craig j. hartley, ph.d. department of medicine, program in cv sciences baylor college of medicine,...

Craig J. Hartley, Ph.D.

Department of Medicine, Program in CV Sciences

Baylor College of Medicine, The Methodist Hospital,

and The DeBakey Heart Center, Houston, TX USA

Measurements and Scaling of Vascular Mechanics in Large and Small Mammals

Professor of Medicine, Program in Cardiovascular SciencesDirector, Instrumentation Development Laboratory

The DeBakey Heart and Vascular CenterBaylor College of Medicine and The Methodist Hospital

Houston, Texas

Ph.D. Electrical Engineering, Univ. of Washington, 1970Post Doctoral Fellow, Bioengineering, Rice Univ. 1970-72Faculty at Baylor College of Medicine 1973 - PresentAdjunct Professor of BME at Rice and Univ. of Houston

Craig J. Hartley, Ph.D.

Dissertation: "Ultrasonic properties of artery walls."

About 15 years ago we started using mice in our research, and we wondered if we could adapt what we had developed for use in patients and larger animals for use in mice.

“Have a nice day at the lab, dear?”

And could we do it noninvasively so our patients don't go home like this.

Why use mice?

Genomicsor

geneticengineering

Allows us to study human cardiovascular diseases and conditions such as: cardiac hypertrophy, atherosclerosis, hypertension, aging, and many others. But… How similar are the cardiovascular systems?

Comparison of Heart sizesDog

Rat

Mouse

Are mice good models for human diseases?

Does the size difference matter?

What are the similarities and differences?

Mice are much smaller and shorter lived, but Their cardiovascular systems appear similar.

Scaling in mammals from elephants to mice

Y = a BW b Relationship to BW(kg)* BW=25gHeart weight BW1 4.3 BW 112 mgLV volume BW1 2.25 BW 56 lStroke volume BW1 0.95 BW 24 lHeart rate BW-1/4 170 BW-1/4 427 bpmCardiac output BW3/4 224 BW3/4 14 ml/minAortic diameter BW3/8 3.6 BW3/8 0.9 mmAortic length BW1/4 13 BW1/4 5.2 cmArterial pressure BW0 100 100 mmHgAortic velocity BW0 100 100 cm/sPW velocity BW0 500 500 cm/sEntrance length BW3/4 20 BW3/4 1 mmLife span BW1/4 7.5 BW1/4 3 years

*T.H. Dawson, “Engineering design of the cardiovascular system of mammals” , Prentice Hall, 1991.

Based on cell metabolism, diffusion distances and times, and energy transport

How to these theoretically derived relationships compare with reality?

Log-log plots of heat production, oxygen consumption, and heart rate versus body weight

3/4 powerOxygen consumption

Heart rate-1/4 power

Heat production3/4 power

• Blood Pressure• Flow & Velocity• Dimensions• Cardiac Function• Impedance• Reflections• Stiffness

Cardiovascular parameters of interest

Challenge is to be noninvasive with high spatial and temporal resolution

mousemouseaortaaorta

All are functionsof time, so we need waveforms

• Fluid-filled catheters

• Micromanometers

• Tonometry

• Tail cuff

• Ultrasonic transit-time

• Ultrasonic Doppler

• Sonomicrometry

• M-mode echo & Doppler

intravascular

Intravascular

extravascular

noninvasive

extravascular

noninvasive

extravascular

noninvasive

Methods to measure pressure,flow, and dimensions in mice

Set-up for noninvasive DopplerSet-up for noninvasive Dopplermeasurements in micemeasurements in mice

10 MHzpulsed

Doppler

ECG

Cardiac Doppler measurements in mice

+90

+60

+30cm/s-0

-30

-60

Aortic

Mitral

A----

mo|

mc|

|ao

------P

Accel

| 380 ms |

------E

|ao

|ac

+12-

+8-

+4-kHz

0-

-4-

-8- R|

ECG

systolic and diastolic function and timing

ProbeProbe

Velocity and waveforms are simliar to man

20 MHzDopplerProbe

mm

Mouse carotid Dopper signal processing

Indus

ECG

256 point FFT125 k-samples/speak Doppler shift

f = 2 fo(V/c)cosθV (cm/s) = 3.75 f (kHz)

Doppler probemm

Carotid arteriesSample volume

HumanCarotid

-60

-40

-20cm/s-0

|— 1 sec —|

What aboutother vessels?

left carotid aortic arch

celiac

left renal abdominal aorta

right carotid

ascending aorta

right renal

-100

-50cm/s-0

| 250 ms |

descending aorta

Stop

20 MHz Doppler Probe

mm

20 MHz Doppler signals fromperipheral arteries in a mouse

Velocities are similar in magnitude and shape to those from humans

Pulse-wave velocity measurements in mice

20 MHzDoppler

40 mmSampleVolume

((((

(((

c = PWV = 40/12 = 3.3 mm/ms

ECG12 ms

Probe

c2 = Eh/d

PWV is similar in man

Normal, n=19 αSMA-/-, n=10 Matrix GLA-/-, n=3

0

300

600

900

1200

PWV

cm/s

Pulse-wave velocity in knockout mice

*p<0.05 vs normal

465 360 1037* *

Control

Phenylephrine

**990 432

*

**p<0.05 vs control

and responses to phenylephrine

What happens if you administer a vasoconstrictor?Again, the values are similar to those from humans.

Arterial Tonometry in MiceMillar 1.4F micromanometer

0.45 mm diameter

ECG

Pressurewaveform

MouseAorta

50 ms/div

-100

-50

0

50

100

800 900 1000 1100 1200 1300 14000 msec 100 200 300 400 500 600

mmHgor cm/s

ECG, Doppler velocity, tonometric pressure,and derivatives from a mouse carotid artery

Velocity

Pressure

dP/dt

dV/dt

ECG

Can we generate a pressure waveform noninvasively?

Real-time 2-D image of a mouse carotid artery takenwith a 30 MHz state-of-the-art VisualSonics scanner

Can we measure the waveform of the diameter pulsations during the cardiac cycle?

Vessel walls generate well-defined moving echoes.

0

30

60

90

120

600 700 800 900

-30

0

30

60

90

| 200 ms |

Diameter change=near-far

Near-wall motion1

gate 1 gate 2 gate 3

cm/sor m

- 90

- 60

- 30

- 0

Far-wall motion 3

Blood Velocity d2/dt

DopplerProbe

carotid artery

skin

((((sound beam

Blood velocity and wall motion measured in a mousecarotid artery

couplinggel

wall motion

wall motion

~500 mSV

SV3

SV1

SV2

xmit samples xmit

time Multigate 20 MHz

Pulsed Doppler

bloodvelocity

How do we stabilize the probe?

Anesthetized mouse showing Doppler probein clip holder at 60o to the right carotid artery

0

40

80

120

160

400 500 600 700

Noninvasive displacement signals from the carotidartery, abdominal aorta, and iliac artery of a mouse

40m

Abdominal aorta (~110m)

Carotid (~50m)

Iliac (~20m)

0 msec 100 200 300

R-wave

Diameters pulsate about 10%Waveforms damp with distanceResemble pressure waves

0

50

100

150

200

10 110 210 310

50mSMA (100 m)

Old (55 m)

WT (45 m)

ApoE (14 m)

0 msec 100 200 300

Carotid artery diameter signals fromdifferent types and strains of mice

Resemble pressure wavesHow good is the resolution?

-20

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

150 200 250 300 3500 ms 50 100 150 200

1 m

Carotid artery wall motionin an ApoE-KO mouse

demonstrating high spatialand temporal resolution

Mousered cell

What about the inflections?

0

30

60

90

120

150

600 700 800 900

-25

5

35

65

95

125

30-

cm/s0-

__

30m__

net diameterchange

blood velocity

0 msec 100 200 300

wall velocity

3-

mm/s0-

infmax

min

local minimum

Vessel diameter and velocity showing how theaugmentation index is calculated from strain

AI = max-infAI = max-inf max-minmax-min

D = max-minD = max-min

In humans,AI increaseswith age andvasc disease

0.3

AI

0.2

0.1

0.00 m 20 40 60 80 100

Diameter change

WTApoESMAOld

0

0.1

0.2

0.3

0 20 40 60 80 100

WT

ApoE

aSMA

Old

Carotid artery augmentation index versus diameterpulsations for several types and strains of mice

Aorta Carotid artery

Velocity

Pressure

ECG

Why do the velocity waveforms look different? Pulse transmission and reflection in a compliant tube

PWV = c = (Eh/d)1/2

•PWV is a function of stiffness and geometry and is faster in hard vessels and slower in floppy ones.

•The interaction of the forward and backward waves generate the shape of the measured pressure and flow waves at each site.

•Because the waves distort and meet at different times, the shape of the measured pressure and flow waves is a function of position.

•In arteries, the speed is fast enough and ejection takes long enough that reflections start to arrive at the heart before the end of cardiac ejection.

Wave transmission and reflection in the aorta

Heart Aorta

Forward wave

Backward wave

Time

Measured wave

Wave transmission and reflection in the aorta

Measured wave

Flow wave

Heart Aorta

Forward wave

Backward wave

Time

Pf

Pb

Pm

Qm

Pressure, diameter, flow, and velocity start up at the same time and have similar shapes until the reflected wave arrives.

Qf = Pf/Zc

Qb = -Pb/Zc

Pm = Pf + Pb

Qm = (Pf - Pb)/Zc

Pf = (Pm + ZcQm)/2Pb = (Pm - ZcQm)/2

Zc = dPs/dQs

-150

-100

-50

0

50

100

150

400 500 600 700

0

10

20

30

40

50

60Velocity, Diameter, and calculated forward and backward waves in a mouse carotid artery

Velocity Diameter

Forward

Backward

D = Df + Db

v = (Df - Db)/Zc

Df = (D + Zcv)/2Db = (D - Zcv)/2

Zc = dDs/dvs (=c)

(f) = Db/Df = || ej

Z(f) = |D/v| ej0 msec 100 200 300

50

40-

30-

20-

10-

cm/s0-

Pressure ~ Diameter Flow ~ Velocity

Why are there 2 peaks in Df? Does this happen in man?

0

20

40

60

80

100

120

140

700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700

-20

0

20

40

60

80

100

120140-Press

120-

100-

80-

60-

40-

20-mmHg

0-

-80Velocity-60

-40

-20cm/s-0

0 Seconds 1 2

Human carotid pressure and velocity signals

Tonometric Pressure

Doppler Velocity

Forward

Backward

Body Worlds 3 - Gunther von Hagen

Can we measure coronary blood

flow in mice?

Cast of Coronary Arteries

What happensto coronary flow?

Doppler catheters can be used to sense flow in man. However, because of compensation, resting flow is often normal even with a severe coronary stenosis. What is limited is maximum flow.

H/B = 3.0

In humans, the physiological significance of coronary artery disease is often assessed by the ratio of peak hyperemic velocity (after administration of a vasodilator) to resting baseline coronary velocity (H/B). A form of stress test.

----Hyperemic

-----Baseline

Injection of contrast agent

1 sec timer

raw phasic velocity

filtered mean velocity

fast | slow paper speed

3

HB

2

1

Can we do this in mice?

Cole & Hartley, Circulation, 1977

Problems:

Coronary arteries are small, ~200m

They are close to many other vessels

Everything around them moves

It seemed impossible to measure flow .... until we tried.

Coronary Blood Flow in Mice?

20 MHz Doppler Probe((((((

Method to sense coronary blood flow noninvasively in mice

-50cm/s-50cm/s

Is this coronary flow?

Left main coronary flow

Common carotid flow

Aortic flow

ECG HR = 550

Velocity in 3 mouse vessels showing relative timing-50

cm/s-0

-50

cm/s-0-100

-50

cm/s-0

---maximum

This give us baseline velocity, but, how can we measure hyperemic velocity and coronary reserve noninvasively?

--80--

--60--

--40--

--20--cm/s---0---

ECG

| 800 ms |

Noninvasive coronary Doppler signals from a mouse

Vmean

HR = 398 b/min

low =1.0% high = 2.5%

H/B = Vhigh/Vlow = 2.2

HR = 412 b/min

anesthetized at low and high levels of isoflurane gas

Vmax

What about old and ApoE mice?

0

20

40

60

80

100

120

140

6 wk 3 mo 2 yr ApoE

140-

120-

100-

80-

60-

40-

20-cm/s

0-

H/B-4

-3

-2

-1

-06 wk 3 mo 2 yr 2 yr ApoE-/-

B

H

H/B

B - Baseline Peak Diastolic Velocity (1.0 % Isofl) H - Hyperemic Peak Diastolic Velocity (2.5 % Isofl)

Mean +/- SE

35 84 2.4 30 84 3.0 25 87 3.6 52 120 2.5

Coronary flow velocity reserve (H/B) in miceas a function of age and atherosclerosis

What about non-coronary forms of heart and vascular disease?

CFR = H/B

n = 10 n = 10 n = 10 n = 20

and carotidremodeling

Right Left

27gauge

Aortic banding in mice

Before After

mm

Produces cardiac hypertrophy-pressure overload

Carotid Flows?

-500

cm/s-0

-20-0-160

cm/s-0

ECG

Aortic Arch Jet Velocity - 10 MHz Doppler

Left Carotid Artery Velocity - 20 MHz Doppler

Right Carotid Artery Velocity - 20 MHz Doppler

AorticBand

left maincoronary

artery

msec

P~75 mmHg

mm scale

Simultaneous Doppler signals from a banded mouse

What happens to coronary flow?

21Days

H/B = 0.9

| 400 ms |

1 Day

H/B = 1.7

-100

-50

cm/s-0

Coronary blood velocityin a banded mouse

PreBand

1% isoflurane

2.5% isofluraneH/B = 2.0

0

1

2

3

4

Pre 1 d 7 d 14d 21d

4-

3-

2-

1-

0-Pre 1 day 7 day 14 day 21 day

Hyperemic/Baseline Velocity

H/B Heart Rate

Response of coronary velocity and heart rate to isoflurane in 10 banded mice during remodeling

(CFR)

(Little change)

3.2 2.2 1.7 1.4 1.1

0.0

0.2

0.4

0.6

0.8

1.0

Pre 1 d 7 d 14d 21d

1.0-

0.8-

0.6-

0.4-

0.2-

0.0-Pre 1 day 7 day 14 day 21 day

S/D Baseline

S/D Hyperemic

Systolic/Diastolic coronary velocity area ratio before and after banding in mice

S S DD

.17 .23 .29 .50 .67 .81 .83 .88 .92 .86

Differences in timing between left and right coronary flow velocity in a patient

200

100mmHg

0

8

4kHz

0

ECG

Pressure

DopplerShift

Left coronary artery Right coronary artery

Systole

Heart weight BW1 Capillary diameter BW1/12

LV volume BW1 Capillary length BW5/24

Stroke volume BW1 Capillary number BW5/8

Blood volume BW1 Capillary velocity BW-1/24

Heart Rate BW-1/4 Cell number BW5/8

Heart Period BW1/4 Cell length BW1/8

Circulation time BW1/4 Cell volume BW3/8

Life span BW1/4 Elastic modulus BW0

Artery length BW1/4 Blood viscosity BW0

Artery diameter BW3/8 Arterial pressure BW0

Wall shear stress BW-3/8 Blood velocity BW0

Cardiac output BW3/4 PW velocity BW0

Entrance length BW3/4 Diameter pulsation BW0

Acceleration, dP/dt BW-1/4 Coronary reserve BW0

*T.H. Dawson, “Engineering design of the cardiovascular system of mammals” , Prentice Hall, 1991.

Scaling in mammals from elephants to mice Y = a BW b

Parameter Power RatioHeart & blood volume 1 2800Cardiac output, flow 3/4 385Cell number 5/8 143Vessel diameter 3/8 20 Linear dimension 1/3 14Vessel length, periods 1/4 7Cell length 1/8 2.7Capillary diameter 1/12 2Blood pressure & vel. 0 1Capillary velocity -1/24 0.7Heart rate, Accel. -1/4 0.14

Human/mouse scale factorsAllometricEquation

Y = a BWb

Human/mouse70kg / 25g

Conclusions - (Measurements)

•Blood velocity signals from the heart and most arteries of mice can be obtained noninvasively

•High-fidelity arterial displacement signals can also be obtained noninvasively at the same time

•Pulse wave velocity, augmentation index, percent diameter change, and coronary reserve can be determined from velocity and displacement signals and their responses to vasoactive agents

Conclusions - (Scaling)

•Blood velocity, blood pressure, pulse wave velocity, and percent wall displacement in mice and humans are similar in both magnitude and shape.

•The arterial time constants are scaled to heart period such that reflections return to the heart at similar times during the cardiac cycle. Waveforms

•Most of the things we can measure in mice and man are altered by age and disease in similar ways.

Anil Reddy Lloyd MichaelMark Entman George TaffetYi-Heng LiDirar KhourySridhar Madala (Indus)Y-X (Jim) Wang (Berlex)

Faculty Collaborators TechniciansFaculty Collaborators Technicians

Thuy PhamJennifer Pocius

Jim BrooksRoss HartleyAlex Tumang

chartley@bcm.edu

CreditsCredits