Measurements and Scaling of Vascular
Mechanics in Large and Small Mammals
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
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
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."
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.
Genomics
Why use mice?
or
genetic
engineering
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 sizes
Dog
Rat
Mouse
Are mice good models for human diseases?
What are the similarities and differences?
Mice are much smaller and shorter lived, but
Their cardiovascular systems appear similar.
Does the size
difference matter?
Scaling in mammals from elephants to mice
Based on cell metabolism, diffusion distances and times, and energy transport
Y = a BW b
Heart weight
LV volume
Stroke volume
Heart rate
Cardiac output
Aortic diameter
Aortic length
Arterial pressure
Aortic velocity
PW velocity
Entrance length
Life span
Relationship to BW(kg)*
a BW1
a BW1
a BW1
a BW-1/4
a BW3/4
a BW3/8
a BW1/4
a BW0
a BW0
a BW0
a BW3/4
a BW1/4
4.3 BW
2.25 BW
0.95 BW
170 BW-1/4
224 BW3/4
3.6 BW3/8
13 BW1/4
100
100
500
20 BW3/4
7.5 BW1/4
BW=25g
112 mg
56 ml
24 ml
427 bpm
14 ml/min
0.9 mm
5.2 cm
100 mmHg
100 cm/s
500 cm/s
1 mm
3 years
How
these“Engineering
theoretically
relationships
compare
reality?
*T.H.to
Dawson,
design of derived
the cardiovascular
system of mammals”
, Prenticewith
Hall, 1991.
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
Cardiovascular parameters of interest
•
•
•
•
•
•
•
Blood Pressure
Flow & Velocity
Dimensions
Cardiac Function
Impedance
All are functions
Reflections
of time, so we
Stiffness
need waveforms
Challenge is to be noninvasive with
high spatial and temporal resolution
mouse
aorta
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
noninvasive
extravascular
noninvasive
extravascular
noninvasive
Set-up for noninvasive Doppler
measurements in mice
Cardiac Doppler measurements in mice
systolic and diastolic function and timing
+12-
+90
Aortic ------P
+8- Accel
Probe
mc
|
mo
|
+410 MHz kHz
0pulsed
Doppler
-4-
|
ao
-8- Mitral
ECG
+60
|
ac
A---------E
|
ao
R
|
+30
cm/s
-0
-30
-60
ECG
380 ms
|
Velocity and| waveforms
are simliar
to man
Carotid arteries
20 MHz
Sample volume
Doppler
Probe
Doppler probemm
mm
Mouse carotid Dopper
signal processing
Indus
peak Doppler shift
256 point FFT
125 k-samples/s
Df = 2 fo(V/c)cosθ
V (cm/s) = 3.75 Df (kHz)
Human
Carotid
|— 1 sec —|
-60
-40
-20
cm/s
-0
ECG
What about
other vessels?
20 MHz Doppler signals from
peripheral arteries in a mouse
right carotid
20 MHz Doppler Probe
left carotid
mm
aortic arch
ascending aorta
-100
descending aorta
-50
cm/s
-0
|
250 ms
right renal
celiac
|
left renal
abdominal aorta
Stop
Velocities are similar in magnitude and shape to those from humans
Pulse-wave velocity measurements in mice
((((
Sample
Volume
Probe
20 MHz
Doppler
40 mm
ECG
12 ms
c2 = Eh/dr
c = PWV
= 3.3
mm/ms
PWV=is40/12
similar
in man
Pulse-wave velocity in knockout mice
and responses to phenylephrine
1200
*p<0.05 vs normal
**p<0.05 vs control
PWV
900
Control
Phenylephrine
600
300
cm/s
0
465
**
990
Normal, n=19
*
360
*
432
αSMA-/-, n=10
*
1037
Matrix GLA-/-, n=3
Again,
the values
are administer
similar to those
from humans.
What happens
if you
a vasoconstrictor?
Arterial Tonometry in Mice
Millar 1.4F micromanometer
Mouse
Aorta
0.45 mm diameter
ECG
50 ms/div
Pressure
waveform
ECG, Doppler velocity, tonometric pressure,
and derivatives from a mouse carotid artery
100
Velocity
mmHg
or cm/s
Pressure
50
0
dP/dt
dV/dt
-50
ECG
-100
1400
1300
1200
1100
1000
900
200
300 waveform
400 noninvasively?
500
600
Can we 100
generate
a pressure
800
0 msec
Real-time 2-D image of a mouse carotid artery taken
with a 30 MHz state-of-the-art VisualSonics scanner
Vessel walls
generate
well-defined
moving
echoes.
Can we measure the waveform of the diameter
pulsations during the cardiac cycle?
Blood velocity and wall motion measured in a mouse
carotid artery
xmit samples
xmit
time
Multigate 20 MHz
Pulsed Doppler
Doppler
Probe
coupling
gel
skin
gate 1
gate 2
gate 3
- 90
120
Diameter change
=near-far
sound beam
wall motion
- 60
90
SV1
carotid artery
Near-wall motion f1
- 30
60
blood
velocity
SV
SV2
~500 mm
Blood Velocity df2/dt
-0
30
SV3
wall motion
Far-wall motion f3
0
600
|How
do
ms
we200
stabilize
700
cm/s
or mm
|
probe?
800
the
Anesthetized mouse showing Doppler probe
in clip holder at 60o to the right carotid artery
Noninvasive displacement signals from the carotid
artery, abdominal aorta, and iliac artery of a mouse
160
120
R-wave
ECG 2
Abdominal aorta (~110mm)
Displ
ECG 2
80
Displ
ECG 2
Carotid (~50mm)
40mm
Displ
40
Iliac (~20mm)
0
400
0
msec
500
100
600
200
Resemble
waves
Waveformspressure
damp with
distance
Diameters
pulsate
about
10%
700
300
Carotid artery diameter signals from
different types and strains of mice
200
aSMA (100 mm)
50mm
150
Old (55 mm)
100
WT (45 mm)
50
ApoE (14 mm)
0
10
0
msec
110
100
210
200
How
Resemble
good ispressure
the resolution?
waves
310
300
-4
Carotid artery wall motion
in an ApoE-KO mouse
demonstrating high spatial
and temporal resolution
-5
-6
-7
-8
-9
1 mm
-10
-11
What about the inflections?
-12
-13
-14
-15
Mouse
red cell
-16
-17
-18
-19
-20
150
0
ms
200
50
250
100
300
150
350
200
Vessel diameter and velocity showing how the
augmentation index is calculated from strain
150
3-
125
local minimum
mm/s
120
0-
AI = max-inf
95
max-min
wall velocity
inf
max
__
90
net diameter
change
DD = max-min
65
Dopp
Near
30mm
__
60
Diam
min
dD/dt
35
30-30
5
blood velocity
cm/s
0-0
0
600
msec
100
700
200
800
In humans,
AI increases
with age and
vasc disease
-25
900
300
Far
Carotid artery augmentation index versus diameter
pulsations for several types and strains of mice
0.3
0.3
AI
0.2
0.2
T
W
WT
ApoE
ApoE
aSMA
aSMA
Old
Old
0.1
0.1
Diameter change
0
0.0
0
0
mm 220
0
40
40
60
60
80
80
100
100
Aorta
Carotid artery
Velocity
Pressure
ECG
Why
do the velocity
different?
Pulse
transmission
and waveforms
reflection inlook
a compliant
tube
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.
Wave transmission and reflection in the aorta
Aorta
Heart
Forward wave
Backward wave
Time
Measured wave
Wave transmission and reflection in the aorta
Aorta
Heart
Forward wave
Pf
Pb
Backward wave
Pm
Measured wave
Time
Qm
Flow wave
Pm = Pf + diameter,
Pb
Pressure,
Qm =and
(Pf -velocity
Pb)/Zc
flow,
start up at the same
Pf = and
(Pm +
ZcQm)/2
time
have
Pb = (Pshapes
)/2
similar
until
m - ZcQm
the reflected wave
Zc = dPs/dQs
arrives.
Qf = Pf/Zc
Qb = -Pb/Zc
150
Velocity, Diameter, and calculated60 forward and
backward waves in a mouse carotid artery
100
50
40-50
40
Diameter
Velocity
30-0
Pressure ~ Diameter
Flow ~ Velocity
D = Df + Db
v = (Df - Db)/Zc
30
50m
20-50
20
Df = (D + Zcv)/2
Db = (D - Zcv)/2
Zc = dDs/dvs (=rc)
-100
10-
10
G(f) = Db/Df = |G| ejf
Forward
cm/s
0-150
400
0
Backward
msec
500
100
600
200
Why
Does
are
this
there
happen
2 peaks
in man?
in Df?
0
700
300
Z(f) = |D/v| ejf
Human carotid pressure and velocity signals
140
140Press
120
120-
120
Tonometric Pressure
100
-80
Velocity
60
-60
100
100-
80
80
80-
Doppler Velocity
-40
60
60-
40
40
40-
20
-20
cm/s
0-0
Forward
20
20mmHg
0-0
700
0
Backward
900
1100
1300
Seconds
1500
1700
1
1900
2100
2300
2500
-20
2700
2
Can we measure
coronary blood
flow in mice?
Body Worlds 3 - Gunther von Hagen
Cast of Coronary Arteries
What happens
to 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.
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
H
B
raw phasic velocity
fast | slow paper speed
filtered mean velocity
H/B = 3.0
2
----Hyperemic
-----Baseline
1 sec timer
Cole & Hartley, Circulation, 1977
3
Can we
do this
1
in mice?
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.
Method to sense coronary blood
flow noninvasively in mice
(((
20 MHz Doppler Probe
-50cm/s
Is this coronary flow?
Velocity in 3 mouse vessels showing relative timing
Left main coronary flow
---maximum
-50
cm/s
-0
Common carotid flow
-50
Aortic flow
cm/s
-0
-100
-50
cm/s
-0
ECG
HR = 550
Noninvasive coronary Doppler signals from a mouse
anesthetized at low and high levels of isoflurane gas
--80--
low =1.0%
--60--
H/B = Vhigh/Vlow = 2.2
Vmax
Vmean
high = 2.5%
--40-- This give us baseline
velocity, but, how can we
--20-measure hyperemic
cm/s
---0--- velocity and coronary
reserve noninvasively?
HR = 398 b/min
ECG
HR = 412 b/min
|
800 ms
|
What about old and ApoE mice?
140
140-
120
120-
Coronary flow velocity reserve (H/B) in mice
as a function of age and atherosclerosis
B - Baseline Peak Diastolic Velocity (1.0 % Isofl)
H - Hyperemic Peak Diastolic Velocity (2.5 % Isofl)
CFR = H/B
Mean +/- SE
100
100-
H/B
-4Base
H
80-80
Hyper
H/Bx
6060
40-40
H/B
B
-3
-2
20-20
-1
n = 10
n = 10
n = 10
n = 20
cm/s
35 84 2.4
30 84 3.0
25 87 3.6
52 120 2.5
0
0-0
6 wk
3 mo
2 yr
ApoE
-/6 wk
3 mo
2 yrand vascular
2 yr ApoE
What about
non-coronary
forms of heart
disease?
Aortic banding
in mice
Produces
cardiac hypertrophy and carotid
-pressure overload remodeling
27
gauge
Before
After
Right
mm
Left
Carotid Flows?
Simultaneous Doppler signals from a banded mouse
mm scale
Aortic Arch Jet Velocity - 10 MHz Doppler
DP~75 mmHg
Left Carotid Artery Velocity - 20 MHz Doppler
Right Carotid Artery Velocity - 20 MHz Doppler
Aortic
Band
left main
coronary
artery
-500
cm/s
-0
-20
-0
-160
cm/s
-0
ECG
What
msec happens to coronary flow?
Coronary blood velocity
in a banded mouse
2.5% isoflurane
H/B = 2.0
-100
-50
1% isoflurane
Pre
Band
cm/s
-0
|H/B = 1.7 400 ms
1 Day
H/B = 0.9
21
Days
|
Response of coronary velocity and heart rate to
isoflurane in 10 banded mice during remodeling
4-4
Hyperemic/Baseline Velocity
H/B Heart Rate
3-3
(CFR)
(Little change)
2-2
H/B
H/B-HR
1-1
0-0
3.2
Pre
Pre
2.2
1d
1 day
1.7
7d
7 day
1.4
1.1
1414dday
2121dday
Systolic/Diastolic coronary velocity area ratio
before and after banding in mice
1.01.0
0.8
0.8-
S/D Baseline
S/D Hyperemic
0.60.6
S/D-B
0.4
0.4-
S
D
S
D
0.2
0.2-
0.0
0.0-
.17 .23
.29 .50
Pre
Pre
1d
1 day
.67 .81
7d
7 day
.83 .88
.92 .86
14 14dday
21 21d
day
S/D-H
Differences in timing between left and
right coronary flow velocity in a patient
Systole
ECG
200
Pressure
100
mmHg
0
8
Doppler
Shift
4
kHz
0
Left coronary artery
Right coronary artery
Scaling in mammals from elephants to mice Y = a BW b
Heart weight
LV volume
Stroke volume
Blood volume
Heart Rate
Heart Period
Circulation time
Life span
Artery length
Artery diameter
Wall shear stress
Cardiac output
Entrance length
Acceleration, dP/dt
a BW1
a BW1
a BW1
a BW1
a BW-1/4
a BW1/4
a BW1/4
a BW1/4
a BW1/4
a BW3/8
a BW-3/8
a BW3/4
a BW3/4
a BW-1/4
Capillary diameter
Capillary length
Capillary number
Capillary velocity
Cell number
Cell length
Cell volume
Elastic modulus
Blood viscosity
Arterial pressure
Blood velocity
PW velocity
Diameter pulsation
Coronary reserve
a BW1/12
a BW5/24
a BW5/8
a BW-1/24
a BW5/8
a BW1/8
a BW3/8
a BW0
a BW0
a BW0
a BW0
a BW0
a BW0
a BW0
*T.H. Dawson, “Engineering design of the cardiovascular system of mammals” , Prentice Hall, 1991.
Human/mouse scale factors
Allometric
Equation
Parameter
Heart & blood volume
Cardiac output, flow
Cell number
Vessel diameter
Y = a BWb Linear dimension
Vessel length, periods
Cell length
Capillary diameter
Human/mouse Blood pressure & vel.
Capillary velocity
70kg / 25g
Heart rate, Accel.-1/4
Power
Ratio
1
3/4
5/8
3/8
1/3
1/4
1/8
1/12
0
-1/24
2800
385
143
20
14
7
2.7
2
1
0.7
0.14
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.
Credits
Faculty Collaborators
Anil Reddy
Lloyd Michael
Mark Entman
George Taffet
Yi-Heng Li
Dirar Khoury
Sridhar Madala (Indus)
Y-X (Jim) Wang (Berlex)
Technicians
Thuy Pham
Jennifer Pocius
Jim Brooks
Ross Hartley
Alex Tumang
chartley@bcm.edu