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

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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

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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

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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.

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Reproducibility / Repeatability:

The ability of an instrument to give the same output for equal

inputs applied at two different times.

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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.

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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

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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

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Basic Concepts

Linearity:

Necessary conditions for a linear system:

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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

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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)

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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

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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

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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

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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

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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.

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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).

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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

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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)

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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