We will be using SI units for this model: meters, volts, siemens, ohms, amperes, farads, seconds. Significant issues are:
Conductivity values from Table 7.3, Bioelectromagnetism,
Malmivuo & Plonsey, http://butler.cc.tut.fi/~malmivuo/bem/bembook/
Table 7.3.
Resistivity values for various tissues
Tissue |
r[Wm] |
Remarks |
Reference |
|
|||
Brain Skeletal muscle Liver Fat |
2.2 |
gray matter Hct = 45 longitudinal longitudinal |
Rush and Driscoll, 1969 Epstein and Foster, 1982 Rush, Abildskov, and McFee, 1963 |
|
Model Volume Conductivity Summary
Tissue |
Conductivity (SI units: S / m) |
Connective Tissue |
|
Endothelium |
.6 |
Perineurium |
.01 |
Intravascular (blood) |
.6 |
Endoneurium |
.333 |
Cell membrane |
28 e-9 |
Axoplasm |
.909 |
Myelin |
28 e-9 |
Epineurium |
.1 |
From Danny:
there are 400 um between each electrode, so a 10 x 10 is a 4mm x 4mm.
since we are using a slant array, depth will vary. the long electrodes
are
1.5mm long, the short electrodes are .5 mm.
we're (i asked dusty) not entirely sure about thickness, but it's probably
about 20 or 30 um, tops.
chris, the waveforms are really pretty simple. the stimuli are
biphasic
pulses, negative first, with a width of 100 µs per phase with a 50 µs
interphase interval. current amplitude varies from 5-50 µA. i
stimulate at
15 Hz.
The square wave is 100 us negative, then 50
us of interphase (maybe i'm not using that word correctly?), then 100 us of
positive phase. this is repeated at 15 Hz, so 16.7 ms later it goes through
this cycle again.
The following values were culled from [Malmivuo], Table
21.1, page 366:
Table 21.1: Electrical properties of myelinated nerve fibers |
||
Parameter |
Value |
Rescaled Value |
axoplasm resistivity |
0.11 kohm * cm |
.909 Siemens / meter |
extracellular resistivity |
0.3 kohm * cm |
.333 Siemens / meter |
nodal membrane capacitance/unit area |
2.0 micro F / cm^2 |
|
nodal membrane conductance/unit area |
0.4 mS / cm ^2 |
4 S / m^2 |
nodal gap width |
0.5 micrometer |
|
ratio of internode spacing to fiber diameter |
100 |
|
ratio of axon diameter (internal myelin) to fiber diameter |
0.7 |
|
nodal membrane resistance |
29.9 Mohm |
|
nodal membrane capacitance |
2.2 pF |
|
internodal resistance |
14.3 Mohm |
|
The following are culled from [Ranck]:
The following are culled from [Nicholson]:
Cell membrane thickness is about 7nm. One online reference is here.
Table 22-2 from Kandel: Afferent fiber groups in peripheral nerve
|
Muscle Nerve |
Cutaneous Nerve |
Fiber Diameter (microns) |
Conduction Velocity (m/s) |
Myelinated |
|
|
|
|
Large |
I |
A alpha |
12-20 |
72-120 |
Medium |
II |
A beta |
6-12 |
36-72 |
Small |
III |
A delta |
1-6 |
4-36 |
Unmyelinated |
IV |
C |
.2-1.5 |
.4-2.0 |
Table 36-1 from Kandel: Classification of Sensory Fibers from Muscle
Type |
Receptor |
Axon (microns) |
Sensitive to |
Ia |
Primary spindle endings |
12-20 myelinated |
Muscle length and rate of change of length |
Ib |
Golgi tendon organs |
12-20 myelinated |
Muscle tension |
II |
Secondary spindle endings |
6-12 myelinated |
Muscle length (little rate sensitivity) |
II |
Nonspindle endings |
6-12 myelinated |
Deep pressure |
III |
Free nerve endings |
2-6 myelinated |
Pain, chemical stimuli and temp |
IV |
Free nerve endings |
.5-2 unmyelinated |
Pain, chemical stimuli and temp |
Tasaki found the resistance and capacitance of the myelin sheath to be 290Mohms*mm and 1.6 microF/mm respectively in isolated frog nerve fiber.
Values from Danny, threshold current values for first
detectable response (using step function for 100us, negative initial polarity,
and 50us gap):
|
||||
Date |
Minimum Stimulus to evoke measurable muscle contraction (uA) |
Maximum stimulus needed to elicit response (uA) |
Minimum stimulus of electrode used in experiment |
Maximum stimulus of electrode used in experiment |
2-2-2 |
5 |
83 |
9 |
9 |
2-14-2 |
9 |
98 |
12 |
26 |
3-4-2 |
4 |
88 |
4 |
9 |
3-11-2 |
7 |
88 |
7 |
17 |
3-19-2 |
7 |
90 |
2 |
15 |
4-19-2 |
5 |
83 |
|
|
4-23-2 |
6 |
92 |
7 |
10 |
6-4-2 |
chronic implant |
|
|
|
6-25-2 |
4 |
58 |
4 |
15 |
7-10-2 |
9 |
63 |
6 |
19 |
Malmivuo J, Plonsey R, Bioelectromagnetism, Oxford University
Press, New York: 1995.
Available online at: http://butler.cc.tut.fi/~malmivuo/bem/bembook/
Ranck JB, Extracellular Stimulation, Electrophysiological Techniques, Nov. 1-2, 1979, Society for Neuroscience, Atlanta GA.
Nicholson C, Generation and Analysis of Extracellular Field Potentials, Electrophysiological Techniques, Nov. 1-2, 1979, Society for Neuroscience, Atlanta GA.
Foster KR, Schwan HP, Dielectric Properties of Tissues and Biological Materials: A Critical Review, Critical Reviews in Biomedical Engineering, Vol 17, Issue 1, 1989, pp:25-104.
Kandel ER, Schwartz JH, Jessell TM, Principles of Neural Science, 4th edition, McGraw-Hill, New York: 2000.
Tasaki I, New measurements of the capacity and the resistance of the myelin sheath and the nodel membrane of the isolated frog nerve fiber, Amer J Physiol, vol. 181, p.639, 1955.