measurement of flow and volume of blood(chapter 8

Measurement of Flow and Volume of Blood (Chapter 8)

• Concentration of O2 and other nutritients in the cells are important f h ifor physians

• These are difficult to measure, second‐class (indirect) measurements are used instead

• These measurements usually correlate with concentration of nutritients

• If blood flow is difficult to measure physicians may settle for third‐• If blood flow is difficult to measure, physicians may settle for third‐class measurements such as blood pressure (which correlates with blood‐flow)Wh th bl d t b d f th l• Whenever the blood pressure cannot be measured, fourth‐class measurement of ECG (which correlates with blood pressure) can be used.

• Measurement of blood flow is typically more difficult and invasive than measuring blood pressure

• Flowmeters are unsuitable for measuring blood flow, since they

Dr. Mustafa Kamaşak BYM 501E - Lecture 10 1

Flowmeters are unsuitable for measuring blood flow, since theyrequire cutting vessels and can cause formations of clots

Indicator-Dilution Method

• Indicator‐dilution method do not measure instantenous pulsatileflow but averaged over a number of heart‐beats

• When a given quantity mo of an indicator is added to a volume V, the resulting concentration C of the indicator is given by C=mo/Vresulting concentration C of the indicator is given by C=mo/V

• When an additional quantity of m of indicator is added the incremental increase in the concentration is ΔC=m/V

• When fluid volume in the measured space is continuously removed and replaced, in order to maintain a fixed change in concentration, clinician must continuously add a fixed quantity of indicator per unitclinician must continuously add a fixed quantity of indicator per unit time

dtdVdtdmC//

=∆


dtdV /

Indicator-Dilution Method

• Flow is then

Cdtdm

dtdVF

∆==

/

• Fick Technique: Cardiac output can be measured as

va CCdtdmF

−=

/

– Where F: blood volume liters/min

va

Where F: blood volume liters/min

– Dm/dt: consumption of O2 liters/min

– Ca: arterial concentration of O2 liters/min


a /

– Cs: venous concentration of O2 liters/min

Indicator-Dilution Method• Blood returning from the upper

h lf d th l h lf f thhalf and the lower half of the body has different O2concentration

• Cv is measured in the pulmunory artery after it has been fixed by the pumping action of the right ventricle

• As blood flows through the lung capillaries, subject adds O2 bycapillaries, subject adds O2 by breathing pure O2 from a spirometer

• Exhaled CO is absorbed in a• Exhaled CO2 is absorbed in a soda‐lime canister, so the consumption of O2 is indicated directly by the net gas flow rate


directly by the net gas‐flow rate

Indicator-Dilution Method• Concentration of oxygenated

bl d C b d iblood Ca can be measured in any artery, because blood from lung capillaries is well mixed by the left

i l d h i Oventricle and there is no O2consumption in the arteries

• An arm or leg artery is generally used

• Fick technique is non toxic, because O2 is a normal metabolitebecause O2 is a normal metabolite that is partially removed as blood passes through the systemic capillariescapillaries

• Presence of catheter causes a negligible change in cardiac output


output

Indicator Dilution Method with Rapid Injection

• Continous infusion method has been largely replaced by rapid injection method

• Bolus of indicator is rapidly injected into the vessel and the variation in downstream concentration of the indicator versusvariation in downstream concentration of the indicator versus time is measured until the bolus has passed



• Dotted lineextention of the exponential decay curve is the concentration if there were no recirculation

• Second peak at point E happens because of recirculation

D h d h id i l ti hi h i di t l ft i ht• Dashed curve shows rapid recirculation, which may indicate left‐right shunt in the heart



• Increment of blood of volume dV passes the sampling site in time dt

• Quantity of indicator dm contained in dV is the concentration C(t) times the incremental volume: dm=C(t)dV

Di idi b th id b dt d /dt C(t)dV/dt• Dividing both sides by dt: dm/dt=C(t)dV/dt

• Since dV/dt=Fi (instantenous flow),

dm/dt=C(t)Fi and dm=C(t)Fidtdm/dt=C(t)Fi and dm=C(t)Fidt

• Taking integration on both sides from time 0 to t1

m=∫FiC(t)dt∫ i

• Average flow can be obtained as

∫=

1

)(t

dttC

mF


∫0

)(

Dye Dilution• A common method of clinically measuring cardiac output is to use a

l d d i d i ( di )colored dye, indocyanine green (cardiogreen)• It meets requirements for an indicator

– InertInert– Harmless– Measurable– Economical– Always intravascular

• Its optical absorbtion peak is 805 nm (wavelength at which opticalIts optical absorbtion peak is 805 nm (wavelength at which optical absorbtion coefficient of blood is independent of oxygenation)

• Dye is available as a liquid that is diluted in isotonic saline and injected directly through a catheter usually into the pulmunory arteryinjected directly through a catheter usually into the pulmunory artery

• About 50% of the dye is excreted by the kidneys in first 10 min


Dye Dilution

• Plot of the curve for concentration versus time is obtained from a constant-flow pump, which draws blood from a catheter placed in the femoral or brachial artery.

• Blood is drawn through a colorimeter cuvette which continously• Blood is drawn through a colorimeter cuvette which continously measures the concentration of dye, using the absorbtion photometry principles

• 805 nm channel of a two-channel blood oximeter can be used for measuring dye-dillution curves

• Shape of the curve can provide additional diagnostic• Shape of the curve can provide additional diagnostic information


Thermodilution

• Most common method of measuring cardiac output is that of injecting a bolus of cold saline as an indicator

• A special four-lumen catheter is used in the pulmunory arteryA s ringe forces a gas thro gh one l men gas inflates a• A syringe forces a gas through one lumen, gas inflates a balloon at the tip

• Force of the flowing blood carries the tip into the pulmonary g p p yartery

• Cooled saline indicator is injected through the second lumen i t th i ht t iinto the right atrium

• Indicator is mixed with blood in the right ventricle• Resulting drop in temperature of the blood is detected by a• Resulting drop in temperature of the blood is detected by a

termistor located near the catheter tip in the pulmonary artery• Third lumen carries termistor wires


• Fourth lumen can be used for blood sampling

Thermodilution• Flow can be computed as

∫ ∆=

1

)(t

dttT

QF

where

∫ ∆0

)(bbb dttTcρ

– Q: heat content of injectate, J– ρb:density of blood, kg/m3

– cb: specific heat of blood, J/(kg.K)b

• Problems that may occur– Inadequate mixing between injection and sampling site

E h f h t b t th bl d d ll f th h t– Exhange of heat between the blood and walls of the heart chamber

– Heat exchange through catheter walls before, during and after


injection

Electromagnetic Flowmeter

• Electromagnetic flowmeter measures pulsatile flow of blood

• Movement of blood through a magnetic field induces emf of

∫ ×=1L

dLBue

• Where

∫ ×=0

.dLBue

– B: magnetic flux density

– L: length between electrodes

– u: instantenous velocity of blood

• For a uniform magnetic field B and uniform velocity u, the induced emf isemf is

e=BLu

if these are orthogonal


if these are orthogonal

Electromagnetic Flowmeter


DC and AC Flowmeter

• If a DC magnetic field is used, output voltage continuously indicates the flow

• Early DC flowmeters were not satisfactory

V lt l t d ’ t l t l ti i t f i i i– Voltage across electrode’s metal‐to‐solution interface is in series with flow signal. Random drift of this voltage is of the same order as the flow signal

– ECG waveform has similar frequency content and causes interference

I th f f i t t (0 30 H ) 1/f i i th– In the frequency range of interest (0‐30 Hz), 1/f noise in the amplifier is large (poor SNR)

• These drawbacks can be avoided by using an AC magnet of 400Hzy g g

• Lower frequencies require bulby sensors

• Higher frequencies cause problems due to stray capacitances


• Another problem with AC magnetic field is transformer voltage

DC and AC Flowmeter

• If the looped formed by electrode wires is not exactly parallel to the AC magnetic field, a transformer voltage is induced proportional to dB/dt and loop overlap

• Even when electrodes and wires are carefully positioned the• Even when electrodes and wires are carefully positioned, the transformer voltage is many times higher than flow voltage

• Amplifier voltage is the sum of flow voltage and transformer voltage

• Solution

– One of the electrodes is divided into two electrodes in the axial di ti T i l d di t d t ti t idirection. Two wires are led some distance and a potentiameter is replaced between them. Signal from potentiameter wiper yields a signal corresponding to a “phantom” electrode which can be moved in axial direction


AC Flowmeter

• By sampling the composite signal when transformer voltage is zero. Gated signal measures the flow signal only. This technique is phasesignal only. This technique is phase sensitive


Probe Design

• Electrodes for blood flow t ll d fmeasurement are usually made of

platinum• Best results are obtained when the

electrodes are platinized (electrolytically coated with platinum)

• When electrodes must be exposed,When electrodes must be exposed, bright platinum is used (coating wears off anyway)

• Bright platinum electrodes have a• Bright platinum electrodes have a higher impedance and a higher noise level than platinized onesA i l b h• A common perivascular probe has a toroidal laminated Permalloy core that is wounded with two oppositely

d il


wound coils

Probe Design

• Resulting magnetic field has low leakage flux

• To prevent capacitive coupling between coils of the magnet and thebetween coils of the magnet and the electrodes, an alectrostatic shield is placed between them

• Probe is insulated with a potting material that has a very high resistivity and impermeability to saltresistivity and impermeability to salt water and blood

• Open slot on one side of the probe makes it possible to slip it over a blood vessel without cutting the vessel


Ultrasonic Flowmeters

• Ultrasound can be beamed through the skin making transcutaneous fl t ti lflowmeters practical

• Transducers: A piezoelectric material is used for electric acoustic conversion

• Lead‐zirconate titanate is a crystal that has the highest conversion efficiency

• It can be molded into any shape by melting It is placed in a strong• It can be molded into any shape by melting. It is placed in a strong electric field during cooling for polarizing the material.

• It is usually formed into disks that are coated on opposite faces with t l l t d d d i b l t i ill tmetal electrodes and driven by an electronic ossillator

• Resulting electric field in the crystal causes mechanical constriction• Piston like movements generate longtitudinal plane waves, which g g p ,

propagate into the tissue• Cavities between crystal and tissue must be filled with a fluid or gel

to prevent reflective losses


to prevent reflective losses


Si h d h fi i di i ill d diff i• Since the transducer has a finite diameter, it will produce diffraction patterns for several transducer diameters and frequencies

• In the near field, beam is largely contained within a cylindrical outline and there is little spreading. The intensity is not uniform and multiple minima and maxima happen because of interference

• Near field extends to a distance d f=D2/4λ


Near field extends to a distance dnf D /4λ– where D: transducer diameter, and λ: wavelength


• In the far field the beam diverges and the intensity is inversely proportional to the square of the distance from the transducer

• Angle of divergence φ isAngle of divergence φ is

• We should avoid far field because of its low spatial resolution Dλϕ 2.1sin =


p


• In the selection of operating frequency

– Power of a beam with constant cross section decays exponentially because of absorbtion of heat in the tissue. Absorbtion coefficient is approximately proportional to frequencyAbsorbtion coefficient is approximately proportional to frequency

– Most ultrasonic flowmeters depend on the power scattered back from moving blood cells. Back scattered power is proportional to f4

• Frequency of 2‐10 MHz is typically used


Transit Time Flowmeter

• Effective velocity of sound in the vessel is equal to the velocity of sound plus a component due to the velocity of flow of blood

• u1: velocity of flow of blood averaged along the path of the ultrasoundultrasound

• u2: velocity of flow of blood averaged over the cross sectional area

• u1=1.33u2 for laminar flow1 2

• u1=1.07u2 for turbulent flow

• Transit time in downstream and upstream is

θcos1ucDt

±=

• Difference between upstream and downstream transit times is

21

2221 cos2

)cos(cos2

cDu

ucDut θ

θθ

≅=∆


1 )cos( cuc θ−

Transit Time Flowmeter

• Average velocity u1 is proportional to Δt

• Δt is in the range of nanoseconds and require complex electronics for adequate sensitivity

R i i i t l• Requires invasive surgery to expose vessel


Continuous Wave Doppler Flowmeter

• When a target recedes from a fixed source that transmits sound, the frequency of the received sound is lowered because of Doppler effect

• For small changes the fractional change in the frequency equals the• For small changes, the fractional change in the frequency equals the fractional change in velocity

ufdcu

ff

o

d =

• where fd: Doppler frequency shift, fo: source frequency, u: target velocity, and c: velocity of sound


Continuous Wave Doppler Flowmeter

• Frequency is lowered twiceFrequency is lowered twice

• One shift occurs between the transmitter and moving celss, another shift between transmitting cells and the receiving transducer

cu

ucu

ffd 22

≅+

=

• Adding the angle factor

cucfo +

Adding the angle factor

cuff o

dθcos2

=

• where φ is the angle between beam of sound and the axis of blood vessel

c


Pulsed Doppler

• Continuous‐wave flowmeters provide little information about flow profile

• Transmitter is excited with a brief burst of signal

T i itt d t l i i l k t d th t itt• Transimitted wave travels in a single packet, and the transmitter can be used as a receiver, since the reflections are received at a later time

• Delay between transmission and reception is a direct indication of distance, so we can obtain a complete plot of reflections across the blood vesselsblood vessels

• By examining the Doppler shift at various delays, we can obtain a velocity profile across the vessel

• A short pulse is required for good range resolution, a long pulse is required for good SNR and good velocity discrimination

T i ll 8Mh i h 1 l d


• Typically 8Mhz with 1 µs pulses are used

measurement of flow and volume of blood(chapter 8

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