Craig J' Hartley, Ph'D'

1
High Resolution Measurements Scaling of
Cardiovascular Mechanics in Mice
Craig J. Hartley, Ph.D.
Department of Medicine, Program in CV Sciences
Baylor College of Medicine, and The Methodist
DeBakey Heart Vascular Center, Houston, TX USA
Mathematical Biosciences Institute, Current
Topics Workshop "Computational Challenges in
Integrative Biological Modeling" Ohio State
University, October 5-8, 2009
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Craig J. Hartley, Ph.D.
Professor of Medicine, Program in Cardiovascular
Sciences Director, Instrumentation Development
Laboratory The DeBakey Heart and Vascular
Center Baylor College of Medicine and The
Methodist Hospital Houston, Texas
Background disclosure
Ph.D. Electrical Engineering, Univ. of
Washington, 1970 Post Doctoral Fellow,
Bioengineering, Rice Univ. 1970-72 Faculty at
Baylor College of Medicine 1973 -
Present Adjunct Professor of BME at Rice and
Univ. of Houston
Dissertation "Ultrasonic properties of artery
walls."
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Research Funding
NIH R01 HL22512-32 1978 - 2013 Ultrasonic
Instrumentation for Cardiovascular Studies
As an instrumentation designer and
experimentalist, my major interest has been the
assessment and modeling of cardiovascular
physiology, function, diseases, and mechanics by
ultrasound.
4
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.
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Why use mice?
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Are mice good models for human diseases?
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Scaling in mammals from elephants to mice
Based on cell metabolism, diffusion distances and
times, and energy transport
Y a BW b Relationship to BW(kg) BW25g Heart
weight a BW1 4.3 BW 112 mg LV volume a
BW1 2.25 BW 56 ml Stroke volume a BW1 0.95
BW 24 ml Heart rate a BW-1/4 170 BW-1/4 427
bpm Cardiac output a BW3/4 224 BW3/4 14
ml/min Aortic diameter a BW3/8 3.6 BW3/8 0.9
mm Aortic length a BW1/4 13 BW1/4 5.2
cm Arterial pressure a BW0 100 100
mmHg Aortic velocity a BW0 100 100 cm/s PW
velocity a BW0 500 500 cm/s Entrance
length a BW3/4 20 BW3/4 1 mm Life span a
BW1/4 7.5 BW1/4 3 years T.H. Dawson,
Engineering design of the cardiovascular system
of mammals , Prentice Hall, 1991.
How to these theoretically derived relationships
compare with reality?
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Log-log plots of heat production, oxygen
consumption, and heart rate versus body weight
Heart rate -1/4 power
Heat production 3/4 power
3/4 power Oxygen consumption
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Cardiovascular parameters of interest

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

All are functions of time, so we need waveforms
mouse aorta
Challenge is to be noninvasive with high spatial
and temporal resolution
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Methods to measure pressure, flow, and dimensions
in mice

• Fluid-filled catheters
• Micromanometers
• Tonometry
• Tail cuff
• Ultrasonic transit-time
• Ultrasonic Doppler
• Sonomicrometry
• M-mode echo Doppler

intravascular Intravascular extravascular noninvas
ive extravascular noninvasive extravascular noninv
asive
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Set-up for noninvasive Doppler measurements in
mice
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Doppler Principle for Reflected Waves
Target
Transducer
Incident Pulse
Blood Cell
fo
) ) ) ) ) ) ) )
Reflected Pulse
( ( ( ( ( ( ( (
V 0
fr fo
fr
((((((((
fr gt fo
V
( ( ( ( ( ( ( (
fr lt fo
-V
fr fo (1 2V/c), f fr - fo 2foV/c
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Cardiac Doppler measurements in mice
systolic and diastolic function and timing
12- 8- 4- kHz 0- -4- -8-
90 60 30 cm/s -0 -30 -60
Aortic
------P
Accel
mc
mo
Probe
10 MHz pulsed Doppler
A----
ac
ao
ao
Mitral
------E
R
ECG
ECG
380 ms
Velocity and waveforms are similar to man
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Carotid arteries
Mouse carotid Doppler signal processing
20 MHz Doppler Probe
Sample volume
Doppler probe
mm
mm
Df 2 fo(V/c)cos? V (cm/s) 3.75 Df (kHz)
Indus
256 point FFT 125 k-samples/s
peak Doppler shift
What about other vessels?
The Doppler spectrum represents the distribution
of velocity components within the sample volume
in the direction of the sound beam.
ECG
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20 MHz Doppler Probe
20 MHz Doppler signals from peripheral arteries
in a mouse
mm
aortic arch
left carotid
right carotid
ascending aorta
descending aorta
-100 -50 cm/s -0
celiac
250 ms
right renal
abdominal aorta
left renal
Velocities are similar in magnitude and shape to
those from humans
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Pulse-wave velocity measurements in mice
Probe
((((
20 MHz Doppler
40 mm
ECG
Sample Volume
12 ms
PWV2 Eh/dr Moens-Korteweg Equation
(((
c PWV 40/12 3.3 mm/ms
PWV is similar in man
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Pulse-wave velocity in knockout mice
plt0.05 vs normal


360
465
1037
Again, the values are similar to those from
humans.
What happens if you administer a vasoconstrictor?
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Arterial Tonometry in Mice
Millar 1.4F micromanometer
Mouse Aorta
0.45 mm diameter
ECG
50 ms/div
Pressure waveform
Can we generate a pressure waveform
noninvasively?
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Blood velocity and wall motion measured in a
mouse carotid artery
Doppler Probe
coupling gel
skin
sound beam
((((
carotid artery
blood velocity
SV
500 mm
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ECG
Tonometry
50- mm
20-
mm
Wall motion
0-
0-
0 msec
400
0 msec
300
Carotid artery
Abdominal aorta
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Noninvasive displacement signals from the
carotid artery, abdominal aorta, and iliac artery
of a mouse
R-wave
Abdominal aorta (110mm)
40mm
Carotid (50mm)
Iliac (20mm)
0 msec 100
200
300
Waveforms damp with distance
Resemble pressure waves
Diameters pulsate about 10
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Carotid artery diameter signals from different
types and strains of mice
aSMA (100 mm)
50mm
Old (55 mm)
WT (45 mm)
ApoE (14 mm)
0 msec 100
200
300
Resemble pressure waves
How good is the resolution?
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Carotid artery wall motion in an ApoE-KO
mouse demonstrating high spatial and temporal
resolution
1 mm
What about the inflections?
Mouse red cell
0 ms 50
100 150
200
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Vessel diameter and velocity showing how
the augmentation index is calculated from strain
3- mm/s 0-
local minimum
AI max-inf max-min DD max-min
wall velocity
max
net diameter change
inf
__ 30mm __
min
In humans, AI increases with age and vasc disease
30- cm/s 0-
blood velocity
0 msec 100
200 300
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Carotid artery augmentation index versus
diameter pulsations for several types and strains
of mice
0.3 AI 0.2 0.1 0.0
WT ApoE aSMA Old
Diameter change
0 mm 20 40 60 80
100
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Aorta Carotid artery
Velocity
Pressure
ECG
Why do the velocity waveforms look different?
Pulse transmission and reflection in a compliant
tube
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PWV c (Eh/dr)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.

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Wave transmission and reflection in the aorta
Aorta
Heart
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Wave transmission and reflection in the aorta
Aorta
Heart
Pm Pf Pb Qm (Pf - Pb)/Zc Pf (Pm
ZcQm)/2 Pb (Pm - ZcQm)/2 Zc dPs/dQs
Pf
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
Forward wave Backward wave
Pb
Pm
Measured wave
Time
Qm
Flow wave
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Velocity, Diameter, and calculated forward and
backward waves in a mouse carotid artery
Pressure Diameter Flow Velocity
40- 30- 20- 10- cm/s 0-
D Df Db v (Df - Db)/Zc Df (D Zcv)/2 Db
(D - Zcv)/2 Zc dDs/dvs (rc) G(f) Db/Df
G ejf Z(f) D/v ejf
Diameter
Velocity
50m
Forward
Backward
0 msec 100 200
300
Why are there 2 peaks in Df?
Does this happen in man?
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Human carotid pressure and velocity signals
140- Press 120- 100- 80- 60- 40- 20- mmHg 0-
Tonometric Pressure
-80 Velocity -60 -40 -20 cm/s -0
Doppler Velocity
Forward
Backward
0 Seconds 1
2
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Cast of Coronary Arteries
Can we measure coronary blood flow in mice?
What happens to coronary flow?
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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.
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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.
Injection of contrast agent
raw phasic velocity
H/B 3.0
fast slow paper speed
Can we do this in mice?
----Hyperemic
filtered mean velocity
-----Baseline
1 sec timer
Cole Hartley, Circulation, 1977
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Coronary Blood Flow in Mice?
Problems Coronary
arteries are small, 200mm They are close to
many other vessels Everything around them
moves It seemed impossible to measure flow ....
until we tried.
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Method to sense coronary blood flow noninvasively
in mice
(((
20 MHz Doppler Probe
Is this coronary flow?
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Velocity in 3 mouse vessels showing relative
timing
-50 cm/s -0
---maximum
Left main coronary flow
Common carotid flow
-50 cm/s -0
-100 -50 cm/s -0
Aortic flow
Modeling of coronary flow is complicated because
waves are generated from both ends of the vessel
at the same time, and the walls are attached to
moving myocardium.
ECG HR 550
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Noninvasive coronary Doppler signals from a mouse
This gives us baseline velocity, but, resting
velocity is usually normal even with a severe
stenosis. How can we measure hyperemic velocity
and coronary reserve noninvasively to estimate
the effects of coronary disease?
--80-- --60-- --40-- --20-- cm/s ---0--- ECG
Vmax
Vmean
HR 398 b/min
800 ms
What about old and ApoE mice?
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Coronary flow velocity reserve (H/B) in mice as a
function of age and atherosclerosis
140- 120- 100- 80- 60- 40- 20- cm/s 0-
B - Baseline Peak Diastolic Velocity (1.0
Isofl) H - Hyperemic Peak Diastolic Velocity (2.5
Isofl)
Mean /- SE
CFR H/B
H/B -4 -3 -2 -1 -0
H
H/B
B
n 10 n 10
n 10 n 20
35 84 2.4 30 84 3.0
25 87 3.6 52 120 2.5
6 wk 3 mo 2 yr
2 yr ApoE-/-
What about non-coronary forms of heart and
vascular disease?
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Aortic banding in mice
27 gauge
Carotid Flows?
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Simultaneous Doppler signals from a banded mouse
-500 cm/s -0
Aortic Arch Jet Velocity - 10 MHz Doppler
DP75 mmHg
Left Carotid Artery Velocity - 20 MHz Doppler
-20 -0
-160 cm/s -0
Right Carotid Artery Velocity - 20 MHz Doppler
left main coronary artery
Aortic Band
ECG
How well does the simplified Bernoulli Eq. work
in mice?
msec
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Validation of simplified Bernoulli
equation (?P4V2) in mice with banded aortic arch
LCPr
SV
Jet velocity
3- 2- 1- m/s 0-
RCPr
)))
V
Probe
80-
4V2 (mmHg)
60-
40-
100- 50- 0-
Pressure
20-
Right Carotid
?P
?P (mmHg)
Left Carotid
0-
mmHg
0 20 40 60 80
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Transesophageal 20 MHz Doppler signals from a
mouse with a banded aorta
Probe
-30 -15 kHz -0
150- 75- cm/s 0-
-30 -15 kHz -0
150- 75- cm/s 0-
Right Carotid
Left Carotid
PI2
PI11
27g Band
SV
300 ms

300 ms

Aortic Arch at Band
Descending Aorta
-90 -45 kHz -0
350- 175- cm/s 0-
150- 75- cm/s 0-
-30 -15 kHz -0
))))
Root
Doppler crystal
?P4V2 49mmHg
250Hz osc.
Mouse Aorta
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Doppler evidence of vortex shedding distal to the
aortic stenosis in a banded mouse
30- 20- 10- kHz 0-
-150 -100 -50 cm/s -0
velocity fluctuations
at 250 - 500 Hz
What happens to coronary flow?
120
ms
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Coronary blood velocity in a banded mouse
2.5 isoflurane
-100 -50 cm/s -0
H/B 2.0
1 isoflurane
Pre Band
400 ms
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Response of coronary velocity and heart rate to
isoflurane in 10 banded mice during remodeling
4- 3- 2- 1- 0-
Hyperemic/Baseline Velocity H/B Heart Rate
(CFR) (Little change)
3.2 2.2 1.7
1.4 1.1
Pre 1 day 7 day 14 day
21 day
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Systolic/Diastolic coronary velocity area ratio
before and after banding in mice
1.0- 0.8- 0.6- 0.4- 0.2- 0.0-
S/D Baseline S/D Hyperemic
S
S
D
D
This suggests that much of the blood is going to
areas of the LV that are not generating full left
ventricular pressure. Is this bad, does it occur
in man, and can it be modeled?
.17 .23 .29 .50 .67
.81 .83 .88 .92 .86
Pre 1 day 7 day 14
day 21 day
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Differences in timing between left and right
coronary flow velocity in a patient
Systole
ECG Pressure Doppler Shift
200 100 mmHg 0 8 4 kHz 0
Left coronary artery Right coronary artery
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Scaling in mammals from elephants to mice Y a
BW b
Heart weight a BW1 Capillary diameter a
BW1/12 LV volume a BW1 Capillary length a
BW5/24 Stroke volume a BW1 Capillary number a
BW5/8 Blood volume a BW1 Capillary velocity a
BW-1/24 Heart Rate a BW-1/4 Cell number a
BW5/8 Heart Period a BW1/4 Cell length a
BW1/8 Circulation time a BW1/4 Cell volume a
BW3/8 Life span a BW1/4 Elastic modulus a
BW0 Artery length a BW1/4 Blood viscosity a
BW0 Artery diameter a BW3/8 Arterial pressure a
BW0 Wall shear stress a BW-3/8 Blood velocity a
BW0 Entrance length a BW3/4 PW velocity a
BW0 Cardiac output a BW3/4 Diameter pulsation a
BW0 Acceleration, dP/dt a BW-1/4 Coronary
reserve a BW0 T.H. Dawson, Engineering design
of the cardiovascular system of mammals ,
Prentice Hall, 1991.
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Human/mouse scale factors
Parameter Power Ratio Heart blood
volume 1 2800 Cardiac output, flow 3/4 385 Cell
number 5/8 143 Vessel diameter 3/8 20
Linear dimension 1/3 14 Vessel length,
periods 1/4 7 Cell length 1/8 2.7 Capillary
diameter 1/12 2 Blood pressure
vel. 0 1 Capillary velocity -1/24 0.7 Heart
rate, Accel. -1/4 0.14
Allometric Equation Y a BWb Human/mouse 70kg
/ 25g
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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

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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.

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Credits
Faculty Collaborators Technicians
Anil Reddy Lloyd Michael Mark Entman George
Taffet Yi-Heng Li Dirar Khoury Sridhar Madala
(Indus) Y-X (Jim) Wang (Berlex)
Thuy Pham Jennifer Pocius Jim Brooks Ross
Hartley Alex Tumang chartley_at_bcm.edu
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How constant is PWV?
We usually assume that PWV varies slightly with
pressure but is relatively constant and is the
same in both directions. But others have shown
small differences based on direction or frequency
content in pulse transit times, so we ran a very
simple test using two Doppler probes to measure
radial and brachial velocities on my arm while a
colleague tapped on my distal radial artery to
generate transient reverse pulses. The results
are shown on the next slide.
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Doppler signals from the brachial and radial
arteries 20 cm apart with external distal
arterial tapping
?
Brachial velocity
10 ms reverse PTT
natural forward pulse
Radial velocity
tapped reverse wave
20 ms forward PTT
100 ms
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Thank you