Biomedical Instrumentation

1
Biomedical Instrumentation

• Chapter 6 in
• Introduction to Biomedical Equipment Technology
• By Joseph Carr and John Brown

2
Signal Acquisition

• Medical Instrumentation typically entails
  monitoring a signal off the body which is analog,
  converting it to an electrical signal, and
  digitizing it to be analyzed by the computer.

3
Types of Sensors

• Electrodes acquire an electrical signal
• Transducers acquire a non-electrical signal
  (force, pressure, temp etc) and converts it to an
  electrical signal

4
Active vs Passive Sensors

• Active Sensor
• Requires an external AC or DC electrical source
  to power the device
• Strain gauge, blood pressure sensor
• Passive Sensor
• Provides it own energy or derives energy from
  phenomenon being studied
• Thermocouple

5
Sensor Error Sources

• Error
• Difference between measured value and true value.

6
5 Categories of Errors

1. Insertion Error
2. Application Error
3. Characteristic Error
4. Dynamic Error
5. Environmental Error

7
Insertion Error

• Error occurring when inserting a sensor

8
Application Error

• Errors caused by Operator

9
Characteristic Error

• Errors inherent to Device

10
Dynamic Error

• Most instruments are calibrated in static
  conditions if you are reading a thermistor it
  takes time to change its value. If you read this
  value to quickly an error will result.

11
Environmental Error

• Errors caused by environment
• heat, humidity

12
Sensor Terminology

• Sensitivity
• Slope of output characteristic curve ?y/ ?x
• Minimum input of physical parameter will create a
  detectable output change
• Blood pressure transducer may have a sensitivity
  of 10 uV/V/mmHg so you will see a 10 uV change
  for every V or mmHg applied to the system.

13
Which is more sensitive? The left side one
because youll have a larger change in y for a
given change in x
14
Sensor Terminology

• Sensitivity Error Departure from ideal slope of
  a characteristic curve

15
Sensor Terminology

• Range Maximum and Minimum values of applied
  parameter that can be measured.
• If an instrument can read up to 200 mmHg and the
  actual reading is 250 mmHg then you have exceeded
  the range of the instrument.

16
Sensor Terminology

• Dynamic Range total range of sensor for minimum
  to maximum. Ie if your instrument can measure
  from -10V to 10 V your dynamic range is 20V
• Precision Degree of reproducibility denoted as
  the range of one standard deviation s
• Resolution smallest detectable incremental
  change of input parameter that can be detected

17
Accuracy

• Accuracy maximum difference that will exist
  between the actual value and the indicated value
  of the sensor

18
Offset Error

• Offset error output that will exist when it
  should be zero
• The characteristic curve had the same sensitive
  slope but had a y intercept

Output
Output
Input
Input
Offset Error
Zero offset error
19
Linearity

• Linearity Extent to which actual measure curved
  or calibration curve departs from ideal curve.

20
Linearity

• Nonlinearity () (Din(Max) / INfs) 100
• Nonlinearity is percentage of nonlinear
• Din(max) maximum input deviation
• INfs maximum full-scale input

21
Hysteresis

• Hysteresis measurement of how sensor changes
  with input parameter based on direction of change

22
Hysteresis

• The value B can be represented by 2 values of
  F(x), F1 and F2. If you are at point P then you
  reach B by the value F2. If you are at point Q
  then you reach B by value of F1.

23
Response Time

• Response Time Time required for a sensor output
  to change from previous state to final settle
  value within a tolerance band of correct new
  value denoted in red can be different in rising
  and decaying directions

24
Response Time

• Time Constant Depending on the source is defined
  as the amount of time to reach 0 to 70 of final
  value. Typically denoted for capacitors as T R
  C (Resistance Capacitance) denoted in Blue

25
Response Time
Tdecay
F(t)
Decaying Response Time
Toff
Time

• Convergence Eye Movement the inward turning of
  the eyes have a different response time than
  divergence eye movements the outward turning of
  the eyes which would be the decay response time

26
Dynamic Linearity

• Measure of a sensors ability to follow rapid
  changes in the input parameters. Difference
  between solid and dashed curves is the non-
  linearity as depicted by the higher order x terms

27
Dynamic Linearity

• Asymmetric F(x) ! F(-x) where F(x) is
  asymmetric around linear curve F(x) then
• F(x) ax bx2cx4 . . . K offsetting for K or
  you could assume K 0
• Symmetrical F(x) F(-x) where F(x) is
  symmetric around linear curve F(x) then
• F(x) ax bx3 cx5 . . . K offsetting for K
  or you could assume K 0

28
Frequency Response of Ideal and Practical System

• When you look at the frequency response of an
  instrument, ideally you want a wideband flat
  frequency response.

29
Frequency Response of Ideal and Practical System

• In practice, you have attenuation of lower and
  higher frequencies
• FL and FH are known as the 3 dB points in
  voltage systems.

30
Examples of Filters

• Ideal Filter has sharp cutoffs and a flat pass
  band
• Most filters attenuate upper and lower
  frequencies
• Other filters attenuate upper and lower
  frequencies and are not flat in the pass band

31
Electrodes for Biophysical Sensing

• Bioelectricity naturally occurring current that
  exists because living organisms have ions in
  various quantities

32
Electrodes for Biophysical Sensing

• Ionic Conduction Migration of ions-positively
  and negatively charge molecules throughout a
  region.
• Extremely nonlinear but if you limit the region
  can be considered linear

33
Electrodes for Biophysical Sensing

• Electronic Conduction Flow of electrons under
  the influence of an electrical field

34
Bioelectrodes

• Bioelectrodes class of sensors that transduce
  ionic conduction to electronic conduction so can
  process by electric circuits
• Used to acquire ECG, EEG, EMG, etc.

35
Bioelectrodes

• 3 Types of electrodes
• Surface (in vivo) outside body
• Indwelling Macroelectrodes (in vivo)
• Microelectrodes (in vitro) inside body

36
Bioelectrodes

• Electrode Potentials
• Skin is electrolytic and can be modeled as
  electrolytic solutions

Metal Electrode
Electrolytic Solution where Skin is electrolytic
and can be modeled as saline
37
Electrodes in Solution

• Have metallic electrode immersed in electrolytic
  solution once metal probe is in electrolytic
  solution it
• Discharges metallic ions into solution
• Some ions in solution combine with metallic
  electrodes
• Charge gradient builds creating a potential
  difference or you have an electrode potential or
  ½ cell potential

38
Electrodes in Solution
2 cells A and B, A has 2 positive ions And B has
3 positive ions thus have a Potential difference
of 3 2 1 where B is more positive than A
A
B
39
Electrodes

• Two reactions take place at electrode/electrolyte
  interface
• Oxidizing Reaction Metal -gt electrons metal
  ions
• Reduction Reaction Electrons metal ions -gt
  Metal

40
Electrodes

• Electrode Double Layer formed by 2 parallel
  layers of ions of opposite charge caused by ions
  migrating from 1 side of region or another ionic
  differences are the source of the electrode
  potential or half-cell potential (Ve).

41
Electrodes

• If metals are different you will have
  differential potential sometimes called an
  electrode offset potential.
• Metal A gold Vae 1.50V and Metal B silver
  Vbe 0.8V then Vab 1.5V 0.8 V 0.7V (Table
  6-1 in book page 96)

Vae
Metal A
Vbe
Metal B
Electrolytic Solution
42
Electrodes

• Two general categories of material combinations
• Perfectly polarized or perfectly nonreversible
  electrode no net transfer of charge across
  metal/electrolyte interface
• Perfectly Nonpolarized or perfectly reversible
  electrode unhindered transfer of charge between
  metal electrode and the electrode
• Generally select a reversible electrode such as
  Ag-AgCl (silver-silver chloride)

43

• Rt internal resistance of body which is low
• Vd Differential voltage Vd
• Rsa and Rsb skin resistance at electrode A and
  B

• R1A and R1B resistance of electrodes
• C1A and C1B capacitance of electrodes

44
Electrode Potentials cause recording Problems

• ½ cell potential 1.5 V while biopotentials are
  usually 1000 times less (ECG 1-2 mV and EEG is
  50 uV) thus have a tremendous difference between
  DC cell potential and biopotential
• Strategies to overcome DC component
• Differential DC amplifier to acquire signal thus
  the DC component will cancel out
• Counter Offset-Voltage to cancel half-cell
  potential
• AC couple input of amplifier (DC will not pass
  through) ie capacitively couple the signal into
  the circuit

45
Electrode Potentials cause recording Problems

• Strategies to overcome DC component
• Differential DC amplifier to acquire signal thus
  the DC component will cancel out
• Counter Offset-Voltage to cancel half-cell
  potential
• AC couple input of amplifier (DC will not pass
  through)
• Capacitively couple the signal into the circuit

46
Medical Surface Electrodes

• Typical Medical Surface Electrode
• Use conductive gel to reduce impedance between
  electrode and skin
• Schematic

47
Medical Surface Electrodes

• Have an Ag-AgCl contact button at top of hollow
  column filled with gel
• Gel filled column holds actual metallic electrode
  off surface of skin and decreases movement
  artifact
• Typical ECG arrangement is to have 3 ECG
  electrodes (2 differentials signals and a
  reference electrode)

48
Problems with Surface Electrodes

1. Adhesive does not stick for a long time on sweaty
   skin
2. Can not put electrode on bony prominences
3. Movement or motion artifact significant problem
   with long term monitoring results in a gross
   change in potential
4. Electrode slippage if electrode slips then
   thickness of jelly changes abruptly which is
   reflected as a change in electrode impedance and
   electrode offset potential (slight change in
   potential)

49
Potential Solutions for Surface Electrodes
Problems

• Additional Tape
• Rough surface electrode that digs past scaly
  outer layer of skin typically not comfortable for
  patients.

50
Other Types of Electrodes

• Needle Electrodes inserted into tissue
  immediately beneath skin by puncturing skin on an
  angle note infection is a problem.
• Indwelling Electrodes Inserted into layers
  beneath skin -gt typically tiny exposed metallic
  contact at end of catheter usually threaded
  through patients vein to measure intracardiac
  ECG to measure high frequency characteristics
  such as signal at the bundle of His

51
Other Types of Electrodes

• EEG Electrodes can be a needle electrode but
  usually a 1 cm diameter concave disc of gold or
  silver and is held in place by a thick paste that
  is highly conductive sometimes secured by a
  headband

52
Microelectrode

• Microelectrode measure biopotential at cellular
  level where microelectrode penetrates cell that
  immersed in an infinite fluid
• Saline.

53
Microelectrode

• Two typical types
• Metallic Contact
• Fluid Filled

54
Microelectrode Equivalent Circuit
R1
RS Spreading Resistance of the electrode and is
a function of tip diameter R1 and C1 are result
of the effects of electrode/cell interface C2
Electrode Capacitance
RS
C2
C1
Vo
V1
55
Calculation for Resistance Rs

• Rs in metallic microelectrodes without glass
  coating

where Rs resistance ohms (?) P Resistivity of
the infinite solution outside electrode 70 ?cm
for physiological saline r tip radius ( 0.5 um
for 1 um electrode) 0.5 x10-4 cm
56
Calculation for Resistance Rs

• Rs of glass coated metallic microelectrode is 1-2
  order of magnitude higher

where Rs resistance ohms (?) P Resistivity of
the infintie solution outside electrode) 3.7
?cm for 3 M KCl r tip radius typically 0.1 u m
0.1 x 10-4 cm a taper angle ( p/ 180)
57
Capacitance of Microelectrode

• Capacitance of C2 has units pF/cm

Where e dielectric constant which for glass
4 R outside tip radius r inside tip radius
58
Capacitance of Microelectrode

• Find C of glass microelectrode if the outer
  radius is 0.2 um and the inner radius 0.15 um

59
Transducers and other Sensors

• Transducers sensors and are defined as a device
  that converts energy from some one form (temp.,
  pressure, lights etc) into electrical energy
  where as electrodes directly measure electrical
  information

60
Wheatstone Bridge
Es
R1
A
R3
R3
R1

-
Eo
EC
ED

Eo

-
Es
ED
EC
-
R2
R4
R4
R2
B

• Basic Wheatstone Bridge uses one resistor in each
  of four arms where battery excites the bridge
  connected across 2 opposite resistor junctions (A
  and B). The bridge output Eo appears across C
  and D junction.

61
Finding output voltage to a Wheatstone Bridge

• Ex A wheatstone bridge is excited by a 12V dc
  source and has the following resistances R1
  1.2K? R2 3 K ? R3 2.2 K ? and R4 5 K ?
  find Eo

62
Finding output voltage to a Wheatstone Bridge

• A wheatstone bridge is excited by a 12V dc source
  and has the following resistances R1 1.2K? R2
  3 K ? R3 2.2 K ? and R4 5 K ? find Eo

63
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64
Null Condition of Wheatstone Bridge

• Null Condition is met when Eo 0 can happen in 2
  ways
• Battery 0 (not desirable)
• R1 / R2 R3/ R4

65
Null Condition of Wheatstone Bridge

• When R1 2K? R2 1K ? R3 10K ? R4 5K ?

66
Null Condition of Wheatstone Bridge

• Key with null condition is if you change one of
  the resistances to be a transducer that changes
  based on input stimulus then Eo will also change
  according to input stimulus

67
Strain Gauges

• Definition resistive element that changes
  resistance proportional to an applied mechanical
  strain

68
Strain Gauges

• Compression decrease in length by DL and an
  increase in cross sectional area.

69
Strain Gauges

• Tension increase in length by DL and a decrease
  in cross section area.

L length
Rest Condition
70
Resistance of a metallic bar is given in length
and area

• where
• R Resistance units ohms (?)
• ? resistivity constant unique to type of
  material used in bar units ohm meter (?m)
• L length in meters (m)
• A Cross sectional area in meters2 (m2 )

71
Resistance of a metallic bar is given in length
and area

• Example find the resistance of a copper bar that
  has a cross sectional area of 0.5 mm2 and a
  length 250 mm note the resistivity of copper is
  1.7 x 10-8?m

72
Piezoresistivity

• Piezoresistivity change in resistance for a
  given change in size and shape denoted as h
• Resistance in tension
• Resistance increases in tension
• L length ?L change in L ? resistivity
• A Area ?A change in A

73

• Resistance in compression
• Resistance decreases in compression
• L length ?L change in L ? resistivity
• A Area ?A change in A

Note Textbook forgot the ? in equations 6-28 and
6-29 on page 110
74
Example of Piezoresistivity

• Thin wire has a length of 30 mm and a cross
  sectional area of 0.01 mm2 and a resistance of
  1.5?.
• A force is applied to the wire that increases the
  length by 10 mm and decreases cross sectional
  area by 0.0027 mm2
• Find the change in resistance h.
• Note ? resistivity 5 x 10-7 ?m

75
Example of Piezoresistivity
76
Example of Piezoresistivity

• Note Change in Resistance will be approximately
  linear for small changes in L as long as ?LltltL.
• If a force is applied where the modulus of
  elasticity is exceeded then the wire can become
  permanently damaged and then it is no longer a
  transducer.

77
Gauge Factor

• Gauge Factor (GF) a method of comparing one
  transducer to a similar transducer

78
Gauge Factor

• where
• GF Gauge Factor unitless
• ?R change in resistance ohms (?)
• R unstrained resistance ohms (?)
• ?L change in length meters (m)
• L unstrained length meters (m)

79
Gauge Factor

• Where e strain which is unitless
• GF gives relative sensitivity of a strain gauge
  where the greater the change in resistance per
  unit length the greater the sensitivity of
  element and the greater the gauge factor.

80
Example of Gauge Factor

• Have a 20 mm length of wire used as a string
  gauge and has a resistance of 150 ?.
• When a force is applied in tension the resistance
  changes by 2? and the length changes by 0.07 mm.
  
• Find the gauge factor

81
Types of Strain Gauges Unbonded and Bonded

• Unbonded Strain Gauge resistance element is a
  thin wire of special alloy stretch taut between
  two flexible supports which is mounted on
  flexible diaphram or drum head.

82
Types of Strain Gauges Unbonded and Bonded

• When a Force F1 is applied to diaphram it will
  flex in a manner that spreads support apart
  causing an increase in tension and resistance
  that is proportional to the force applied.
• When a Force F2 is applied to diaphram the
  support ends will more close and then decrease
  the tension in taut wire (compression force) and
  decrease resistance will decrease in amount
  proportional to applied force

83
Types of Strain Gauges Unbonded and Bonded

• Bonded Strain Gauge made by cementing a thin
  wire or foil to a diaphragm therefore flexing
  diaphragm deforms the element causing changes in
  electrical resistance in same manner as unbonded
  strain gauge

84
Types of Strain Gauges Unbonded and Bonded

• When a Force F1 is applied to diaphram it will
  flex in a manner that causes an increase in
  tension of wire then the increase in resistance
  is proportional to the force applied.
• When a Force F2 is applied to diaphram that cause
  a decrease the tension in taut wire (compression
  force) then the decrease in resistance will
  decrease in amount proportional to applied force

85
Comparison of Bonded vs. Unbonded Strain Gauges

• Unbonded strain gauge can be built where its
  linear over a wide range of applied force but
  they are delicate
• Bonded strain gauge are linear over a smaller
  range but are more rugged
• Bonded strain gauges are typically used because
  designers prefer ruggedness.

86
Typical Configurations
A
R3 SG3
R1 SG1

Vo
ES
C
D
-
R4 SG4
R2 SG2
B
Mechanical Configuration
Electrical Circuit

• 4 strain gauges (SG) in Wheatstone Bridge

87
Strain Gauge Example

• Using the configuration in the previous slide
  where 4 strain gauges are placed in a wheatstone
  bridge where the bridge is balanced when no force
  is applied,
• Assume a force is applied so that R1 and R4 are
  in tension and R2 and R3 are in compression.
• Derive the equation to depict the change in
  voltage across the bridge and find the output
  voltage when each resistor is 200 ?, the change
  of resistance is 10 ? and the source voltage is
  10 V

88
Strain Gauge Example
Derivation
Circuit
A
R1 R h
R3 R-h
Es

-
Eo

C
D
-
R2 R - h
R4 R h
B
Note Text book has wrongly stated that tension
decreases R and compression increases R on page
112
89
Transducer Sensitivity

• Transducer Sensitivity rating that allows us to
  predict the output voltage from knowledge of the
  excitation voltage and the value of the applied
  stimulus units µV/Vunit of applied stimulus

90
Transducer Sensitivity

• Example if you have a force transducer calibrated
  in grams (unit of mass) which allows calibration
  of force transducer then sensitivity denoted as f
  µV/Vg (another ex f µV/VmmHg)

91
Transducer Sensitivity

• To calculate Output Potential use the following
  equations
• where
• Eo output potential in Volts (V)
• E excitation voltage
• f sensitivity µV/Vg
• F applied force in grams (g)

92
Transducer Sensitivity

• Example Transducer has a sensitivity of 10
  µV/Vg, predict the output voltage for an applied
  force of 15 g and 5 V of excitation.

• note book has typo where writes µV/V/g for
  sensitivity

93
Inductance Transducers

• Inductance Transducers inductance L can be
  varied easily by physical movement of a permeable
  core within an inductor 3 basic forms
• Single Coil
• Reactive Wheatstone Bridge
• Linear Voltage Differential Transformer LVDT

94
LVDT
95
Capacitance Transducers

• Quartz Pressure Sensors capacitively based where
  sensor is made of fused quartz
• Capacitive Transducers Capacitance C varies with
  stimulus

96
Capacitive Transducers

• Three examples
• Solid Metal disc parallel to flexible metal
  diaphragm separated by air or vacuum (similar to
  capacitor microphone) when force is applied they
  will move closer or further away.
• Stationary metal plate and rotating moveable
  plate as you rotate capacitance will increase or
  decrease
• Differential Capacitance 1 Moveable metal Plate
  placed between 2 stationary Places where you have
  2 capacitors C1 between P1 and P3 and C2 between
  P2 and P3 where when a force is applied to
  diaphragm P3 moves closer to one plate or vice
  versa

97
Temperature Transducers

• 3 Common Types
• Thermocouples
• Thermistors
• Solid State PN Junctions

98
Thermocouple

• Thermocouple 2 dissimilar conductor joined
  together at 1 end.
• The work functions of the 2 materials are
  different thus a potential is generated when
  junction is heated (roughly linear over wide
  range)

99
Thermistors

• Thermistors Resistors that change their value
  based on temperature where
• Positive Temperature Coefficient (PTC) device
  will increase its resistance with an increase in
  temperature
• Negative Temperature Coefficient (NTC) device
  will decrease its resistance with an increase in
  temperature
• Most thermistors have nonlinear curve when
  plotted over a wide range but can assume
  linearity if within a limited range

100
BJT Bipolar Junction Transistor
IC

• Transistor invented in 1947 by Bardeen,
  Brattain and Schockley of Bell Labs.

B Base C Collector E Emitter IE I B
I C
101
BJT Bipolar Junction Transistor

• Transistor rely on the free travel of electrons
  through crystalline solids called semiconductors.
  Transistors usually are configured as an
  amplifier or a switch.

102
Solid State PN Temperature Transducers

• Solid State PN Junction Diode the base emitter
  voltage of a transistor is proportional to
  temperature. For a differential pair the output
  voltage is

K Boltzmans Constant 1.38 x10-23J/K T
Temperature in Kelvin IC1 Collector current of
BJT 1 mA IC2 Collector current of BJT 2 mA q
Coulombs charge 1.6 x10 -19 coulombs/electron
103
Example of temperature transducer

• Find the output voltage of a temperature
  transducer in the previous slide if IC1 2 mA
  IC2 1 mA and the temperature is 37 oC

104
Homework

• Read Chapter 7
• Chapter 6 Problems 1, 3 to 6, 9
• Problem 1 resistivity 1.7 10-8?m
• Problem 4 sensitivity 50 µV/(VmmHg)
• Problem 4 1 torr 1 mmHg
• Problem 6 sensitivity 50 µV/(Vg)

105
Review

• What are two types of sensors?
• List 5 categories of error
• How do we quantify sensors?
• What is an electrode?
• How do you calculate Rs and C2 of a
  microelectrode that is metal with and without
  glass coating?
• What is a transducer?
• What is a Wheatstone Bridge? How do you derive
  the output voltage
• Find resistance of a metallic bar for a given
  length and area
• How does resistance change in tension and in
  compression and how do you calculate resistance

106
Review

• How do you find resistance change in
  piezoresistive device
• How do you determine gauge factor
• What is the definition of a strain gauge and what
  is difference between bonded and unbonded strain
  gauge.
• Determine the output potential given a
  transducers sensitivity.
• What are inductance, capacitance, and temperature
  transducers?
• How do you calculate the temperature for a solid
  state PN Junction Diode?