Download Lecture 10

BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
September 26, 2002
Lecture #10 - Data Analysis (September 26, 2002)
DATA ANALYSIS
A. Techniques
1. Time Domain - beat-to-beat analysis, measure morphological (shape) waveform
features (i.e. mean-systolic-diastolic pressure, heart rate, stroke volume, cardiac
output, heart rate, etc.)
***HEART program demonstration (please read manuscript posted on website)
2. Frequency Domain – Fourier analysis (magnitude and phase)
Figure 10-1. Illustration of Fourier series (frequency-based) construction of a waveform.
Lecture 10 - Data Analysis
1
BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
September 26, 2002
Figure 10-2. Illustration of Fourier series (frequency-based) representation of an aortic
flow waveform.
Figure 10-3. Systemic input impedance (magnitude and phase) from aortic pressure
and flow measurements.
Lecture 10 - Data Analysis
2
BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
September 26, 2002
Uncertainty Analysis
1. Taylor Series
f{(x1 + x1), (x2 + x2), … (xn + xn)}
Equation 1
f(x1, x2, … xn) + x1(f/x1) + x2(f/x2) + … + xn(f/xn)
Equation 2
We define our variables as xn and our variation or ‘uncertainty’ in xn as xn.
Let us now define xn = un
The maiximum uncertainty is defined as,


u f  f x1  u x1 , x 2  u x 2 ,   x n  u x n  f x1 , x 2 ,  x n 
Equation 3
 f
f
f 
u f   u1
 u2
  un

x 2
x n 
 x1
Equation 4
The probable uncertainty can then be defined as,
2
2


f  
f 
f 
   u x2
       u xn

u f   u x1
x 2 
x n 
 x1  

2
Equation 5
Example-1
Given the equation Q = k(P1 – P2), where we have measured Q, P1, and P2 and need to
solve for k.
k
Q
Q

P1  P2 ΔP
uk  uQ
Equation 1.1
k
k
 uP
Q
P
Equation 1.2
Solving for the uncertainty for P,
u ΔP  u P1
k
k
 u P2
P1
P2
Lecture 10 - Data Analysis
Equation 1.3
3
BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
September 26, 2002
We measure P1 = 95 mmHg, P2 = 80 mmHg, and Z = 3 L/min. Assuming we know the
resolution of our pressure (P1 and P2) and flow (Q) measurements are P1=P2=1 mmHg
and Q = 0.5 L/min.
u ΔP  u P1  u P2
u k  u P1
, uP = 2 mmHg
Equation 1.4
1
Q
1
 3 
 2 2  0.5   2
  0.033  0.026 , uk = 0.059 L/min/mmHg Equation 1.5
ΔP
ΔP
 15 
 225 
Thus, k = 3/15  uk. k = 0.2  0.06 L/min/mmHg.
Example-2
Calculate the compliance of a tube (shown below) of length ‘L’ and diameter ‘d’ as well as the
uncertainty in the calculation. Given a graduated syringe used to inject saline into a tube. The
tube has a least count of 0.1 cc. We can measure the pressure within the tube with a solid state
pressure transducer that has been calibrated to read to within 1 mmHg. The tube without any
saline injected has an internal pressure, Pi = 60 mmHg, and volume, Vi = 10 cc. When injected
with saline, the internal pressure, Ps = 70 mmHg, and volume, Vs = 20 cc.
L
syringe
d
From previous lectures, we know that compliance is defined as a change in volume
divided by a change in pressure.
C
Δvolume
ΔV

Δpressure ΔP
Equation 2.1
The uncertainty in the compliance is then defined as,
u c  u Δv
C
C
 u ΔP
ΔV
ΔP
C
1

ΔV ΔP
and
Equation 2.2
C - V

ΔP ΔP 2
Lecture 10 - Data Analysis
Equation 2.3
4
BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
September 26, 2002
Recall, V = 10 cc, P = 10 mmHg, uV = 0.1 cc, and uP = 2 mmHg.
Then,
C
1

ΔV 10
and
C
10
1


ΔP 100 10
Equation 2.4
Then, the uncertainty in our compliance calculation (uc) becomes,
u c  0.1
1
1
2
10
10
or uc = 0.21 cc/mmHg
Equation 2.5
Solving for our compliance,
C = 1  0.21 cc/mmHg
Assignment #10:
1. A cardiologist wishes to determine the left ventricular external work (EW) in an
elderly patient. Recall, external work is area within the left ventricular pressure-volume
loop [EW = (LVPed – LVPbd)/SV]. During a cardiac catheterization procedure, you
measure the left ventricular pressure and aortic flow. Left ventricular beginning diastolic
pressure (LVPbd) is 4 mmHg, left ventricular end-diastolic pressure (LVPed) is 20
mmHg, cardiac output is 3 L/min, and heart rate is 65 bpm. The resolution of your left
ventricular pressure and aortic flow measurements are 1 mmHg and 0.1 L/min.
Calculate the left ventricular external work, EW, and the uncertainty, UEW.
2. You have been appointed to a blue ribbon panel scientific advisory board by
President Bush to help decide whether funding for xenotransplantation (i.e. pig donor
heart transplants into human recipients). Given experimental data from a healthy pig
heart (pig_data.txt) and a diseased human heart (human_data.txt), you can compare
hemodynamic parameters to help determine compatibility. Using data sets posted on
website containing one beat of healthy pig and one beat of healthy human, please
complete the tables below and provide a recommendation to President Bush.
Data Set
Pig
Human
LAPmean
LVPsystolic
LVPbd
LVPed
Data Set
AoPmean
AoPsystolic
AoPdiastolic
+dP/dt
Stroke
Volume
Pig
Human
*Assignment #10 due in class on Thursday, October 3, 2002
Lecture 10 - Data Analysis
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-dP/dt
Heart
Rate
LV EW
Cardiac
Output
BME Class (Physiology - Steven C. Koenig, Ph.D. and George Pantalos, Ph.D.)
Lecture 10 - Data Analysis
6
September 26, 2002