1. 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

2. 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,
Post Doctoral Fellow, Bioengineering, Rice Univ
Faculty at Baylor College of Medicine Present
Adjunct Professor of BME at Rice and Univ. of Houston
Dissertation: "Ultrasonic properties of artery walls."

3. 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.

4. 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?
Why use mice?

5. Comparison of Heart sizes
Dog
Rat
Mouse

6. Does the size difference matter?
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.

7. 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)* BW=25g
Heart weight a BW BW 112 mg
LV volume a BW BW 56 ml
Stroke volume a BW BW 24 ml
Heart rate a BW-1/4 170 BW-1/ bpm
Cardiac output a BW3/4 224 BW3/ ml/min
Aortic diameter a BW3/8 3.6 BW3/ mm
Aortic length a BW1/4 13 BW1/ cm
Arterial pressure a BW mmHg
Aortic velocity a BW cm/s
PW velocity a BW 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?

8. Log-log plots of heat production, oxygen consumption, and heart rate versus body weight
-1/4 power
Heat production
3/4 power
3/4 power
Oxygen consumption

9. 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

10. 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

11. Set-up for noninvasive Doppler
measurements in mice

12. 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---- | ao | ac | ao
Mitral
------E R |
ECG
ECG
| ms |
Velocity and waveforms are simliar to man

13. Mouse carotid Dopper signal processing
Carotid arteries
Mouse carotid Dopper signal processing
20 MHz
Doppler
Probe
Sample volume
Doppler probe mm mm
Df = 2 fo(V/c)cosθ
V (cm/s) = 3.75 Df (kHz)
Indus
256 point FFT
125 k-samples/s
peak Doppler shift
Human
Carotid
-60
-40
-20
cm/s -0
|— 1 sec —|
What about
other vessels?
ECG

14. 20 MHz Doppler signals from peripheral arteries in a mouse
20 MHz Doppler Probe
20 MHz Doppler signals from
peripheral arteries in a mouse mm
right carotid
left carotid
aortic arch
ascending aorta
-100
-50
cm/s -0
descending aorta
celiac
| ms |
right renal
left renal
abdominal aorta
Stop
Velocities are similar in magnitude and shape to those from humans

15. Pulse-wave velocity measurements in mice
Probe
((((
20 MHz
Doppler
40 mm
ECG
Sample
Volume
12 ms
c2 = Eh/dr
This shows the method we use to measure pulse-wave velocity noninvasively in mice. Mice are anesthetized and placed supine on a small board containing ECG electrodes connected to a high-fidelity amplifier. Doppler signals are processed by a ZCIH processor as in the last slide or sampled at 125 kHz for subsequent processing by an FFT analyzer as shown here. Doppler signals are acquired first from the aortic arch by placing the probe laterally on the left side of the upper chest and searching for the highest velocity signal with an aortic velocity waveform. A mark is then made under the probe, and a second mark is made 40 mm distal on the abdomen. The probe is then moved to the new site, and another velocity signal is recorded from the abdominal aorta. The pulse transit-time is measured from the FFT display which is updated every 0.1 ms by subtracting the arrival times with respect to the ECG. Pulse-wave velocity is determined by dividing the separation distance (40mm) by the pulse transit-time (12ms here) = 3.3m/s.
(((
c = PWV = 40/12 = 3.3 mm/ms
PWV is similar in man

16. Pulse-wave velocity in knockout mice
Control
Phenylephrine **
990
432 *
**p<0.05 vs control
and responses to phenylephrine
300
600
900
1200
PWV
cm/s
*p<0.05 vs normal
Figure 7. Bar graph showing pulse-wave velocity in 19 normal, 10 alpha smooth muscle actin knockout (αSMA-/-), and 3 Matrix GLA protein knockout, mice. The response to an IV injection of phenylephrine is shown for the normal and αSMA-/- mice. * *
465
360
1037
Normal, n=19
αSMA-/-, n=10
Matrix GLA-/-, n=3
Again, the values are similar to those from humans.
What happens if you administer a vasoconstrictor?

17. Arterial Tonometry in Mice
Millar 1.4F micromanometer
Mouse
Aorta
0.45 mm diameter
ECG
50 ms/div
Pressure
waveform

18. ECG, Doppler velocity, tonometric pressure,
and derivatives from a mouse carotid artery
Velocity
mmHg
or cm/s
Pressure
dP/dt
dV/dt
ECG
Can we generate a pressure waveform noninvasively?
0 msec

19. 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?

20. Blood velocity and wall motion measured in a mouse carotid artery
SV3
SV1
SV2
xmit samples xmit
time
Multigate 20 MHz
Pulsed Doppler
| ms |
Diameter change
=near-far
Near-wall motion f1
gate gate gate 3
cm/s
or mm
- 90
- 60
- 30
- 0
Far-wall motion f3
Blood Velocity df2/dt
Doppler
Probe
coupling
gel
skin
sound beam
((((
wall motion
carotid artery
blood
velocity SV
~500 mm
How do we stabilize the probe?

21. Anesthetized mouse showing Doppler probe
in clip holder at 60o to the right carotid artery

22. 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)
msec
Resemble pressure waves
Diameters pulsate about 10%
Waveforms damp with distance

23. Carotid artery diameter signals from
different types and strains of mice
aSMA (100 mm)
50mm
Old (55 mm)
WT (45 mm)
ApoE (14 mm)
msec
How good is the resolution?
Resemble pressure waves

24. Carotid artery wall motion in an ApoE-KO mouse
demonstrating high spatial
and temporal resolution
1 mm
What about the inflections?
Mouse
red cell ms

25. 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
inf
net diameter
change __
30mm
min
In humans,
AI increases
with age and
vasc disease
Figure 3. Blood velocity, near and far artery wall motion, and net diameter change and velocity are shown from a normal wild-type mouse. The net diameter change is calculated by subtracting far and near wall motion and wall velocity is calculated as the derivative of diameter change. For determination of augmentation index, the inflection point on the diameter signal (inf) is measured at the local minimum of velocity during the increase in diameter from minimum (min) to maximum (max).
30-
cm/s 0-
blood velocity
msec

26. 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

27. Aorta Carotid artery
Velocity
Pressure
ECG
Pulse transmission and reflection in a compliant tube
Why do the velocity waveforms look different?

28. 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.

29. Wave transmission and reflection in the aorta
Heart
Aorta
Forward wave
Backward wave
Time
Measured wave

30. Wave transmission and reflection in the aorta
Heart
Aorta Pf
Pm = Pf + Pb
Qm = (Pf - Pb)/Zc
Pf = (Pm + ZcQm)/2
Pb = (Pm - ZcQm)/2
Zc = dPs/dQs
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

31. 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
msec
Why are there 2 peaks in Df?
Does this happen in man?

32. 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
Seconds

33. Can we measure coronary blood flow in mice?
Body Worlds 3 - Gunther von Hagen

34. Cast of Coronary Arteries
What happens
to coronary flow?

35. Doppler catheters can be used to sense flow in man
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.

36. Can we do this in mice? 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.
Injection of contrast agent 3 H B 2 1
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

37. 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.

38. Method to sense coronary blood flow noninvasively in mice
(((
20 MHz Doppler Probe
-50cm/s
Is this coronary flow?

39. Velocity in 3 mouse vessels showing relative timing
---maximum
-50
cm/s -0
Left main coronary flow
Common carotid flow
-50
cm/s -0
-100
-50
cm/s -0
Aortic flow
ECG HR = 550

40. Noninvasive coronary Doppler signals from a mouse
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
--80--
--60--
--40--
--20--
cm/s
ECG
Vmean
Vmax
This give us baseline velocity, but, how can we measure hyperemic velocity and coronary reserve noninvasively?
HR = 398 b/min
| ms |
What about old and ApoE mice?

41. 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)
CFR = H/B
Mean +/- SE
H/B -4 -3 -2 -1 -0 H
H/B B
n = n = n = n = 20
What about non-coronary forms of heart and vascular disease?
6 wk mo yr yr ApoE-/-

42. Aortic banding in mice Produces cardiac hypertrophy -pressure overload
Before After mm
Produces
cardiac hypertrophy
-pressure overload
and carotid
remodeling
Right Left 27
gauge
Fig. 1. Drawing of a mouse heart and great vessels (A) showing the placement of a 0.4 mm constricting band around the aortic arch to produce cardiac hypertrophy (B-C) via pressure overload. A Doppler probe (D) was used to measure flow velocity at the aortic valve (1), the mitral valve (2), the right (3) and left (4) carotid arteries, at the site of the band (5), and distal to the band (6) noninvasively 1 and 7 days after surgical placement.
Carotid Flows?

43. Simultaneous Doppler signals from a banded mouse
-500
cm/s -0
mm scale
Aortic Arch Jet Velocity - 10 MHz Doppler
DP~75 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
What happens to coronary flow?
msec

44. Coronary blood velocity
in a banded mouse
2.5% isoflurane
-100
-50
cm/s -0
H/B = 2.0
1% isoflurane
Pre
Band
1 Day
H/B = 1.7
| ms | 21
Days
H/B = 0.9

45. Response of coronary velocity and heart rate to isoflurane in 10 banded mice during remodeling4- 3- 2- 1- 0-
Hyperemic/Baseline Velocity
H/B Heart Rate
(CFR)
(Little change)
Pre day day day day

46. 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 D S D
Pre day day day day

47. Differences in timing between left and right coronary flow velocity in a patient
Systole
ECG
Pressure
Doppler
Shift
200
100
mmHg 8 4
kHz
Left coronary artery Right coronary artery

48. 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
Cardiac output a BW3/4 PW velocity a BW0
Entrance length 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.

49. Human/mouse scale factors
Parameter Power Ratio
Heart & blood volume
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/
Heart rate, Accel. -1/
Allometric
Equation
Y = a BWb
Human/mouse
70kg / 25g

50. 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

51. 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.

52. 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