Instrumentation and bioimpedance - Forsiden
Transcript of Instrumentation and bioimpedance - Forsiden
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