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? Why use mice?

Comparison of Heart sizes Dog Rat Mouse

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.

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 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?

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

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

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

Set-up for noninvasive Doppler measurements in mice

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 | 380 ms | Velocity and waveforms are simliar to man

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

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 | 250 ms | right renal left renal abdominal aorta Stop Velocities are similar in magnitude and shape to those from humans

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

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?

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 Velocity mmHg or cm/s Pressure dP/dt dV/dt ECG Can we generate a pressure waveform noninvasively? 0 msec 100 200 300 400 500 600

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 SV3 SV1 SV2 xmit samples xmit time Multigate 20 MHz Pulsed Doppler | 200 ms | Diameter change =near-far Near-wall motion f1 gate 1 gate 2 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?

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 R-wave Abdominal aorta (~110mm) 40mm Carotid (~50mm) Iliac (~20mm) 0 msec 100 200 300 Resemble pressure waves Diameters pulsate about 10% Waveforms damp with distance

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 How good is the resolution? Resemble pressure waves

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

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 0 msec 100 200 300

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

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

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 Heart Aorta Forward wave Backward wave Time Measured wave

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

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?

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

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 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.

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

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 ---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

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 ---0--- ECG Vmean Vmax This give us baseline velocity, but, how can we measure hyperemic velocity and coronary reserve noninvasively? HR = 398 b/min | 800 ms | What about old and ApoE mice?

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 = 10 n = 10 n = 10 n = 20 35 84 2.4 30 84 3.0 25 87 3.6 52 120 2.5 What about non-coronary forms of heart and vascular disease? 6 wk 3 mo 2 yr 2 yr ApoE-/-

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?

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

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 | 400 ms | 21 Days H/B = 0.9

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

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 .17 .23 .29 .50 .67 .81 .83 .88 .92 .86 Pre 1 day 7 day 14 day 21 day

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

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.

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

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 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@bcm.edu