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Sahand University of Technology
Medical Measurement
2
Measurand
• biopotential, pressure, flow, dimensions, displacement (velocity,
acceleration, force), impedance, temperature, chemical concentrations
Transducer
• convert one form of energy to another; sensor converts measurand to an
electric signal
• minimize energy extracted, minimally invasive, respond only to form of
energy present in measurand
Signal Conditioning
• filter (shape frequency content), amplify (or attenuate), shift (add DC
component), digitize for storage
Output Display
• numerical or graphical, discrete or continuous, permanent or temporary,
visual or auditory
• Human factors engineering guidelines and preferred practices for the design
of medical devices (AAMI, 1993)
Basic Concepts
3
Auxiliary Elements
• calibration signal (known voltage)
• control and feedback (insulin delivery)
• alarms (intensive care monitors)
• transmission of data to remote locations (nurses’ stations)
Basic Concepts
Operational Modes
• Direct - measurand directly interfaced with sensor
e.g. a catheter placed in left ventricle
Indirect - another measurand with known relation to desired measurand
e.g. x ray, photoplethysmography, optical blood glucose measurments
• Sampling vs. Continuous / Analog vs. Digital (acquisition, storage, display)
• Generating vs. Modulating Sensors
GS produces output from Energy in measurand (biopotentials)
MS measures changes in flow of Energy from an external source
through the sensor [strain gage; sensitivity = f(external energy)]
e.g. 1 V/g/Vex
4
Basic Concepts
5
Basic Concepts
6
Basic Concepts
7
Basic Concepts Desired input: the measurand the instrument is designed to isolate.
Interfering inputs: quantities that inadvertently affect the instrument as a
consequence of the principles used to acquire and process the desired
inputs.
Modifying inputs: undesired quantities that indirectly affect the output by
altering the performance of the instrument itself.
8
Compensating for modifying or interfering inputs:
• Increase specific sensitivity
• Negative feedback
•Signal filtering
• electronic, mechanical, pneumatic, thermal, EM, etc.
• input, output, or in between
• Opposing inputs
• add a signal which is equal and opposite to the undesired input to
the (desired input + undesired input)
Basic Concepts
d
df
d
dfdd
dfd
xGH
Gy
GHyGx
yGyHx
1
)1(
)(
f
d
df
H
xy
GH
1
yGx dd
9
mean: central tendency
median: the value for which half the observations are smaller and half larger
mode: the observation that occurs most frequently
geometric mean: used with data on a logarithmic scale
range: difference between the largest and smallest observations
standard deviation: a measure of the spread of data about the mean; when used with
symmetric distributions of data, at least 75% of the values will always lie between
Basic Concepts Biostatistics
n
XX
i
nnXXXXGM 321
1
2
n
XXs
i
sXandsX 22
1,10,100,1000,10000
Xavg = 2222.2, GM = 100
10
Corelation coefficient: a measure of the relationship between numerical variables X
and Y for paired observations
r = -1 for a negative linear relationship,
+1 for a positive linear relationship,
0 indicates that there is no linear relationship
may be small for strong nonlinear relationships
Basic Concepts Biostatistics
22
YYXX
YYXXr
ii
ii
-40
-20
0
20
40
60
80
100
0 5 10 15 20 25 30
r = 1
r = 0.595
r = 0.182
r = 0.892
11
r2: The square of the Pearson product moment correlation
coefficient through data points in known y's and known x's.
The r-squared value can be interpreted as the proportion of
the variance in y attributable to the variance in x.
Basic Concepts
Biostatistics
2222
2
YYnXXn
YXXYnr
12
Basic Concepts
Instrument performance must be accurately described with quantitative
criteria so that different instruments may be compared and evaluated for
specific tasks.
Static Characteristics - system performance for DC or very low
frequency inputs
Dynamic Characteristics - system performance for AC inputs
Static Characteristics:
Accuracy Precision
Resolution Reproducibility
Statistical Control Static Sensitivity
Zero Drift Sensitivity Drift
Linearity Input Ranges
Input Impedance
13
Basic Concepts
Accuracy: 100True
MeasuredTrue
X
XX
where XTrue is often the accepted or reference value set by the
National Institute of Standards and Technology (NIST).
A measure of the total error; possibility that the measurement is low or high
are presumed equal. Usually expressed as % of full scale (% FSO).
Precision: The number of distinguishable alternatives from which a given result is
selected (2.434 V is a more precise value than 2.43 V). High precision
does not imply high accuracy.
14
Reproducibility / Repeatability:
The ability of an instrument to give the same output for equal
inputs applied at two different times.
15
Basic Concepts
Accuracy and Precision;
Another point of view:
Reproducibility
Basic Concepts
Statistical Control:
Considering all the elements of the system under measurement, and the
measurement system, how much variation is there from measurement to
measurement under measurement conditions.
Systematic errors - removed by calibration and correction factors.
Random errors - averaging multiple measurements made under “controlled,
measurment” conditions.
Static Sensitivity:
The ratio of the incremental output quantity to the incremental input
quantity, under static conditions, within the operating range of the
instrument, e.g. 5V / mm Hg or 0.5V / mm Hg.
16
Resolution:
The smallest incremental quantity that can be measured with
certainty; i.e. the degree to which nearly identical values can be
discriminated.
Basic Concepts
2
2
2
n
d
n
d
n
d
n
d
n
d
n
xxn
xyxxy
b
2
2
nn
d
nn
d
n
d
xdxn
yxyxn
m
Static calibration: 1) hold all inputs constant except one. 2) Vary this one input
incrementally over the n.o.r., recording the resulting incremental outputs.
Static sensitivity may only be constant over a limited range of inputs; for modulating
sensors, it may be given per volt of excitation (e.g. 5 V/ Vex / mm Hg).
Line displaying minimum least
squared error is described by:
17
Basic Concepts
Zero Drift:
All output values increase or decrease by the same absolute amount (i.e. the output
axis intercept increases or decreases).
Sources of zero drift:
misalignment
ambient temperature changes
hysteresis
vibration
shock
forces from undesired directions
18
Basic Concepts
Sensitivity Drift:
The slope of the calibration curve changes; i.e. the error is proportional to the
magnitude of the input.
Sources of sensitivity drift:
Misalignment
Nonlinearities
power supply variations
ambient temperature changes
ambient pressure changes
19
Basic Concepts
Linearity:
Necessary conditions for a linear system:
20
Input Ranges:
Basic Concepts
Maximum linear range
static linear range
dynamic linear range
Maximum operating range
Input Impedance:
For every input Xd1, there is an implicit input Xd2, such that
(Xd1)(Xd2) has the dimensions of power.
This product represents the instantaneous rate at which energy is
transferred across an interface (tissue-sensor, sensor-instrument,
instrument-instrument).
The input impedance is the ratio Xd1 / Xd2 = ZX
21
Basic Concepts
Input Impedance:
variable flow
variableeffort
2
1 d
dX
X
XZ
2
2
2
121 dX
X
ddd XZ
Z
XXXP
Effort - Flow
voltage - current
pressure - flow
force - velocity
P is the time rate of energy transfer from the measurement medium.
In general, Xd1 and Xd2 are phasor equivalents of the variables (i.e. have
magnitude and phase properties). In the realm of physiological signals (low
frequencies), phase differences are usually small and can often be ignored.
(In electronic terms, represents Ohm’s law, R=V/I)
22
Input Impedance:
Basic Concepts
2
2
2
121 dX
X
ddd XZ
Z
XXXP 5 mm Hg
23
variable flow
variableeffort
2
1 d
dX
X
XZ
Input Impedance:
Basic Concepts 2
2
2
121 dX
X
ddd XZ
Z
XXXP
Example 2: Assume that you wish to output a 10
V signal from your waveform generator. This
signal will be monitored by your oscilloscope (top
figure). The current, i, will be
mAV
R
Vi
i
out 01.0101
106
which is well within the capabilities of your
waveform generator.
Vout
Vout
mWmAV 1.001.010
24
Input Impedance:
Basic Concepts 2
2
2
121 dX
X
ddd XZ
Z
XXXP
Now you wish to apply this voltage across a
resistance, R1 = 20 , as in the bottom
figure. Now the current in the circuit is
mAV
RR
RR
Vi
i
i
out 5009996.19
10
1
1
The maximum current that your waveform
generator can produce is 200 mA. This
circuit therefor pushes the waveform
generator beyond its capabilities, and the
voltage you read on the scope will be far
different from the 10 V you would expect.
Vout
Vout
WmAV 550010
25
Input Impedance:
Basic Concepts
In general, for signal transfer applications, the input impedance of the
second stage of instrumentation should be much greater than the output
impedance of the first stage of instrumentation, Zin >> Zout. (However,
the “flow variable” cannot be reduced to zero.)
For power transfer applications, the input impedance of the second stage
of instrumentation should be the same as the output impedance of the
first stage of instrumentation, Zin = Zout. (Generally, both very low to
minimize power dissipation as heat.)
2
2
2
121 dX
X
ddd XZ
Z
XXXP
26
Specifications
Channels
Number 4 to 32 in steps of four channels
Amplification
Amplification 50 minimum to 200,000 maximum
Amplification Settings 5, 10, 20, 50, 100 and 200; x10, x1000
Filters
Low Cutoff Frequencies (-6 dB) 0.01, 0.1, 0.3, 1, 3, 10, 30 and 100 Hz
High Cutoff Frequencies (-6 dB) 0.03, 0.1, 1 and 3 kHz
Line Filter Notch-type filter (50/60 Hz) jumper selectable
Input Characteristics
Input Impedance 20 Megohm, differential, 35pF at connector per terminal
CMR (Common Mode Rejection) 30,000:1 (90dB) at 60 Hz
Noise 6 microvolts peak to peak, referred to input, inputs shorted, 3 kHz bandwidth
Output
Type Single-ended, clipped at approximately 10V peak to peak
Output Impedance 500 ohms
Output DC level less than or equal to 20 mV adjustable
Connector 37 pin DSUB
Trace Restorer Pushbutton control to return output to 0V
Calibrator
Range 8 values from 5 micro volts to 1 millivolt in 1, 2, 5 steps; plus or minus 2% accuracy
Frequency DC, 0.3, 1, 3, 10, 30, 100, 300 Hz and 1 kHz
Power
Supply Type Grass Approved power supply
Physical Specifications
Dimensions 19" (483 mm) x 5.25" (133mm) x 11" (279mm)
Weight 17 lbs. maximum
Rack-Mount Mounts in standard 19" rack with supplied hardware
Interface
Interface Supported RS-232
Software Windows Model 15 Link and LabVIEW drivers
Grass Instruments Model 15 Neurodata Amplifier System
27
Generalized Dynamic Characteristics:
Basic Concepts
Differential equations are needed to relate dynamic inputs to dynamic outputs.
Many instruments can be described by ordinary linear differential equations:
linear: coefficients are not functions of time or the input
ordinary: only one dependent variable
txbdt
dxb
dt
xdbtya
dt
dya
dt
yda
m
m
mn
n
n 0101
Introducing the differential operator
txbDbDbtyaDaDa m
m
n
n 0101
k
kk
dt
dD
Most instruments can be described with n = 0, 1, or 2, and most inputs with m = 0.
28
Transfer Function:
Basic Concepts
A mathematical description of the relationship between the system input and
output. If known, the output can be predicted for any input.
01
01
aDaDa
bDbDb
Dx
Dy
nn
mm
Operational transfer function
Frequency transfer function
01
01
ajaja
bjbjb
jX
jYn
n
m
m
Where and is the angular frequency in radians per second. 1j
Used for transient (i.e. non-repeating)
inputs; output is expressed as a function
of time, y(t).
Used for continuous inputs; output is
expressed as an amplitude ratio and
phase angle as a function of frequency
(Bode plots).
29
Zero-order instrument:
Basic Concepts
txbtya 00
ysensitivitstaticKa
b
jX
jY
Dx
Dy
0
0
Ideal dynamic performance - output related to the input for all frequencies; no
amplitude or phase distortion.
No instrument is ideally a zero-order instrument, but within limits, some
instruments can be reasonably modeled this way.
e.g. Flow of a low-mass, incompressible fluid through a rigid tube
Movement of a mass-less lever about a pivot with constant friction
Light output from a light-emitting diode as a function of current
through it
* No energy storage involved!! 30
Zero-order instrument:
Basic Concepts txbtya 00
ysensitivitstaticKa
b
jX
jY
Dx
Dy
0
0
31
First-order instrument:
Basic Concepts
txbtya
dt
tdya 001
tKxtyD 1
ysensitivitstatica
bK
0
0
stantcontimea
a
0
1
k
kk
dt
dD
D
K
tx
ty
1)(
)(
j
K
jX
jY
1
Operational transfer function Frequency transfer function
32
Basic Concepts First-order instrument:
Complex impedance sidebar:
CjZ
LjZ
RZ
C
L
R
1
R
XjXRZ
ParallelZZ
ZZZ
SeriesZZZ
eq
eq
eq
arctan,
21
21
21
2, Hzf Real quantity X is the reactance, is the phase angle.
33
Basic Concepts
CjiV
CjRiV
out
in
1
1
RCjV
V
in
out
1
1
functiontransferV
V
tx
ty
Vty
Vtx
in
out
out
in
)(
)(
)(
)(
First-order instrument: low-pass filter (integrator)
34
Basic Concepts
RCjV
V
in
out
1
1
t
out eV
1
First-order instrument: low-pass filter (integrator)
35
Basic Concepts
RCfCC
2
11
fC is the cutoff, or corner,
frequency. It is the frequency at
which the output has decreased
to 0.707 of the “flat” region of
the curve.
First-order instrument: low-pass filter (integrator)
jV
V
in
out
1
1
Gain 1 when < 1/
221
K
V
V
in
out
Gain = 0.707 when = 1/
1arctan
36
Basic Concepts First-order instrument: low-pass filter (integrator)
The magnitude portion of a pair of
Bode plots usually uses a logarithmic
scale for the ordinate axis. This scale
is often labeled in decibels (dB),
which are units of relative magnitude:
1
210
1
210
log20
log10
V
VdB
P
PdB (Power)
(Voltage)
At the cutoff frequency, the output
of a circuit is “3 dB down” from
its value in the flat portion of the
curve (i.e. 1.000 20 dB
0.707 17 dB). 37
Basic Concepts First-order instrument: low-pass filter (integrator)
38
Basic Concepts
IRV
Rcj
IV
out
in
1
RCj
RCj
V
V
in
out
1
functiontransferV
V
tx
ty
Vty
Vtx
in
out
out
in
)(
)(
)(
)(
First-order instrument: high-pass filter (differentiator)
RCfCL
2
11
39
Basic Concepts First-order instrument: high-pass filter (differentiator)
40
Basic Concepts Second-order instrument
Instruments with two opposing energy storage components generally
require a second-order differential equation to describe them:
txbtya
dt
tdya
dt
tyda 0012
2
2
tKxtyDD
nn
1
22
2
nsionlessdimeratiodampingaa
a
frequencynaturalundampeda
a
unitsinputbydividedunitsoutputysensitivitstatica
bK
n
,2
,
20
1
2
0
0
0
41
Basic Concepts Second-order instrument
> 1, overdamped
= 1, critically damped
< 1, underdamped
42