Biomedical Instrumentation

Chapter 6 in Introduction to Biomedical

Equipment Technology

By Joseph Carr and John Brown

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.

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

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

Sensor Error Sources Error:

• Difference between measured value and true value.

5 Categories of Errors:1. Insertion Error2. Application Error3. Characteristic Error4. Dynamic Error5. Environmental Error

Insertion Error: • Error occurring when inserting a

sensor

Application Error:• Errors caused by Operator

Characteristic Error:• Errors inherent to Device

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.

Environmental Error:• Errors caused by environment

• heat, humidity

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.

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

Sensor Terminology

Sensitivity Error = Departure from ideal slope of a characteristic curve

Ideal Curve

Sensitivity Error

Output

Input

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.

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

Accuracy

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

XoXi

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

Zero offset errorOffset Error

Input Input

Output Output

Linearity

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

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

Hysteresis Hysteresis = measurement of how sensor

changes with input parameter based on direction of change

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.

Input = x

Output = F(x)

B

F1

F2P

Q

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

Tresponse100%70% Rising Response Time

Time

F(t)

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

Tresponse100%70% Rising Response Time

Time

F(t)

Response Time

Decaying Response Time

Toff

TdecayF(t)

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

Dynamic LinearityMeasure 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) = m

x + K

F(x)* = ax + bx2+cx4+ . . . +K

Input X

OutputF(x)

KF(x) =

mx + K

F(x)* = ax + bx3+cx5+ . . . +K

Input X

OutputF(x)

K

Dynamic Linearity Asymmetric = F(x) != |F(-x)| where F(x)* is asymmetric around linear curve F(x) then

F(x) = ax + bx2+cx4+ . . . +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

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

Frequency () radians per second

Av Av = Vo/Vi1.0

Frequency Response of Ideal and Practical System

Frequency Response of Ideal and Practical System

Av Av = Vo/Vi1.00.707

FL FHFrequency () radians per second

In practice, you have attenuation of lower and higher frequencies

FL and FH are known as the –3 dB points in voltage systems.

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

Examples of Filters

Electrodes for Biophysical Sensing

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

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

Electrodes for Biophysical Sensing

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

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.

Bioelectrodes

3 Types of electrodes:

• Surface (in vivo) outside body

• Indwelling Macroelectrodes (in vivo)

• Microelectrodes (in vitro) inside body

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

Electrodes in Solution

Have metallic electrode immersed in electrolytic solution once metal probe is in electrolytic solution it:

1. Discharges metallic ions into solution

2. Some ions in solution combine with metallic electrodes

3. Charge gradient builds creating a potential difference or you have an electrode potential or ½ cell potential

Electrodes in Solution

A++

B+++

2 cells A and B, A has 2 positive ions And B has 3 positive ions thus have aPotential difference of 3 –2 = 1 where Bis more positive than A

Electrodes

Two reactions take place at electrode/electrolyte interface:• Oxidizing Reaction: Metal -> electrons +

metal ions

• Reduction Reaction : Electrons + metal ions -> Metal

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 BVae Vbe

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 Metal BVae Vbe

Electrolytic Solution

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)

R= 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

CellularPotentials

Rsb

Rsa

R1a

R1b

C1a

C1b

RcCellularResistance

R Vd

Veb

Vea

Ionic Conduction Electronic Conduction

Electrode B

Electrode A

VoMassTissue

Resistance

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

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

Medical Surface Electrodes Typical Medical Surface Electrode: Use conductive gel to reduce impedance between electrode

and skin Schematic:

Electrode Surface

Binding SpotPin-Tip Connector Shielded Wire

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)

Problems with Surface Electrodes1. 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)

Potential Solutions for Surface Electrodes Problems

1. Additional Tape2. Rough surface electrode that digs past scaly

outer layer of skin typically not comfortable for patients.

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

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

Microelectrode

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

• Saline.

Microelectrode

Two typical types:1. Metallic Contact2. Fluid Filled

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

V1Vo

C2C1

R1

RS

Calculation for Resistance Rs

Rs in metallic microelectrodes without glass coating:

r

PRs

4

K

cm

cmRs

4111

10501434

704

.

*..

where Rs = resistance ohms (Ώ)

P = Resistivity of the infinite solution outside electrode = 70 Ώcm for physiological saliner = tip radius ( ~0.5 um for 1 um electrode) = 0.5 x10-4 cm

Calculation for Resistance Rs Rs of glass coated metallic microelectrode is

1-2 order of magnitude higher:

rP

Rs2

M

cm

cmRs

513180

1431010143

7324

.

.*..

.

where Rs = resistance ohms (Ώ)P = Resistivity of the infintie solution outside electrode) = 3.7 Ώcm for 3 M KClr = tip radius typically 0.1 u m = 0.1 x 10-4 cm = taper angle (~ / 180)

Capacitance of Microelectrode

Capacitance of C2 has units pF/cm

rRe

Cln

.5502

Where e = dielectric constant which for glass = 4R = outside tip radius r = inside tip radius

Capacitance of Microelectrode

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

cm

pF

mm

rRe

C 7.7

15.02.0

ln

)4)(55.0(

ln

55.02

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

Wheatstone Bridge

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.

Es

R1

R2 R4

R3

ECED

+-

A

B

EoEo

R1R3

R2 R4

ECED

Es

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

VVE

VE

RR

R

RR

REsE

o

o

o

24027

5

24

312

1051022

105

1031021

10312

43

4

21

2

33

3

33

3

...

**.

*

**.

*

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

43

4

21

2

RR

REsE

RR

REsE

EEE

D

C

DCo

VVE

VE

RR

R

RR

REsE

o

o

o

24027

5

24

312

1051022

105

1031021

10312

43

4

21

2

33

3

33

3

...

**.

*

**.

*

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

Null Condition of Wheatstone Bridge

When R1 = 2KΏ; R2 = 1K Ώ; R3 = 10K Ώ; R4 = 5K Ώ

25

10

1

24

3

2

1

1*43*2

2*41*44*23*2

21443243

4

21

2

K

K

K

KR

R

R

R

RRRR

RRRRRRRR

RRRRRRRR

R

RR

R

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

Strain Gauges

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

Strain Gauges

Compression = decrease in length by L and an increase in cross sectional area.

Rest ConditionL = length

L - L = length Compression

Strain Gauges Tension = increase in length by L and a

decrease in cross section area.

Rest ConditionL = length

TensionL + L = length

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 )

A

pLR

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

0085.0

10001

5.0

10001

25010*7.1 2

2

8

mmm

mm

mmm

mmm

A

LR

Piezoresistivity Piezoresistivity = change in resistance for a

given change in size and shape denoted as h

Resistance in tension =

Resistance increases in tensionL = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

AA

LLhR

Resistance in compression =

Resistance decreases in compressionL = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

AA

LLhR

Note: Textbook forgot the ρ in equations 6-28 and 6-29 on page 110

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 0.0027 mm2 Find the change in resistance h.

• Note: ρ = resistivity = 5 x 10-7 Ώm

Example of Piezoresistivity

24.1

74.25.1

10001

*)0027.001.0(

10001

*)1030(10*5 2

2

7

h

h

mmm

mm

mmm

mmmhR

AA

LLhR

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.

Gauge Factor

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

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)

LLR

RGF

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.

LL

RR

GF

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:

71.3

2007.0

1502

mmmm

LLR

RGF

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.

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

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

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

Comparison of Bonded vs. Unbonded Strain Gauges

1. Unbonded strain gauge can be built where its linear over a wide range of applied force but they are delicate

2. Bonded strain gauge are linear over a smaller range but are more rugged

• Bonded strain gauges are typically used because designers prefer ruggedness.

Typical Configurations

R2 = SG2R4 = SG4

R3 = SG3

C+-

A

B

Vo

R1 = SG1

DES

Electrical Circuit Mechanical Configuration

4 strain gauges (SG) in Wheatstone Bridge:

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

+

Strain Gauge Example

R2 = R - h R4 = R +h

R3= R-h

C+-

A

B

Eo

R1 = R +h

D

VVEo

R

hEs

R

hEs

R

hR

R

hREsEo

hRhR

hR

hRhR

hREsEo

RR

R

RR

REsEo

5.0200

1010

2

2

22

43

4

21

2

Circuit Derivation:

s

Note: Text book has wrongly stated that tension decreases R and compression increases R on page 112

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

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)

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)

FEEo **

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

VgVVg

VEFEo 750155

10

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:

LVDT:

Diaphragm

Cor

e

External Load

L2

L3

L1

Axis of Motion

AC Excitation

Capacitance Transducers

Quartz Pressure Sensors: capacitively based where sensor is made of fused quartz

Capacitive Transducers: Capacitance C varies with stimulus

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

Temperature Transducers

3 Common Types:• Thermocouples

• Thermistors

• Solid State PN Junctions

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)

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

BJT = Bipolar Junction Transistor

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

C

VCB

VCE

VBE

B = Base C = CollectorE = EmitterIE = I B + I C

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.”

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:

q

II

KT

V C

C

BE

2

1ln

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 x10 -19 coulombs/electron

VCB

VEE-

VBE

VCB

VCC+

VBE

ccs1 ccs2

Ic1 Ic2

VBE

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

VVCoulombs

mAmA

KKJV

q

II

KT

V

BE

BE

C

C

BE

0185.010*6.1

12

ln27337/10*38.1

ln

19

23

2

1

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)

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

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?