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: Insertion Error Application Error
Characteristic Error
Dynamic Error
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 Δy/ Δx;
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. Input
Output
Input
Output
Which is more sensitive? The left side one because you’ll 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
Ideal Curve
Sensitivity Error
Output
Input

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 σ
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 Xo Xi

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
Input
Output
Ideal
Measure
Din(Max)
Full Scale Input

21. Hysteresis
Hysteresis = measurement of how sensor changes with input parameter based on direction of change

22. Hysteresis Output = F(x) P Input = x B Q
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.
Input = x
Output = F(x) B F1 F2 P Q

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
Tolerance Band
Ton
Tresponse
100%
70%
Rising Response Time
Time
F(t)

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
Tolerance Band
Ton
Tresponse
100%
70%
Rising Response Time
Time
F(t)

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 sensor’s 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
F(x) = mx + K
F(x)* = ax + bx2+cx K
Input X
Output
F(x) K
F(x)* = ax + bx3+cx K

27. Dynamic Linearity
Asymmetric = F(x) != |F(-x)| where F(x)* is asymmetric around linear curve F(x) then
F(x) = ax + bx2+cx 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 + cx 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.
Frequency (w) radians per second Av
Av = Vo/Vi
1.0

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. Av
Av = Vo/Vi
1.0
0.707 FL FH
Frequency (w) radians per second

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 -> electrons + metal ions
Reduction Reaction : Electrons + metal ions -> Metal

40. Electrolytic Solution
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).
Metal A
Metal B
Vae
Vbe
Electrolytic Solution

41. Electrolytic Solution
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)
Metal A
Vae
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. Electronic Conduction Vo
Cellular
Potentials
Rsb
Rsa + -
R1a
R1b
C1a
C1b Rc
Resistance Rt Vd
Veb
Vea
Ionic Conduction
Electronic Conduction
Electrode B
Electrode A Vo
Mass
Tissue
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:
Electrode Surface
Binding Spot
Pin-Tip
Connector
Shielded Wire

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
Adhesive does not stick for a long time on sweaty skin
Can not put electrode on bony prominences
Movement or motion artifact significant problem with long term monitoring results in a gross change in potential
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 -> typically tiny exposed metallic contact at end of catheter usually threaded through patient’s 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
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 (Ώ)
P = Resistivity of the infinite solution outside electrode = 70 Ώcm 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 (Ώ)
P = Resistivity of the infintie solution outside electrode) = 3.7 Ώcm 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 + Eo - + + - - Es A R1 R3 R1 R3 EC Eo Es EC R2 R4 R4ED + + 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 = 1.2KΏ R2 = 3 K Ώ R3 = 2.2 K Ώ; and R4 = 5 K Ώ; 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 = 1.2KΏ R2 = 3 K Ώ R3 = 2.2 K Ώ; and R4 = 5 K Ώ; find Eo

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 = 2KΏ; R2 = 1K Ώ; R3 = 10K Ώ; R4 = 5K Ώ

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.
Rest Condition
L = length
L - DL = length
Compression

69. Strain Gauges
Tension = increase in length by DL and a decrease in cross section area.
L = length
Rest Condition
Tension
L + DL = length

70. Resistance of a metallic bar is given in length and area
where
R = Resistance units = ohms (Ώ)
ρ = resistivity constant unique to type of material used in bar units = ohm meter (Ώm)
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 10-8Ώm

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; ΔL = change in L; ρ = resistivity
A = Area; ΔA = change in A

73. Resistance in compression = Resistance decreases in compression
L = length; ΔL = change in L; ρ = resistivity
A = Area; ΔA = change in A
Note: Textbook forgot the ρ 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 1.5Ώ.
A force is applied to the wire that increases the length by 10 mm and decreases cross sectional area by mm2
Find the change in resistance h.
Note: ρ = resistivity = 5 x 10-7 Ώm

75. Example of Piezoresistivity

76. Example of Piezoresistivity
Note: Change in Resistance will be approximately linear for small changes in L as long as ΔL<<L.
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
ΔR = change in resistance ohms (Ώ)
R = unstrained resistance ohms (Ώ)
ΔL = change in length meters (m)
L = unstrained length meters (m)

79. Gauge Factor
Where ε 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 Ώ.
When a force is applied in tension the resistance changes by 2Ώ 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
R1 = SG1
R3 = SG3 + 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 Ώ, the change of resistance is 10 Ώ and the source voltage is 10 V +

88. Strain Gauge Example Derivation: Circuit Es + - + - A R1 = R +hEo 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/V*unit 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 φ = μV/V*g (another ex φ = μV/V*mmHg)

91. Transducer Sensitivity
To calculate Output Potential use the following equations:
where
Eo = output potential in Volts (V)
E = excitation voltage
φ = sensitivity μV/V*g
F = applied force in grams (g)

92. Transducer Sensitivity
Example: Transducer has a sensitivity of 10 μV/V*g, 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: Core Diaphragm AC Excitation External Load Axis of Motion L2 L1

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 TransistorIC
VCB
VCE
VBE + - IB IE
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
VCB
VEE-
VBE + -
VCC+
ccs1
ccs2
Ic1
Ic2
DVBE
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 = Boltzman’s 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 = Coulomb’s charge = 1.6 x 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 * 10-8Ώm
Problem 4: sensitivity = 50 μV/(V*mmHg)
Problem 4: 1 torr = 1 mmHg
Problem 6: sensitivity = 50 μV/(V*g)

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 transducer’s sensitivity.
What are inductance, capacitance, and temperature transducers?
How do you calculate the temperature for a solid state PN Junction Diode?