Instrumentation and bioimpedance

1

-1.00E+01

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Z'Z''

• Offset voltage• Bias current (can give a big voltage over 

the output impedance of a sensor)• Noise

2

Driven shield e.g. because of high impedance input

LP: fc = 1,6 MHz

Operational amplifier ‐ OPAMP

NC

V-

NC

V+

NC

a) b) c)

v iv o

v iv o

R2

R1v i

v o

R2R1

i

v o

R

vvKvo “Golden rules”

3

More amplifiers

v 1v o

R2

R1

R1R2

v2

v 1

v o

RfR1

v2R2

v3R3

Differential amplifier Summation amplifier

4

Light‐to‐voltage transformerPhoto sensor + transimpedance amplifier

• Photo sensor• Photo diode• Photo transistor• Photo resistor

• Albert Einstein – Photo‐electric effect – Nobel Prize 1921

5

Constant current source

6

Howland current pump

7

• Each stage shifts 90 degrees• Gives positive feedback

8

Quadratureoscillator

Digital to analog converter

• Wide range of R’s• High values of R’s• Temperature drift

Vo

RfRR

2R4

R8

VR

Vo

Rf2R

VR

2R2R2R

2RRRR

Also: One‐bit DAC

9

Analog to digital converter

vo1 kVDAC

Vu5 V

VREF

CRVIN

VINT

VINT

VREF

Tid TINT

VINT

TidTINT TDE-INT

Single slope Dual slope

Generic type

Successive approximation

ININT VT

constant

INT

INT

INTDEREFIN

TT

TVV

10

Flash ADC

• Similar to succ. approx.• All tests simultaneously• n‐bit  2n‐1 comparators• Fast but much hardware

Analogspenning

0

0001111

MSB

MSB

Dig

ital

term

omet

erko

de

Dek

oder

R

R

R

R

R

R

R

R

R

+ Vref

-Vref

X1

X2

X3

X4

X(2n-4)

X(2n-3)

X(2n-2)

X(2n-1)

11

Synchronous rectifier, square wave

-1Signal in

Reference in

Signal outR

C

Phase Sensitive Detector Low Pass Filter

Signal in

Reference in

Signal outbefore filter

0 deg. 90 deg. 60 deg.

12

Digital syncronous rectifier (lock‐in amplifier)

If the reference signal is: v tr r sin

and the input signal is: v v ti i 1 sin

the output signal will be:

v v t t

vt t

o i r

i r i r

1

1

2

sin sin

cos cos

A low pass filter will follow this multiplier module, and the right hand cosine expression may therefore be ignored. In fact the only dc signal that will appear at the low pass filter output, will be the one corresponding to i = r , which gives:

vv

o 1

2cos vi

vr

vo

13

Total suppression of noise in this system is of course only possible if the integration time is infinite, i.e. the multiplication is carried out over an infinite number of signal cycles. Gabrielli (1984) shows that the suppression of random (white) noise is given by an equivalent filter function with a bandwidth f given by

Nf

f r

where fr is the analysed frequency and N the number of cycles. Hence, in a 10 Hz measurement, the bandwidth is 0.1 Hz when integrating over 100 cycles, but only 2 Hz when integrating over only five cycles of the signal. The corresponding transfer function is given by

2

0

0

/1/sin2

N

NH

where /0 is the normalised angular frequency. The transfer function is also shown in the figure as a function of number of integration cycles.

Digital syncronous rectifier (lock‐in amplifier)

14

Relative measurements• Measure relative to a reference that is influenced in the same way by noise, aging, 

temperature, unstable power supply, etc.• A division is made between the two signals• Suitable for multiplicative errors• Differential measurement is better for additive errors

15

Wheatstone bridge• If Z1 is the sensor, it can be shown 

that:

4• Balanced bridge• Disbalanced bridge• Autobalancing bridge

16

Current loop• No voltage reduction for long transmissions (e.g. ships)• Resistive sensor with long leads: four point measurements

17

Internal (endogenous) noise

• LSB in a digital representation• Input offset voltage and bias current• Johnson noise (white noise)

– Thermal movement of electrons– Noise voltage mean‐square‐value:

• Shot noise (white noise)– Because of DC currents in semiconductors– Worse the more bias current (better in FET and CMOS)

• 1/f (flikker) noise (pink noise)– < 100 Hz

18

Frequency range for the measurements

External (exogenous) noise

• Transients in mains supply, 50 Hz, radio transmitters, electromagnets

• Additive noise: Differential measurements

19

CMRR shows how much stronger the input signal will be represented at the output compared to a common mode noise signal of the same amplitude

CMRR

20

Shielding• Shielded cable is «grounded» on the signal side• Split shields are series connected• The shield must only be grounded one place• If the sensor is encapsulated, then the shielded cable is grounded to the box• The shield must always be 0 V (except for driven shields)• Use short leads to reduce inductance

• Difficult to shield magnetic fields, especially LF fields• Must use metal with high permeability (my‐metal)

Reduce cable length, distance or use twisted pair  less flux 21

Ground plane

22

• Mainly to reduce inductance (by reducing the magnetic field)

• Gives a return path for the current directly beneaththe conductor (by correct design of ground plane)

• Lower resistance due to less skin effect

• Connects stray capacitance to ground

• Extra important below digital or HF signals

• Use separate analog and digital ground that is only connected one place (at the connection to the power supply)

Ground loops

Never use same conductor for a reference signal and power supply

23

Direct current ‐ DC

• From direct current (DC) theory we know that resistors in series: 

• If resistors are in parallel:

• The inverse value of resistance is then called conductance, which gives: 

• Equations often become simpler using conductance for circuits which predominantly are in parallel and resistance for series‐circuits. But only a practical matter !

Alternating current ‐ AC

• R = 1/G Z = 1/Y• Immittance is common for impedance or admittance

CBL

B

:Capacitor 1 :InductorjBG Y

conductance G

susc

epta

nce

B

admittance Y

phase angle

Impedance

jBG

11Y

Z 22

1BGjBG

jBGjBG

jBG

Z

2222 og BG

BXBG

GR

jXR Z

resistance R

reac

tanc

e X impedance Z

phase angle

Example using three components

111 where

121

11C

X

Xj

R

R

Z

11212

11221 2

2

2

CRCRj

CRRR

Z

1221)12(

1)12(12

1)12(2

11

12

2

2

2

2

CjRRCR

CRCRj

CRRR

Z

Y

12

1 CjR

Y

28

101 102 103 104 105 1060

50

100

150

Frekvens

|Z|

101 102 103 104 105 106-30

-25

-20

-15

-10

-5

0

Frekvens

Fase

vinke

l

101 102 103 104 105 1060

50

100

150

Frekvens

R

101 102 103 104 105 106-50

-40

-30

-20

-10

0

Frekvens

X

0 50 100 150 200

-60

-40

-20

0

20

R

X

0 0.005 0.01 0.015 0.02 0.025-2

0

2

4

6

8

x 10-3

G

B

RX

XR

atan

22

ZR1 = 50 R2 = 100 C1 = 1 µF

29

Material propertiesSimple parallel plate:

AdC

AdG

r

0 :tyPermittivi

:tyConductivi

dAR :yResistivit

Complex values

= ’ + j ’’

ρ = ρ’ + j ρ’’

= ’ + j ’’

30

In tissue• Electrode = transfer between ionic and electronic current

• Susceptance – polarization due to:

– Ions moving along cell surface (low frequency)

– Membrane as dielectric (higher frequencies)

– Water dipole orientation (GHz)

Conductance: Na+, K+, Ca++, Cl—

Susceptance: 2

A few nanometers

1 /

Dispersions

Counter-ions

Charging of cell membranes

Relaxation ofwater molecules

E.g. makromolecules

32

Important to speak the same language …

Multi‐sine, chirp, etc.

The raw data• Measured with Solartron 1260 + 

1294• Four electrodes on lower leg• Exported as text file

Bode plot of impedance

-1.00E+01

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Z'Z''

Bode plot of admittance

-2.00E-02

-1.00E-02

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

Y'Y''

2222 XRXB

XRRG

Bode plot of |Z| and 

-20

-10

0

10

20

30

40

50

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

|Z|f

Bode plot of |Y| and 

0

0.01

0.02

0.03

0.04

0.05

0.06

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06-1.50E+01

-1.00E+01

-5.00E+00

0.00E+00

5.00E+00

1.00E+01

1.50E+01

|Y|f

Wessel, Nyquist, Argand, Cole, …

-6.00E+00

-4.00E+00

-2.00E+00

0.00E+00

2.00E+00

4.00E+00

1.5E+01 2.0E+01 2.5E+01 3.0E+01 3.5E+01 4.0E+01 4.5E+01

Impedance

-1.00E-02

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

2.0E-02 2.5E-02 3.0E-02 3.5E-02 4.0E-02 4.5E-02 5.0E-02 5.5E-02

AdmittanceCPE

Fish and meat

• Measured on haddock muscle with surface electrodes

0

10

20

30

0 20 40 60 80 100 120 140 160

R (

-jX (

130 min.195 min.245 min.305 min.

0

10

20

30

0 20 40 60 80 100 120 140 160

R (

-jX (

305 min.425 min.490 min.550 min.610 min.790 min.

Two‐electrode system

sinIm Reactance

cosRe Resistance

Impedance

iv

ivX

iv

ivR

ivZ

sinIm eSusceptanc

cosRe eConductanc

1 Admittance

vi

viB

vi

viG

ZviY

sin1sin90 ifonly 1 and

cos1cos0 ifonly 1

BX

GR

Four‐electrode system

Transfer impedance

i v i v

• Input: i ,   output: v ,   transfer function: 

• This is transfer impedance, not impedance

• Cannot use for calculation of ,  or 

• Except for homogenous, uniform material

A B

Ziv

Four electrodes – be aware:

• Measures transfer impedance

• Current shunt paths through the pick‐up electrodes ( over‐estimation of Z)

• Multiple current paths (often  false positive phase angle)

• Common mode problems

• What happens if the frequency dependence is not the same?

Sensitivity field calculations

• Simple and very powerful tool, but not used very much

• Example: Direct current resistance measurement with a four‐electrode system on a homogeneous medium

Sensitivity field calculations #1

Imagine that you inject a current I between the two current electrodes, and compute the current density J1 in each small volume element in the material as a result of this current

Sensitivity field calculations #2

Imagine that you instead inject the same current between the voltage pick-up electrodes, and again compute the resulting current density J2 in each small volume element.

Sensitivity field calculations #3

• The sensitivity S and total measured resistance R are then (reciprocal system): 

• Positive S: Increased resistivity in this area  higher total measured resistance• Negative S: Increased resistivity in this area  lower total measured resistance• High absolute value of S: Very sensitive to changes in resistivity

dvI

RI

SV

2

212

21 and JJJJ

Four‐electrode system

Closer look …

If you multiply the sensitivity with the resistivity in each small volume element, you get “a” resistance, 

but is it:‐ the “resistance” of that volume element, or …‐ the volume element’s contribution to the measured resistance ?

Adding a low‐conducting slice

A slice with only 20% of the conductivity of the surrounding medium is added

Volume impedance density

The plot now shows the sensitivity divided by the conductivity (same as multiplying with the resistivity, since this is DC).

Electrodes further apart

Larger electrodes

Closer look …

Two electrodes on the sides

Closer look …

Increased electrode separation

Closer look …

Two‐electrode system

Closer look …

Simple four‐electrode FEM modelComsol Multiphysics  ‐ 2D, DC conductive media

Voltage sensingelectrodes

Cur

rent

inje

ctin

g el

ectro

de

Cur

rent

inje

ctin

g el

ectro

de

Object

Sensitivity field – no object

• Sensitivity is the dot product of the current density vector lead fields from the two pair of electrodes

• Can be positive and negative• Shows that the system is reciprocal

Sensitivity field – metal object

Measured resistance is increased by 7.3 %

Sensitivity field – insulating object

Measured resistance is reduced by 7.0 %

Two popular skin surface ECG electrode designs

EEA(cm2)

EA(cm2)

gel:

metal:insulator:

Fig. 8.10

Wet gel or solid gel (hydrogel)?

Monopolar skin impedance spectrum as a function of gel penetration.

No significant influence from electrode polarization impedance.

100 101 102 103 104 105 106102

103

104

105

106

Frequency (Hz)

|Z|

020219d.z60020219k.z60020219y.z60

100 101 102 103 104 105 106-90

-65

-40

-15

Frequency (Hz)

thet

a

Gel penetration

1. Onset2. 1 hour3. 4 hours