minutes,

so repeat measurements is possible

Thermodilution

The indicator is cold – saline, injected into the right atrium using a catheter

Temperature change in the blood is measured in the pulmonary artery using a thermistor

The temperature change is inversely proportional to the amount of blood flowing through the pulmonary artery

Measuring Cardiac Output

Several methods of measuring cardiac output In the Fick method, the indicator is O2; consumption is measured by a spirometer. The arterial-venous concentration difference is measure by drawing simples through catheters placed in an artery and in the pulmonary artery. In the dye-dilution method, dye is injected into the pulmonary artery and samples are taken from an artery. In the thermodilution method, cold saline is injected into the right atrium and temperature is measured in the pulmonary artery.

Electromagnetic Flowmeters

Based on Faraday’s law of induction that a conductor that moves through a uniform magnetic field, or a stationary conductor placed in a varying magnetic field generates emf on the conductor:

When blood flows in the vessel with velocity u and passes through the magnetic field B, the induced emf e measured at the electrodes is.

L

de0

LBu

For uniform B and uniform velocity profile u, the induced emf is e=BLu. Flow can be obtained by multiplying the blood velocity u with the vessel cross section A.

ElectromagneticFlowmeter Probes

• Comes in 1 mm increments for 1 ~ 24 mm diameter blood vessels

• Individual probes cost $500 each

• Made to fit snuggly to the vessel during diastole

• Only used with arteries, not veins,

as collapsed veins during diastole lose contact with the electrodes

• Needless to say, this is an INVASIVE measurement!!!

• A major advantage is that it can measure instantaneous blood flow, not just average flow

Ultrasonic Flowmeters

Based on the principle of measuring the time it takes for an acoustic wave launched from a transducer to bounce off red blood cells and reflect back to the receiver.

All UT transducers, whether used for flowmeter or other applications, invariably consists of a piezoelectric material, which generates an acoustic (mechanical) wave when excited by an electrical force (the converse is also true)

UT transducers are typically used with a gel that fills the air gaps between the transducer and the object examined

Near / Far Fields

Due to finite diameters, UT transducers produce diffraction patterns, just like an aperture does in optics.

This creates near and far fields of the UT transducer, in which the acoustic wave exhibit different properties The near field extends about dnf=D2/4λ, where D is the

transducer diameter and λ is the wavelength. During this region, the beam is mostly cylindrical (with little spreading), however with nonuniform intensity.

In the far field, the beam diverges with an angle sinθ=1.2 λ/D, but the intensity uniformly attenuates proportional to the square of the distance from the transducer

Higher frequencies and larger transducers should be used for nearfield operation. Typical operating frequency is 2 ~ 10 MHz.

UT Flowmeters

Zero-crossingdetector / LPF

Determine direction

High acoustic impedance material

Transit time flowmeters

Effective velocity of sound in blood: velocity of sound (c) + velocity of flow of blood averaged along the path of the ultrasound (û)

û=1.33ū for laminar flow, û=1.07ū for turbulent flowū: velocity of blood averaged over the cross sectional area, this is differentthan û because the UT path is along a single line not over an averaged of cross sectional area

Transit time in up/down stream direction:

Difference between upstream and downstream directions

cosˆvelocityconduction

distance

uc

Dt

2222

cosˆ2

)cosˆ(

cosˆ2

c

uD

uc

uDt

Transit Time Flowmeters

The quantity ∆T is typically very small and very difficult to measure, particularly in the presence of noise. Therefore phase detection techniques are usually employed rather then measuring actual timing.

Doppler Flowmeters

The Doppler effect describes the change in the frequency of a received signal , with respect to that of the transmitted signal, when it is bounced off of a moving object. Doppler frequency shift

c

uff od

cos2

Speed of sound in blood(~1500 m/s)

Angle between UT beamand flow of blood

Speed of blood flow(~150 cm/s)

Source signal frequency

Doppler Flowmeters

c

ufF s )cos(cos

Problems Associated withDoppler Flowmeters

There are two major issues with Doppler flowmeters Unlike what the equations may suggest, obtaining direction

information is not easy due to very small changes in frequency shift that when not in baseband, removing the carrier signal without affecting the shift frequency becomes very difficult

Also unlike what the equation may suggest, the Doppler shift is not a single frequency, but rather a band of frequencies because

• Not all cells are moving at the same velocity (velocity profile is not uniform)

• A cell remains within the UT beam for a very short period of time; the obtained signal needs to be gated, creating side lobes in the frequency shift

• Acoustic energy traveling within the beam, but at an angle from the bam axis create an effective ∆θ, causing variations in Doppler shift

• Tumbling and collision of cells cause various Doppler shifts

Directional Doppler

Directional Doppler borrows the quadrature phase detector technique from radar in determining the speed and direction of an aircraft.

Two carrier signals at 90º phase shift are used instead of a single carrier. The +/- phase difference between these carriers after the signal is bounced off of the blood cells indicate the direction, whereas the change in frequency indicate the flowrate

Directional Doppler

(a) Quadrature-phase detector. Sine and cosine signals at the carrier frequency are summed with the RF output before detection. The output C from the cosine channel then leads (or lags) the output S from the sine channel if the flow is away from (or toward) the transducer. (b) Logic circuits route one-shot pulses through the top (or bottom) AND gate when the flow is away from (or toward) the transducer. The differential amplifier provides bi-directional output pulses that are then filtered.