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1
Introduction to Biomedical Engineering
Kung-Bin Sung
Device/Instrumentation I – bioelectric phenomena
2
Outline
• Chapter 11: bioelectric phenomena– Origin of potential across cell membrane– Quantitative derivation and calculation of
resting membrane potential– Action potential
• Measuring biopotential– ECG– EMG, EEG, etc.
3
Origin of membrane potential
• Cell membrane– permeable to some but not all ions– Consists of a lipid bilayer and has capacitive
properties• Different concentrations of ions inside
and outside of the cell membrane– Ion channels– Active ion pumps
4
What ions are there?
Cytoplasm ExtracelluarIon (mM) fluid (mM)
K+ 400 20Na+ 50 440Cl– 52 560
Data obtained from squid giant axon
Note:There are also negatively charged proteins inside cell membrane
5
Driving forces of ion movement• Diffusion – particles move from high-
concentration to low-concentration
• Drift – flow of charged particles due to electric fields
dxKdDdiffusionJK][)(
+
−=
dxdvKZdriftJ K ][)( +−= µ
D: diffusivity constant (m2/s)
µ: mobility (m2/sV)Z: ionic valence = +1 for K+
v: voltage across membrane
Electric field
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Resting potential – one ion
0)()( =+ diffusionJdriftJ KK
0][][ =−−+
+
dxKd
qkT
dxdvKZ µµ
qkTD µ
=
Now consider K+ only, and in the case of steady state
k: Boltzmann’s constantT: absolute temperatureq: charge of electron
][][
+
+
−=KKd
qkTdv
i
ooiK K
KqkTvvE
][][ln +
+
=−= Nernst equation
= 26mV at room temperatureNernst potential
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Resting potential – two ions
o
iCl
i
oK Cl
ClqkTE
KK
qkTE
][][ln
][][ln −
−
+
+
===
Suppose membrane is permeable to K+ and Cl-, and in the case of steady state
o
i
i
o
ClCl
KK
][][
][][
−
−
+
+
=
Space charge neutrality: the number of cations in a given volume (both inside and outside of the membrane) is equal to the number of anions
Donnan equilibrium
Example 3.1: determine steady-state concentrations using the Donnan equilibrium and space charge neutrality
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Example 3.1
1000][][
500][][
=+
=+−−
++
oi
oi
ClCl
KK
oo
ii
ClK
ClK
][][
][500][−+
−+
=
=+
o
i
i
o
ClCl
KK
][][
][][
−
−
+
+
=
mVEClClKK Koioi 18333][667][333][167][ ===== −−++
Inside cell :[KCl] = 100 mM[RCl] = 500 mM
Outside cell :[KCl] = 400 mM
Initial condition:
Donnan equilibriumSpace charge neutrality
Steady-state concentrations
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Goldman equation
⎟⎟⎠
⎞⎜⎜⎝
⎛++++
= +−+
+−+
iNaoCliK
oNaiCloKm NaPClPKP
NaPClPKPqkTV
][][][][][][ln
Concentrations of ions of squid giant axonThe resting potential is -60 mV
PK is the permeability of K+
δK
KDP = δ is the thickness of the membrane
Each ion’s contribution to the membrane potential depends on its relative permeability
Goldman equation
10
Resting potential and ion pumps• Resting potential must be maintained at a
relatively stable level• Na+ ions tend to move into the cell due to
electric field (resulting from resting potential) and diffusion along the concentration gradient
• K+ ions tend to move out of the cell• Active Na-K pump prevents change in
concentration and hence maintains the resting potential (3 Na+ out and 2 K+ in)
• Concentration of other ions (Cl-) is determined by the resting potential
11
Ion channelsChannels: - Made of trans-membrane proteins- Water-filled passages allow ions and very small molecules (water and urea) to pass through the cell membrane
Open channel: depends on size and charge
Gated channel: Usually closed; the opening of such channels is controlled chemically, electrically, or mechanically
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Na-K Ion pumpActive transport protein (pump) moves molecules against their concentration gradient ⇒ needs energy (provided by ATP)
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Origin of action potential• Neuron’s ability to conduct “signal”• Voltage-gated Na+ channels open once the
membrane potential is raised (stimulated) to certain threshold
• Further increase in membrane potential is achieved by an influx of Na+ (positive feed back)
• The membrane is “depolarized”• Opening of voltage-gated K+ channels lowers
the membrane potential (back to resting potential)
• Propagation of the action potential
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Action potential (cont.)Nernst potential of Na+
Nernst potential of K+
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Action potential – experimental resultsVoltage clamp experiments by Hodgkin and Huxley in 1952- Apply a fixed voltage (above threshold) across the membrane of a squid giant axon- There are only two types of voltage-time-dependent permeable channels (Na+ and K+) in a squid giant axon- Study the time-dependent characteristics of these channels
Sodium and Potassium currents due to a −20mV voltage clamp
into cell
out of cell
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Action potential (cont.)What happens if voltage clamp is turned off immediately after the membrane potential reaches the threshold? (similar to natural activation of neurons)
- Na+ channels close quickly and K+ channels remain open and then close slowly- Net current becomes outward (due to K+)- Membrane potential decreases to Nernst potential of K+
(the membrane is now hyperpolarized)- Na+ channels cannot be reopened until the membrane has been hyperpolarized ⇒ refractory period- The Na-K pump restore the membrane potential to its resting level and “recycle” the ions involved in the action potential
17
Action potential (cont.)
Depolarization propagates in one direction – refractory period prevents the back-propagation of the action potential
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Action potential of muscle cells
- Muscle cells are also excitable- Similar mechanism involving ion channels-Depolarization results in contraction of the muscle
Action potential of neuron
Action potential of muscle fiber
Force of muscle contraction
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Action potential (cont.)
Different excitable cells (note the difference in time-scale)
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Refractory periods in cardiac muscle
Refractory period: determines how fast the cell can be excited repeatedly
Skeletal muscle
Cardiac muscle
Repeated stimulationAction potential (red) and muscle contraction (blue)
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Pacemaker (autorhythmic) tissueSpontaneous action potential without input from the nervous system
Some “leaking” channels allow Na+ and K+ to pass the membrane at negative membrane potentialSince flow of Na+ > K+, the net effect is an increase in membrane potential
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Electrocardiogram (ECG)
PQRST pattern
Period = 1/heart rate
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ECG
• Measure the electrical activity of the heart (myocardium)
• Non-invasive – potential measured on body surface
• Human body can be considered as a conductor (ions in cells and body fluids)
• Measured potential is the total effect
24
From action potential to ECG
VA-C
VC-B
Conceptually, action potential propagates and measurements from different locations can tell you the direction of propagation
25
From action potential to ECG
VA-B
Differential potential between A and B
26
ECG measures integrated signal from the heart
Representative electric activity from various regions of the heart
27
ECG measures direction and relative magnitude of action potential
Cardiac vector of the QRS complex using Einthoven’s triangle
The direction of the mean vector at any time can be obtained from signals of two of the three leads
28
Example ECG pre-amplifier
Differential signal between two arms, with right-leg feed back to reduce common-mode interference (more on circuits later)
29
More ECG measurements
3 leads (left arm, right arm, and left leg), using right leg as commonChest leads
V1-V6
30
Electrode: ion-metal interface
C
C
C
C+
C+
C+A–
A–
e–
e–
e–
Electrolyte (human body)Electrode (metal)
Coupling of biopotential to electronic circuit
C C+ + e− A− A + e−
31
Electrode for ECGElectrolyte soaked foam provides good electrical contact with the skin, and reduces motion artifacts
Ag-AgCl electrode: Ag base coated with a thin layer of AgCl
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Electrode: half-cell potential
Results in a DC offset in measured signal; can be removed by high pass filtering
33
ECG circuitBlock diagram
High pass filter
Low pass filter
pre-amp
V+
V-
amp A/D converter
Signal ground
Block DC component
Cut-off 100~200Hz
Isolation
More on instrumentation later
Rg
Total gain >1000
34
Electromyogram (EMG)
Electrodes for EMG- Non-invasive, disk electrodes (similar to ECG)- Percutaneous needle electrodes for direct recording of electrical signals from nerves and muscle fibers
Bipolar Unipolar
35
Electroencephalogram (EEG)
Non-invasive electrode: cup electrodes- Made of platinum or tin- 5-10mm in diameter- Filled with conducting electrolyte gel- Attached to the scalp
Invasive electrode: subdermal needle electrodes- Made of platinum or stainless-steel- 10mm long and 0.5mm wide- Inserted under the skin to provide better electrical contact
36
Electroencephalogram (EEG)Example of EEG signals
8-13 Hz
14-30 Hz
4-7 Hz
<3.5 Hz
Frequency of EEG signal increases with higher degrees of cerebral activity.During period of metal activity, the signal becomes asynchronous and measured magnitude decreases
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Microelectrodes
Tip formed by drawing, diameter 0.1-10µm
Tip formed by etching, diameter a few microns
Micromachined silicon substrate with openings
38
References
• Medical Instrumentation: Application and Design, edited by John G. Webster
• Human Physiology: an Integrated Approach (2nd edition), by D.U. Silverthorn