APPENDICES

APPENDIX A

VALUES OF CONSTANTS

SYMBOL NAME VALUE UNIT -12 €o Permittivity of free space 8.85 x 10 farad/meter (F/m) -6 JL o Permeability of free space 1.26 x 10 henry/meter (Him)

e Elementary charge 1.60 F< 10-19 coulomb (C) -24 JL B Bohr magneton 9.27 x 10 joule/tesla (J/T) -15 ~o Flux quantum 2.07 x 10 weber (W) -34 h Planck constant 6.63 x 10 . joule' second (J's) 8 c Speed of light in vacuum 3.00 x 10 meter/sec (m/s) -23 kB Boltzmann constant 1.38 x 10 joule/kelvin (J/K) -8 0 Stefan-Boltzmann constant 5.67 x 10 watt(m2 'K' (w/m 'K')

1\ 23 1 NA Avogadro number 6.02 x 10 mole- (mole -1 )

633 634 APPENDICES

R Universal gas constant * 8.31 joule/mole'kelvin (J/mole'K)

* The word "mole" means a gram-mole in both cgs and SI units. The definition has not been changed to kilogram-mole. Thus one mole of a substance comprised of molecules is an amount whose mass in grams is numerically equal to its molecular weight, or if comprised of atoms its atomic weight.

APPENDIX B

CONVERSION BETWEEN CG5 AND SI UNITS Many scientists who deal with magnetic quantities and measure- ments still use the so-called unrationalized electromagnetic units in the centimeter-gram-second system ("cgs" or "cgs-emu" system). Therefore a conversion table is given here. This in no way consti- tutes a recommendation for the use of these units. Multiply the value in cgs units by the number in the fourth column to obtain the value in 51 units.

SYMBOL QUANTITY CGS UNIT FACTOR SI UNIT

B flux dens.tty gauss 10-4 tesla (G) (T) -3 H field strength oersted 411 Ie 10 ampere/meter (oe ) (Ajm) -8 ~ flux maxwell 10 weber 2 (G'em ) (W or T'm ) 3 X susceptibility emu/em 411 dimensionless -3 3 Xp mass emu/g 411 x 10 m /kg susceptibilty

-6 3 Xm molar .,. emu/mole 411 x 10 m /mole susceptibility

* One mole of a substance comprised of molecules is an amount whose mass in grams is numerically equal to its molecular weight, or if comprised of atoms its atomic weight. APPENDICES 635

APPENDIX C

CALCULATION OF INDUCTANCE

P. Carelli, I. Modena, G.L. Romani

Istituto di Elettronica dello Stato Solido - C.N.R. Rome, Italy

S.J. Williamson

New York University New York, New York, U.S.A.

Most biomagnetic research is now done with commercial SQUIDs, and the only component of the field-sensing system that the experi- menter is free to design is the detection coil of the flux trans- former. As explained in Chapter 5, the geometry and size of the coil should be chosen to maximize sensitivity for the biomagnetic source of interest while minimizing sensitivity for interfering "noise" sources. In relatively quiet environments, the intrinsic noi.se of the SQUID or SQUID electronics limits the sensitivity of the field-mesuring system, in which case greater sensitivity is achieved by increasing the radius of the pickup coil and number of turns of wire to increase the total magnetic flux of the signal within it. However as the size of the coil increases there is a corresponding degredation in the lateral resolution, which may be- come intolerable if a field pattern having fine detail is to be measured. Consequently a compromise must be made between sensitivi- ty and spatial resolution. Some analysis to help with this choice has been provided by Williamson and Kaufman (1981b) and by Romani et al. (1982e).

An additional consideration when designing a coil for maximum sensitivity is the desire to transfer the greatest possible signal energy from the detection coil to the input coil of the the SQUID. To accomplish this, the detection coil's inductance Ld should match the input coil's inductance L .. The match need not De done very l. precisely because a small mis-match (up to ~20') has a comparative- ly small effect (see Eq. 5.3.2). Thus when designing a detection coil for a particular application, it is necessary to calculate its inductance. This appendix shows how to do that ..

C.l.

The first example of a d.etection coil is a simple pickup coil 636 APPENDICES of one turn of wire (a "magnetometer"). We recall from Section 2.6.2 that the inductance L of a coil specifies the magnetic flux ~ within it when a current I flows in the wire, as given by ~ .. LI. For a single-turn coil of radius "a" and wire radius "c" the induc- tance is

-7 L (C.1 ) o 47TxlO a[ Ln( sa/c) - 1. 75] This gives L in the SI unit of the henry (H) when "a" and "c" are o expressed in meters; and "Ln" indicates the natural logarithm (to the base e = 2.171S ... ), which can be found in standard tables. To illustrate the use of this formula, we take typical values of a = 2 em and b .. 0.1 mm and obtain Lo .. 0.141 ~H. The value of inductance is insensitive to the wire radius "b" since the radius enters log- arithmically in the formula. For instance, if "c" is doubled to the size c .. 0.2 mm, L decreases by only 13'. o For a given coil diameter, the total signal flux increases with increasing number of turns N of wire. However the total in- ductance should not appreciably exBeed that of the SQUID'S input coil. If turns of the same radius are wound close to one another, the total inductance increases by more than a factor of N expected if the individual self inductances were simply to add. TRis is be- cause of the mutual inductance between the various pairs of turns: the flux within a given turn is enhanced by a factor of N owing to the contribution of the other turns. Therefore the total ~nductance L of the closely-wound coil is proportional to N 2: c p L .. N 2 L (C.2 ) cpo

Accordingly, if the coil of the preceding example is wound with N P .. 3 turns its inductance becomes L a 1.27 ~H. P It should be noted that winding turns close to one another is not the most advantageous way to increase the inductance of a pick- up coil. If instead a separation is allowed between adjacent turns, the mutual inductance is reduced and therefore more turns can be added while still respecting the condition for inductance matching to the SQUID. The additional turns are an advantage because they increase the total signal flux within the coil. We let "s" denote the separation distance (between wire centers) and for convenience introduce as a parameter the "reduced" separation distance x s/2a, where "a" is the coil's radius. The mutual inductance between two coaxial, single-turn coils of equal radii varies with "x" as shown in Fig. C.l. By conSidering the mutual inductances between all pairs of turns for a multiple-turn coil, it is found that the total inductance L can be expressed as p

L N 2-a L (C.3 ) P p 0 APPENDICES 637

IU5+-______~------_+------~~------~

-6 10 E "- I

0 "- ~ Qj u c 0 t; :> -7 "0 E 10 (5 :> "S ~ "0 Q) u :> "0 n:Q)

10- 8

169+-~------~------~------_+------~--~ 10-3 10- 1 10 Reduced separation, x Fig. <':.1. Reduced mutual inductance (mutual inductance divided by the coil radius "a") versus reduced separation distance x = s/2a between two coaxial, single-turn coils of equal radius.

For a coil whose turns are closely spaced, a = 0, and so the formu- la reduces to that in Eq. C.2; for a coil with turns far apart, a = I, and the total inductance is just the sum of the individual self inductances of the turns. A general expression for a is

N -2 P 2 - !n{2 + L 2[N -n] K[(n+I)X]}/!n(Np ) (C.4 ) n=O p 638 APPENDICES

The function K(x) is the coupling coefficient of mutual inductance between two turns of reduced separation "x" (Grover 1962), which is approximately

K(X) = - 0.08 - 0.139 Ln(x) (C.s)

This expression is valid for values of x that range between 10- 3 and 2X10- 2 , covering the range appropriate for most coils used for biomagnetic measurements.

As an example of using Eqs. C.3 - C.S we consider the three- turn coil of radius a = 2 cm discusssed earlier, but now we allow a separation s = 1 mm between the adjacent turns. Thus only two terms appear in the sum of Eq. C.4, and we have x - 0.025. Adding terms gives a(3, 0.025) = 0.23. With this calculated a, Eq. C.3 then gives an inductance of 0.99 #H. This is a substantial reduction from the close-wound value of 1.27 ~H. The decrease of inductance by separating turns allows the addition of one more turn without appreciably exceeding the inductance.of the closely-wound case, as- sumed to match the input coil of the SQUID. A four-turn coil of s = 1 mm and a = 2 cm has a = 0.31 and a total inductance of 1.29 ~H. This is virtually the same inductance as for the three-turn closely wound coil. The extra turn permitted by separating turns thus en- hances the coil's sensitivity by 33\ over that of the closely wound geometry.

calculations of this sort can be carried out to optimize coil size and number of turns once the general desired features of a pickup coil have been selected. However, increasing the separation by more than a millimeter or so may be undesirable, because it shifts the geometrical center of the coil further from the source to the measured, with a corresponding decrease in the detected flux.

C. 2 • GRADIOMETERS

We turn now to consider the inductance of detection coils hav- ing gradiometer geometries such as the first-order configuration in Fig. C.2a and second-order configuration in Fig. C.2b. The baseline "b" between adjacent coils is assumed to be long in comparison with the overall separation between the end turns of an individual coil. Then the inductance L of an individual coil labeled "n" can be calculated as explained ~ve, and the only new feature to be taken into account is the mutual inductance M between one turn of coil "m" and one turn of coil "n". For the s~etrical first-order gra- diometer the total inductance is

(C.6 ) APPENDICES 639

Fig. C.2. (a) symmetric first-order grad10meter and (b) second- order gradiometer illustrating the notation for coil di- mens ions as well as the self inductances L and mutual inductances M ; (c) asymmetric first-ordeP gradiometer. mn

We use the convention where all values of mutual inductance are po- sitive, so that the signs of their effects are explicitly shown in the formulas. The minus sign appears in Eq. C.6 because the two coils are wound in opposite directions, so the field from one op- poses the self-generated field in the other. The factor of "2" ap- pears in front of M12 because each coil affects the flux in the other. The value of M12 can be calculated from the curve in Fig. C.l. If each coil has N turns instead of a single turn, this for- p mula becomes

(C.7 )

where the factor N 2 represents the product of the number of turns in each coil to acc8unt for the enhanced flux that one coil pro- duces in the other. Thus for a gradiolReter of b = 5 em baseline consisting of two coils of 2 cm radius, each of which has four turns spaced by 1 mm, the total inductance is -6 -9 (2 x 1.29x10 ) - (2 x 6.8x10 ) -6 2.571(10 B

Because of the relatively large baseline in this example the mutual inductance has only a meager effect on the total inductance.

A similar procedure can be used for a second-oraer gradiometer (Fig. C.2b). The total inductance of the configuration having one turn for each of the end coils and two for the center coil is 640 APPENDICES

Ld - 2Ll + L2 - 4Ml2 + 2Ml3 (C.S) If instead the end coils each have N turns, the generalization of this would have Ml2 and Ml3 each multiBlied by Np 2 • In the preceding illustrations we assumed that the overall coil lengths were much shorter than the baseline "b". If on the other hand the lengths of the coils are not negligible, the appro- priate formulas are invalid and the actual mutual inductances between all pairs of turns must be calculated. Fig. C.I can be used for this, or if greater precision is desired, the tables given in the next section.

C.2.1. Tables for Coils of Unequal Radii

It is common to design gradiometers with an asymmetric geome- try to improve the transfer of flux from the pickup coil to input coil of the SQUID. Then the calculation of the mutual inductance between turns of differing radii may be necessary. We consider two one-turn coils of radii a. and a , separated by the distance "s" as illustrated in Fig. C.2c. 1The mu~ual inductance, as shown by Grover (1946), depends on the two parameters P - a~/a2 and ~ - s/a2 and is proportional to the coils' linear size. Tfie mutual inductance M (in henrys) can be written as 12

(C.9)

Here again, the coil radius a2 must be expressed in meters. The parameter "f" is to be obta1ned from an appropriate table corres- ponding to the value of the variable K2 defined by

(1 p)2 + ~2 2 K (C.10) (1 + p)2 + ~2

Thus, once the values 20f P and ~ are calculated for a given set of coils, the value of K can be calculated from Eq. C.IO and the cor- responding value of "f" can be obtained from the appropriate table. Table C.1 is useful for most radii and separations met in biomag- netic applications. Table C.2 lists values when the coils' separa- tion is very small, and Table C.3 when very large. For obtaining approximate values, a linear interpolation between the tabulated numbers will suffice; but for more accurate values second differ- ences should also be taken into account. When entries in these tables are very small, the logarithm (to the base 10) is given. An underline indicates a negative value for the characteristic. APPENDICES 641

Table C.l. values of the parameter "f" in Eq. C. 9 for coils of differing radii. (From "Inductance Calculations," 1946, 1973, Fre- derick W. Grover, published by the Instrument Society of America under an arrangement with Dover Publications, Inc., New York. Tables used with the permission of Dover Publications, Inc.)

f f

0.010 0.021474 0.260 0.003805 .020 .017315 .270 .003649 .030 .014937 .280 .003500 .040 .013284 .290 .003359

0.050 0.012026 0.300 0.003224 .060 .011017 .310 .003095 .070 .010179 .320 .002971 .080 .009464 .330 .002853 .090 .008843 .340 .002740

0.100 0.008297 0.350 0.0026317 .110 .007810 .360 .0025276 .120 .007371 .370 .0024276 .130 .006974 .380 .0023315 .140 .006611 .390 .0022391

0.150 0.006278 0.400 0.0021502 .160 .005970 .410 .0020646 .170 .005685 .420 .0019821 .180 .005420 .~30 .0019026 .190 .005173 .440 .0018259

0.200 0.004941 0.450 0.0017519 .210 .004723 .460 .0016805 .220 .004518 .470 .0016116 .230 .004325 .480 .0015451 .240 .004142 .490 .0014808 0.250 0.003969 0.500 0.C014186 642 APPENDICES

Table C.l. ( Continued)

k 2 f k 2 f

0.500 0.0014186 0.750 0.0003805 .510 .0013585 .760 .0003545 ;520 .0013004 .770 .0003295 .530 .0012443 .780 .0003054 .540 .0011900 .790 .0002823

0.550 0.0011374 0.800 0.00025998 .560 .0010865 .810 .00023859 .570 .0010373 .820 .00021806 .580 .0009897 .830 .00019840 .590 .0009436 .840 .00017959

0.600 0.0008990 0.850 0.00016162 .610 .0008558 .860 .00014450 .620 .0008141 .870 .00012821 .630 .0007736 .880 .00011276 .640 .0007345 .890 .00009815

0.650 0.0006966 0.900 0.00008438 .660 .0006600 .910 .00007146 .670 .0006246 .920 .00005940 .680 .0005903 .930 .00004824 .690 .0005571 .940 .00003798

0.700 0.0005251 0.950 0.00002866 .710 .0004941 .960 .00002035 .720 .0004642 .970 .00001312 .730 .0004353 .980 .00000708 .740 .0004074 .990 .00000249 0.750 0.0003805 1.000 0 APPENDICES 643

Table C.2. Values of the parameter "f" for coils very close to- 2 gether: K "1. (From "Inductance calculations," 1946, 1973, Fre- derick W. Grover, published by the Instument Society of America under an arrangement with Dover Publications, Inc., New York. Tables used with permission of Dover Publications, Inc.)

f

6.0 0.079093 4.5 ~.042938 6.1 .077647 4.6 .041494 6.2 .076200 4.7 .040051 6.3 .074753 4.8 .038608 6.4 .073306 4.9 .037167

6.5 0.071860 3.0 0.035727 6.6 .070413 3.1 .034288 6.7 .068966 3.2 .032851 6.8 .067520 3.3 .031416 6.9 .066073 3.4 .029984

5.0 0.064626 3.5 0.028554 5.1 .063180 3.6 .027128 5.2 .061733 3.7 .025707 5.3 .060287 3.8 .024291 5.4 .058840 3.9 .022881

5.5 0.057394 2.0 0.021478 5.6 .055947 2.1 .020084 5.7 .054500 2.2 .018700 5.8 .053055 2.3 .017329 5.9 .051609 2.4 .015972

4.0 0.050163 2.5 0.014632 4.1 .048717 2.6 .013311 4.2 .047272 2.7 .012013 4.3 .045827 2.8 .010742 4.4 .044382 2.9 .009502 4.5 .042938 1.0 .008297 644 APPENDICES

Table C.3. Values of the parameter "f" for coils very far apart: 1(2 (1. (From "Inductance calculations," 1946, 1973, Frederick W. Grover, published by the Instrument Society of America under an ar- rangement with Dover Publications, Inc., New York. Tables used with the permission of Dover Publications, Inc.)

2 2 10g10( I( ) 10g1O(£) 10g10( I( ) 10g10(f)

4.0 9.39227 3.5 7.64327 '4.1 9.54228 3.6 7.79354 4.2 9.69229 3.7 7.94388 4.3 9.85230 3.8 6.09430 4.4 9.99232 3.9 6.24484

!.5 8.14234 2.0 6.39551 4.6 !.29237 2.1 6.54636 4.7 8.44240 2.2 6.69744 4.8 8.59244 2.3 6.84879 4.9 8.74250 2.4 5.00051

3.0 8.89257 2.5 5.15268 3.1 7.04265 2.6 5.30542 3.2 7.19276 2.7 5.45891 3.3 7.34289 2.8 5.61334 3.4 7.49306 2.9 5.76899 3.5 7.64327 1.0 5.92622 REFERENCES

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Dr. Pasquale Carelli Istituto di Elettronica dello stato Solido, C.N.R. Via Cineto Romano 42 00156 Rome, Italy (L)

Dr. David Cohen Francis Bitter National Magnet Laboratory M.I.T. 170 Albany Street Cambridge, MA, 02139, U.S.A. (L)

Dr. sergio Erne Physikalische-Technische Bundesanstalt-IB Abbestrasse 2-12 1 Berlin 10, west Germany (L)

Prof. David E. Farrell Physics Department Case western Reserve University Cleveland, OH, 44106, U.S.A. (L)

Dr. Riccardo Fenici Biomagnetic Unit, 1st Patologia Medica Facolta' di Medicina e Chirurgia Universita' Cattolica del Sacro Cuore 00168 Rome, Italy (L )

Dr. Pirkko-Liisa Kalliomaki Institute of occupational Health Haartmanink 1 SF-00290 Helsinki. 29, Finland (L) Dr. Veikko Kariniemi Department of Obstetrics and Gynocology Helsinki UniverSity Central Hospital Haartmanink 2 00290 Helsinki 29, Finland (L)

Prof. Toivo E. Katila Department of Technical Physics Helsinki University of Technology 02150 Espoo 15, Finland (L) 687 688 LECTURERS AND DIRECTORS

Prof. Lloyd Kaufman Department of Psychology New York University 6 washington Place New York, NY, 10003, U.S.A. (D)

Prof. .Joseph L. Kirschvink Division of Geological and Planetary Sciences California Institute of Technology pasadena, CA, 91125, U.S.A. (L)

Dr. Hans Lehmann Physikalische-Technische BUndesanstalt IB Abbestrasse 2-12 1 Berlin 10, west Germany (L)

Prof. Peter Lennie center for Visual Science University of Rochester Rochester, NY, 14627, U.S.A. (L)

Prof. Ivo Modena Istituto di Elettronica dello Stato Solido, C.N.R. Via Cineto Romano 42 00156 Rome, Italy (D)

Prof. Yoshio Okada Department of Psychology New York University 6 washington Place New York, NY, 10003, U.S.A. (L)

Dr. Gian-Luca Romani Istituto di Elettronica dello Stato Solido, C.N.R. Via Cineto ~.ano 42 00156 Rome, Italy (D)

Prof. Bruno Taccardi Istituto di Fisiologia Generale Via Gramsci, 14 43100 parma, Italy (L)

Dr. John H. Tripp Physics Department Case Western Reserve University Cleveland, OH, 44106, U.S.A. (L)

Dr. John P. Wikswo, Jr. Department of Physics and Astronomy Vanderbilt University Box 1807, Station B Nashville, TN, 37235, U.S.A. (L)

Prof·. Samuel J. Williamson Department of Physics New York University 4 Washington Place New York, NY, 10003, U.S.A. (D) LECTURERS AND DIRECTORS 689

Dr. James E. Zimmerman Cryoelectronic Metrology Group Division 724 National Bureau of standards Boulder, CO, 80303, U.S.A. (L) INDEX

Accommodation, 144, 151 Action potential (continued) Action current, 173, 187, 196, response of cel1s (continued) 205 slow, 212, 214 dipole model, 106, 175-176 in , 156 Action field, 173-207 threshold, 149 of isolated axon, 196-197 Adaptive filter, 624 origin, 174-182 Alpha rhythm, 473-475 pattern, 176 Aluminum of Purkinge fiber resistivity, 571 in vitro, 205 skin depth, 571 in vivo, 275-279, 295-298 susceptibility, 29 recording instrumentation, Alveoli, 535-537 187-201 macrophages, 542-543 of sciatic nerve, 192 Ampere, Andre' strength estimate, 176-178 law, 19, 21, 107 Action potential, 149-150 unit of current, 21, 27 and cable model, 176-182 Amplitude response, of filter, in cardiac conduction 580, 582 system, 159, 202, 212- Analog-to-digital conversion, 216 599-600 current densities, 179, 196, Antiferromagnetism, 33, 509 156, 205 Arrhythmia, 219-222, 230 and current dipole source, magnetic studies, 292, 294, 175-176 298 and dynamic range, 364-365 Asbestos miners, electrical model, 154-156 lung contamination, 560 extracellular potential, 155 Atrioventricular node, 157, equivalent current dipole 163, 214-215 source, 106, 175-176 response to stimulation, monophasic, 228-229 232-233 in myocardial fibers, 158, Attenuation 160-161 of field, 118 in nerve fibers, 154-156 by eddy currents, 118, 570- in pacemaker fibers, 159 572 refractory period, 144, 150 by feedback, 576 response of cells by magnetic shielding, 572- fast, 212-213 576

691 692 INDEX

Attenuation (continued) Biomagnetic field (continued) of electrical signal brain (continued) by analog filter, 580-587 spontaneous activity by digital filter, 614-624 (continued) 469-482 Audition breast, 334 sound localization, 388-389 eye, 341-351 Auditory evoked field, 433-442 heart, 8-9, 237-298 hemispheric asymmetry, 436- perinatal, 299-307 438 isolated tissue, 173-207 pattern, 433-436 limbs, 333-334 tonotopic representation, liver susceptibility, 483-499 438-441 lung, 545-568 Automaticity, 159, 213 scalp, 332-333 disturbances of, 220-222 skeletal muscle, 11 Avogadro number, 46 torso, 334 Axon action field, 196-197 Biomagnetism definition, vii Bacteria, magnetism of, 502, Biomineralization, 502-508 504, 512-513 Biopsy, ~ Magnetic biopsy Balancing procedure Biot-Savart law, 105 for gradiometer, 97-99 Bipolar leads, 217 Bardeen, John, 72 Black-body radiation, 51 Barlow, H.B., 371, 375 Boltzmann, Ludwig, 45 specific nerve energies, Boltzmann's constant, 45 370-371, 390 Brain Baseline of gradiometer, 91 cortex, 356 Bee cytoarchitecture, .357-358 magnetic dance, 515 somatic area, 362 magnetic particles, 530- visual area, 360-362 531 evoked fields Bereitschaftspotential, 424, psychophysical thresholds, 460 396 Bessel filter, 582-583 hemispheric asymmetry, 363 Beta rhythm, 476 single-unit activity, 364, B field, 17, 22 378 Biogenic ferrimagnetism, 13, evoked potentials, 382-383 501-531 psychophysical thresholds, crystal morphologies, 505- 390-382 507 structural features, 355-363 detection of, 522-531 (~ also Perception) distribution among phyla, Brain activity 503 evoked responses, 399-468 functions, 512-516 spontaneous activity, 9-10, Biomagnetic field 469-482 abdomen, 329 Breast field, 334 biogenic materials, 501- Bronchioles, 535 531 Bundle branches, 157, 163 brain, 9-10, 399-482 branch block, 270-271, .290- evoked responses, 399-468 291 spontaneous activity, 9-10, in vector cardiograms, 313 INDEX 693

Butterworth filter, 582 Coil detection, for SQUID, 70, 85, Cable model 89-95 for action potential, 182-187 Helmholtz geometry, 97 for graded potential, 151-154 induction, 6, 37, 46 Cardiac field (~ also Induction coil) of conduction system Rubens geometry, 97 in vitro fiber, 204-205 Comb filter, 281, 584-587 in vivo, 275-284, 295-298 Compass, biological, 513 of fetus, 300-302 European robin, 515 of myocardium, 201-202, 241- homing pigeon, 514 245, 265-274, 287-294, honey bee, 515 298 other species, 516, 519 of neonate, 302-305 Compass, field indicator, 102 (see also Computer simulations Magnetocardiography) His-Purkinje activity, 296- Cardiac potential, 202-204 298 Ca~diac electrophysiology, 211 magnetocardiogram, 243-245 clinical aspects, 227 Conduction, cellular invasive, 228-233 of cardiac activity, 215-217 late potential, 298 decremental, 216 non-invasive, 233 disturbances of, 223 Cardiac stimulation, 230-233 of excitable cell, 143, 213 Carnot, Sadi, 61 saltatory, 156 coefficient of efficiency, 61 Conduction cells, 143, 213 Catheter techniques, 227 Conduction system of heart, Cellular excitations, 141-142 157, 216-217 Cellular fields Conductivity observation, 187-192, 196- electrical, 35 197, 201-206 anisotropic, 160, 324-325 Ceramic magnets, 34 thermal, 50 Charge dipole, 108 Contamination and current dipole, 108-109 magnetic, 521 Chebyschev filter, 582 Contingent negative variation, Chemical transmitters, 142 460 Chitons, 502, 512 Cooper, Leon, 72 Cilia, 540 Copper Clearance, of lung particles resistivity, 571 540-543 skin depth, 571 from alveoli, 540-543 Core conductor model, 151-154, isotope studies, 542 182-187 mechanisms, 541-543 Coronary artery disease from tracheobronchial tree, ST depression, 270 540 Coronary artery occlusion Closed-field neuron, 402-403 current of injury, 265 Coal miners Cortex, 356-363 lung contamination, 560, 566 structure, 357-358, 403-405 Coercive field, 512 (~ also the specific and sample treatment, 546 sensory area) spectrum, particles, 526-528 Coulomb, Charles, 21 694 INDEX

Coulomb, Charles (continued) Current quadrupole, 246 unit of charge, 21 of action potential, 177 Coupling coefficient coefficients, 249 of mutual inductance, 90 tensor, 249, 255-256 Cruciform model, 443 cylindrical conductor model, 128 Cryocoolers, 60-67 cryogenics, 43, 49 Dc fields, !!! steady fields Cryostat, 49, 54-58 Dc magnetocardiogram, 265-273 Curl, Ill, 315 Decay time, 48 Current, 17-18 RlL, 48 cellular, for graded De-gaussing, 520 potential, 399-402 Delta rhythm, 476 density Demagnetizing, 520 current dipole density, 106 alternating field, 527-529 sheet, 20 Demagnetization volume, 22 of magnetic contaminants, 271 displacement, 104 Dendrites, 357-358, 400, 404 induced, 24-26 graded potential, 400 impressed, 117 Depolarization, of injury, 161 cellular, 149, 155 primary, 123, 314, 317 late, in heart, 298 volume, 106, 117 of myocardium, 163-166 Current dipole, 104 slow phase-4, 214 and charge dipole, 108 Deposition of particles in deduced from field data, 130- lung, 537-540, 563 132, 406-408 Detection coil, 70, 85, 89-95 multiple dipoles, 132-133 gradiometers, 330-332 field pattern of, 11, 105-108 inductance, 635-638 in a half space, 130-132, for localized sensitivity, 406-408 551, 492-496 in a sphere, 406-407 magnetometer, 90-91 and magnetic dipole, 315 2-D system, 268, 330-332 of injury current, 265 for uniform sensitivity, 548 layer of myocardium, 161 Dewar, 54-58 moment, 105 Dewar, James, 54 and cellular parameters, Diamagnetism, 30, 485 407-408 Diastole, 161 multiple dipole model of Dielectric constant, 102 heart, 243-245 Digital filtering, 614-624 potential pattern, 105-108 ! posteriori, 614, 621 source strength, 119 frequency response, 617 vector potential, III impulse response, 615-617 vorticity, 119 non-recursive, 615-617 Current of injury, 161-163, windowing technique, 612- 265-266, 338 613, 619-622 measurement of, 265-272 recursive, 615, 621-624 Current multipole expansion, Dipole, !!! Current dipole and 319-321, 245-252 !!! Magnetic dipole for field., 250-252 Displacement current, 102, 116 for potential, 246-250 and ohmic current, 117 INDEX 695

Divergence, 118, 315 Electrolytic gradients,. 335 Domain, magnetic, 31, 510 magnetic fields, 335 growth, 547 Electromyogram, 425 in magnetite, 510 Electronic filtering reorientation, 547 active, 598 single, 511, 519, 527 adaptive, 624 Double layer model, 318-319 amplitude response, 580, 582 Dust, magnetic properties, 547 analog, 579-589 artifacts, 587 Eddy currents, 24-26 digital, 614-624 attenuation of field frequency response, 579, 588, in body, 118 617 in magnetic shield, 8, 519- general theory, 588-589 521, 570-572 group delay, 579, 582 for cylinder, 570 order of filter, 581, 588 shielding, 569-572 phase response, 580 shielding factor, 571 signal averaging, 592-598 skin depth, 570, 574 types of filters, 582-584 Einthoven's hypotheses, 216 Electrotonic spread, 154 triangle, 217 Endogeneous field, 460-468 Electric heart vector, 248 components, 463-465 bundle branch block, 313 pattern, 465-466 and magnetic heart vedtor, source localization, 465-468 322-323 Endogeneous potential, 460-463 Electric potential components, 460-462 of current dipole, 105, 108 source localization, 462-463 of current distribution, 112 Energy sensitivity of current element, 105 definition, 41 dependence on solid angle, for SQUID system, 70, 83 124-126, 164-165 Epilepsy of impressed current, 118 magnetic activity, 479-482 in inhomogeneous medium, 122 Equipartition theorem, 45, 47 in homogeneous medium, 119 Evoked field relationship to electric latency, 450-452 field, 105 neurogenesis, 399-408 Electrocardiography, 216, 227 primary source, 400, 404-405 for bundle branch block, and psychophysics, 396 261-262 secondary source, 405 comparison with MeG, 311-314, steady-state response, 394- 317-321 395 current dipole source, phase information, 450 257-259 transient response, 393-394 genesis, 166 (see also specific normal morphology, 167, 216 modalities) 12-lead recordings, 218 Evoked potential, 391 vector cardiogram, 256 averaging, 392 Electroencephalography neurogenesis, 399-402 spontaneous activity and psychophysics, 383, 395- and MEG, 474-475 396 pathological activity, 478-482 and Single-unit activity, 696 INDEX

Evoked potential (continued) Fluxgate magnetometer and single-unit activity ( continued) (continued), 382-383 in lung studies, 548-553, 557 steady-state response, 394- Flux-locked mode, 81-82 395 Flux quantum, 24, 41 transient response, 393-394 Flux transformer, 69, 89-90 (see also specific Flow field, 317 modalities) Follicle, 11 Excitability, 143, 149 field of, 332-333 Excitable cell Force, magnetic properties, 143-144 on current, 22, 26 electrical model, 147-156 on compass, 102-103 Excitations Forward problem, 170, 173 action potential, 149-150, multipole representations, 202-204 237 cardiac sequence, 163-166 Foundry workers graded potential, 151-154 lung contamination, 566 Eye Fourier series, 601 associated fields coefficients, 602, 606 oculogram, 343, 346-348, sampling theorem, 604-605 351 Fourier transform, 600-614 model for sources, 343-345 aliasing, 606-607 retinogram, 348-351 discrete, 605-606 structure, 341-345 power spectrum, 607-608 Frequency compensation circuit, Faraday, Michael, 24 197-200 law of induction, 24, 116 Frequency response, of filter, Fast-Fourier transform, 601, 580 609-613 aperiodic signals, 610-613 Galvanic skin potential, 327 windowing, 612-613 Gamma rhythm, 476 Ferrimagnetism, 33, 509 Gap junctions, 142, 160 Ferrite, 34 Gas constant, 46 Ferritin, 483, 48.6-487 Gastro-intestinal field, 11, Ferromagnetism, 32, 485, 509 268-269, 329 magnetically "soft", 572 Gates, in membrane, 148, 213 Fetal magnetocardiography, 299- Gauss, Karl F. 302 unit of field, 23, 634 heart rate variability, 300, Gaussian filter, 582-583 309 Geomagnetic field, 87 interval index, 308-310 Goldman equation, 146 instrumentation for, 301, Graded field, 401 305-310 Graded potential, 151, 400 Field, 17, 102 and dynamic ranqe, 364-365 !!! Magnetic field Gradient, lOS Field potential, 400-402 definition, 34 Filtering, see Electronic Gradiometer filtering first-order, 91-92 Fissure, of cortex, 356, 405 inductance, 638-640 Fluxgate magnetometer, 36-37 off-diagonal, 6 INDEX 697

Gradiometer (continued) Hippocampal formation second-order, 92-95 ( continued) SQUID-system, 7 and endogeneous activity, Grinders 465-468 lung contamination, 560 His bundle, 157, 163 Group delay, 580, 583 electrogram, 228 Grover, F.W. invasive recording, 228-230 inductance tables, 641-644 magnetocardiogram, 277-279 magnetic activity, 295-298 Hair follicle, 11 model, 296-297 field of, 332-333 non-invasive recording, Half-space model, 126, 130-132 233-235 Hall-effect magnetometer, 38 His-Purkinje field, 275-284, Hamming window, 620 295-298, 593-598 Heart Hodgkin-Huxley model, 148 anatomy, 157-158 Honey bee conduction system, 157, 216 magnetic compass, 515 displacement, 289 superparamagnetism, 530 excitation, 163-166, 318 Hysteresis loop, 32, 36 multipole expansion, 319- 321 Ideal gas law, 52 fetal rate variability, 300 Impedance, electrical, 48 instrumentation, 305-308 Impressed current, 117 field, see cardiac field Impulse response of filter, muscle, 157-162 615-616 tangential currents, 319 Indifferent electrode (~ also Myocardium) and ECG, 217 Heart studies, see Inductance, 46 Magneotcardiography calculations, 635-644 Heat conduction, 50 mutual, 90, 638-640 Heat convection, 52-53 tables, 641-644 Helium, properties, 59 unit of, 26 Helmholtz, Hermann von, 168 Induction coil, 24, 37 coils, 97 inductance calculation, 635- current decomposition, 316 638 specific nerve energies, 370- toroidal, 187, 190 371 Induction, of voltage, 24 non-uniqueness theorem, 169 Infarction of the myocardium Hematite, 546 magnetic studies, 291-293 Hemochromatosis, 483, 496-498 Inhomogeneities, in conducting Henry, Joseph, 26 bodies unit of inductance, 26, 46 cylindrical, 128 Hertz, Heinrich, 25 half-space, 126 unit of frequency, 25 spherical, 126-128 High-pass filter, 581 Injury current, see Current High-resolution MCG, 276-284, of injury 295-297 Input coil, 69 clinical evaluation, 295-296 Iron oxides, 5.6 instrumentation for, 279-282 Iron workers Hippocampal formation, 467 lung contamination, 560, 565 698 INDEX

Isolated active tissue Lead field theory (continued) first measurements, 10 electric lead field, 135 Intercalated disks, 143, 160 lead currents, 311-312 Intracellular action current magnetic lead field, 137 measurement of, 186 uniform field, 138 source of field, 106, 175-182 unipositional lead, 261 Inverse problem, 102, 129-133, for remanent moment studies, 173 549-553 current dipole model, 130- for susceptibility, 138-139, 132, 407-408 492-495 in electrocardiology, 168-171 Lenz, Heinrich, 24 multipole expansions, 237 law, 24 Ionic channels, 148, 213 Limb field, 333-334 Ionic concentrations Liver magnetic susceptibility resting condition, 145 and chemical biopsy, 496-498 Ionic current clinical studies, 496-498 source of steady field, 334- instrumentation, 494-496 338 methodology, 484-489 Ionic pumps, 146 Lock-in amplifier, 595 Ischemia of the heart, 161, 222 noise bandwidth, 598 magnetic studies, 291-293 Low-pass filter, 581 Isolated preparations, 189-190, digital recursive filter, 201-205 622-624 frequency response, 623 Johnson noise, 49 Lungs of toroidal coil, 192 magnetic contaminants Josephson, Brian, 42 clearance, 540-543 effects, 74 depoSition, 537-540, 559 frequency, 74 detection methods, 548-557 junction, 42 magnetic properties, 547 current bias, 75 occupational exposure, 561- parametric effect, 77 568 Joule, James, 25 total lung burden, 556-557 unit of energy, 25 respiratory system, 535-537 Joule-Thomson effect, 64 ventilation, 537 refrigerator, 64-67 Lung studies, see Magnetopneumography Kelvin, Lord, 45 unit of temperature, 45 Machinists Kepler, Johannes, 386 lung contamination, 560 projection theory, 386-387 Macrophages, 542-543 Maghemite, 502 Langevin function, 516 Magnet Latency of evoked response permanent, 524 from steady-state responses, ceramiC, 34 451-452 pulsed, 524-525 of visual evoked response, superconductivity, 517-519 450-45) Magnetic biopsy, 483-499 Lateral inhibition, 366-367 clinical studies, 496-498 Lead field theory, 133-139 instrumentation, 494-496 INDEX 699

Magnetic biopsy (continued) Magnetic measurements methodology, 484-489 ( continued) quantitative aspects, 489-492 instrumentation, torso contribution, 487-489 field detection, 35-42 Magnetic contaminants moment measurement, 517-519 detection methods, 548-557 remanent moment measurement, localized sensitivity, 551- 548-553 553, 557 susceptibility measurement, uniform sensitivity, 548- 494-496 551, 556 (~ also SQUID system) in dewars, 31, 56 sensitivity pattern, 311-312 of lungs, 547-548 (see also Lead field theory) in subjects, 267 Magnetic moment, 28, 509 Magnetic dipole, 27, 102, 112 remanent, 523 current dipole in sphere, 128 isothermal, 523, 526 field pattern, 28, 112-113 Magnetic multipole expansion, moment, 28 252-257 of ferromagnet, 509 and current multipoles, 254- scalar potential, 114 256, 320-321 sum of current quadrupoles, generators for adult MeG, 257- 254-256 259 vector potential, 113 generators for neonatal MeG, Magnetic field, 17, 102 304-305 of action potential, 176-182 quadrupole coefficients, 320- as ambient noise, 86-87 321 of earth, 86 Magnetic navigation, 513 flux density, 22-23 homing pigeon, 514 of power lines, 87 Magnetic particles, sources of, II, 103-104 magnetic characterization, current element, 104 525-531 current distribution, 110 (~ also Ferrimagnetism impressed current, 118-121 and Ferromagnetism) homogeneous medium, 119 Magnetic relaxation, 554-556 inhomogeneous medium, 121 Magnetic scalar potential, 114 magnetic materials, 27-30 of magnetic dipole, 114 and scalar potential, 114 of magnetization, 115 strength or intensity, 17, 19 Magnetic shielding, 7-8 and vector potential, III active, 576-577 Magnetic flux, 24 room, 569-578 Magnetic flux density, 17, 22 shielding factor, 572 Magnetic heart vector, 260-261 skin depth, 574 adult MeG, 263, 313 soft iron, 519-521 bundle branch block, 263, 313 "soft" materials, 8, 570-572 and electric heart vector, Magnetic susceptibility, 28 263, 322-323 in vivo studies, 10, 483-499 neonatal MeG, 304-305 mass, 29 Magnetic induction, 17, 22 molar, 29 Magnetic materials Magnetic vector potential, III "soft" materials, 572 of current dipole, Magnetic measurements III 700 INDEX

Magnetic vector potential Magnetocardiography (continued) ( continued) current of injury, 265-274 current multipole expansion, fetal, 300-302, 309-310 250-252 instrumentation for, 301 of magnetic dipole, 113 first recording, 8 Magnetic viscosity, 553-554 by SQUID, 9 Magnetically clean room, 521- fetal, 11 522 high resolution, 275-284 Magnetism His-Purkinje system, 275-279, antiferromagnetism, 509 295-298 diamagnetism, 30-31 instrumentation for, 278-282 ferrimagnetism, 33-34, 509 magnetic dipole source, 259 ferromagnetism, 31, 509 for mass screening, 286 paramagnetism, 31 morphology, 238-241 superparamagnetism, 510 neonatal, 302-305 Magnetite, 33, 545 morphology, 303 coercive field, 523 multipole generators, 304- domains, 510-512 305 magnetic tracer, 560-567 numerical predictions, 241 oxidation of, 502 perinatal, 299-310 physical properties, 508-512 quadrupole sources, 258-260 saturation magnetization, 510 simulated infarction, 244 single-domain condition, 511, standard grid, 238 519, 527 steady field, 265-274 specific remanent moment, vector cardiography, 257-261 545-546 Magnetoencephalography unblocking field, 527-530 endogeneous activity, 460- Magnetization, 28, 114 468 easy direction, 505 evoked responses, see isothermal remanent moment, specific modality 523-526 first measurements, 9 Magnetobiology, 501 spontaneous activity, 469-482 magnetic compass, 513-515 and EEG, 474-475 magnetotaxis, 512-513 instrumentation for, 470- Magnetocardiography 471 and atrial repolarizatiQn, normal activity, 471-476 279, 282, 296 pathological activity, 476- for bundle branch block, 261- 482 263, 290-291, 313 Magnetometer clinical assessment, 285-298 detection coil, 90-91 bundle branch block, 290- inductance of, 635-638 291 moment measurement, 517-519, delayed depolarization, 298 525-526 premature beats, 294 Magneto-oculogram, 343, ventricular hypertrophy, 346-348, 351 287-289 Magnetopneumography, 545-568, comparison with ECG, 311-314, instrumentation for, 548- 317-321 553 current dipole source, 257- magnetizing time, 553-554 259 relaxation, 554-556 INDEX 701

Magnetopneumography (continued) Multipo1e expansions total lung burden, 556-557 ( continued) occupational groups, 559- magnetic, 252-254 568 Muscle field and radiological findings, skeletal, 11 564-565 (see also viscosity, 553 Magnetocardiography Magnetoretinogram, 11, 348-351 and Myocardium) Magnetosome, 505 Mutual inductance Magnetostriction magnetometer, coupling coefficient, 90 38 Myocardium, 157 Magnetotaxis, 512-513 circuit model, 162 Magnetotactic bacteria, 502, excitation, 158, 160-161 503, 512-513 pattern, 314, 318, 319, 324 Maximum diastolic potential, magnetic studies 214 infarction, 291-293 Maxwell, James Clerk ischemia, 291-293 unit of flux, 634 source equation, 116 Neonatal heart rate, 307 Medium, conducting interval index, 308 effect on field, 119, 121 Neonatal magnetocardiogram, effect on potential, 118, 122 302-305 Meissner, Hans, 72 morphology, 303 effect, 72 multipole generators, 303- Membrane structure, 212-213 305 Models, of sources Nernst equation, 145 current dipole, 104 Nerve in half space 130-132, 406- specific nerve energies, 370- 408 371 in sphere, 406-407 Nerve fibers current multipoles, 246-252, action potential, 154 319-321 Neuron magnetic dipole, 27, 102, 112 morphology, 402-403 magnetic multipoles, 252-257 Newton, Isaac, 23 Modulation transfer function, unit of force, 23 448-450 Nodes of Ranvier, 142, 156 Molypermalloy core, 194 Noise, electronic Motor cortex, 361 from induction coil, 48 function, 422 and measuring bandwidth, 35- Motor field, 422-432 36, 46-49, 598 characteristics, 425-428 power line compensation, and somatotopic projection, 200-201, 584-587 431 as Signal interference, 591 source location, 428-432 Noise, magnetic Motor potential, 422-425 ambient field, 86-87 MUller, J. NyqUist, 37, 43-49, 193 specific nerve energies, 370- power lines, 87 371 compensation for, 200-201 Multipole expansions in SQUID, 70-71, 83-84 current, 254-259, 319-321 of subject, 268, 271, 282- 702 INDEX

Noise, magnetic (continued) Pial somatically evoked of subject (continued), 283, potential, 420 329 and evoked field, 420 Noise, sensory Pickup coil and sensitivity, 367-370 of detection coil, 89, 91 threshold measures, 377, inductance of, 636 380 toroidal, 187, 190 Notch filter, 583-584 circuit model, 193 pigeon Oculogram, 343, 346-348, 351 magnetic navigation, 514 oddball paradigm, 461 pigment epithelium Oersted, Hans, 1, 19 field sources, 344-345 unit for field strength, 634 Planck, Max, 40 Ohm, Georg, 34 Planck's constant, 40 law of conductance, 34 Polio patients' field, 334 unit of resistance, 26, 34 Point contact, superconducting, Ohmic current, 34, 117 75 and displacement current, 117 post-synaptic potential, 400 Onnes, Kamerlingh, 72 potential, see Electric Open-field neuron, 402-403 potential Optical magnetometer, 38 Power spectrum of Fourier transform, 607-608 pacemaker, 157 scaling factors, 613-614 Paleomagnetism, 517 Premature beats Paramagnetic amplification, 71 magnetic studies, 294 in Josephson junction, 77 Pre-motor potential, 424 Paramagnetism, 31, 484 Primary source, 123, 314, 317 Pascal, Blaise, 52 of action field, 106, 175-176 unit of pressure, 52 in myocardium, 314, 318 Perception, 385 of neuromagnetic field, 399- binocular stereopsis, 386 402 disparity detection, 387- Proprioceptive evoked field, 389 430-431 psychophysical thresholds Proprioceptive evoked and evoked fields, 396 potential, 424-425 and evoked potentials, 383 Proprioceptors, 424 size constancy, 389 Psychophysics, 375 permeability reaction times ionic, 146 and evoked fields, 396, magnetic, 27 450-452 of free space, 26 threshold measures, 375 relative, 27, 29 and evoked field, 452 of "soft" materials, 572 and evoked potential, 383, Phase response, of filter, 580 395-396, 452 Phase-sensitive detection, 595- and noise, 377 598 P300, 461-462, 464-468 noise bandwidth, 598 Pump, of parametric amplifier, Photoreceptors 71 field source, 343-344 Purkinje system, 157, 163 response to light, 364 magnetic activity, 295-298 INDEX 703

Purkinje system (continued) Retinogram (continued) model of, 296-297 magnetic, 11 Pyramidal cells, 358, 404 Retinotopic representation, 443-448 Quality factor Rhythm strip, 219 of filter, 584, 587 Right-hand rule, 20, 23, 26 of lock-in, 596 Robin Quadrupole coefficients magnetic navigation, 515 magnetic, 256, 258 Rubens coils, 97-99 current, 248-250, 254-256, 320-321 Salmon Quasi-static regime, 117 magnetic particles, 528-529 Saltatory conduction, 156 Radiation shield, 56 Sampling theorem, 604-605 Reaction time Saturation, magnetic, 33 and evoked field, 396, 450- isothermal remanent moment, 452 523-526 Readiness field, 425 Scalar potential source location, 428 electric, 105 Readiness potential, 424, 460 of current dipole, 105 Receiver operating magnetic, 114 characteristics, 380- of magnetic dipole, 114 381 of magnetization, 115 Reciprocity, 133 Scaling factors, 613-614 lead currents, 311-312 Schrieffer, John, 72 lead magnetic field, 492 Sciatic nerve for susceptibility, 138 action field, 192 Recursive filter, 615, 621-624 Secondary source, 123, 316, 317 Reentry, 223-226 cylinder, 128 functional, 226 half space, 126 micro, 224 sphere, 126-128 Refractoriness, 144, 150 Semiconductor amplifier, 194- Refrigerators, 60-67 195 Joule-Thomson, 64-67 sensitivity, magnetic stirling, 61-64 of induction coil, 37, 48-49 Rejection factor of filter, 584 of SQUID sensor, 94 Relaxation, magnetic, 554-556 Shielded room Remanent moment, 546-547 active method, 576-577 of industrial dusts, 547, 561 applications, 577-578 specific, 546 eddy-current, 569-572 Repolarization, 150, 155 magnetic, 8, 519-521, 572-576 of atria, 279, 282 Shielding early, 270-271 eddy current, 7 of myocardium, 165-166 magnetic, 7 Resistance, 34 Siemens family Resistivity, 35 unit of conductance, 35 Resonance magnetometer, 38 Signal averaging, 592-598 Respiratory system, 535-537 Signal processing, 591-624 Resting potential, 144 averaging, 592 Retinogram, 348-351 backward, 593 704 INDEX

Signal processing (continued) Spontaneous brain activity averaging (continued) ( continued) forward, 592 pathological (continued) template trigger, 594 epilepsy, 479-482 Signal-to-noise improvement, Jacksonian disease, 479 592 theta, 475 Sinus node, 157, 163, 214 SQUID detector, 7 response to stimulation, multiloop, 89 230-232 types of, 76 Skeletal muscle, II, 156-157 SQUID system, 38-42, 69-71, action potential, 156 81-84 Skin depth dc bias, 39, 79-81 and eddy currents, 570 (see also Detection coil) of magnetic materials, 574 energy sensitivity, 41 Slew rate, 83 feedback loop, 40, 81-83 Solid angle formalism, 124-126 gradiometers, 91-95 applied to heart, 164-165 input impedance, 70 Somatic evoked field, 409-421 input energy sensitivity, field pattern, 409-410 70-71, 83 latency, 410 magnetometer, 91 .lateralization, 411 moment magnetometer, 517-519, somatotopiC prOjection, 413- 525-526 419 rf bias, 39, 77-91 somatotopic representation, slew rate, 83 413-219 steady field Sound applications, 338 localization, 388-389 electrophysiological source, Source models, !!! Current 335-337 dipole, !!! Magnetic and muscle morphology, 337- dipole 338 Source strength, 119 instrumentation, 330-332 Space constant, 153 measurement Spatial discrimination, 91 eye, 346-348 Spatio-contrast sensitivity, gastrOintestinal system, 368-370 329 and visual evoked field, 448- heart, 265-274 450, 452 limbs, 333-334 Spectral density scalp, 332-333 definition, 36 torso, 334 for induction coil, 48 steel workers spherical model, 126-128 lung contamination, 560-565 Spontaneous brain activity Stefan-Boltzmann law, 51 alpha, 472-475 Stefan, Josef, 51 beta, 476 stirling, Robert, 61 delta, 476 refrigerator, 61-64 gamma, 476 ST shift, 265-274 normal activity, 471-476 primary, 265, 270 power spectrum, 472-473, secondary, 265, 268-269 475, 480-481 Subcortical activity, 460-468 pathological, 476-482 Subject noise, 268, 271, 282- INDEX 705

Subject noise (continued) Threshold measures (continued) 283 psychophysical vs. evoked abdominal, 329 field, 452 cold water reflex, 329 psychophysical vs. evoked torso diamagnetism, 488-489, potential, 383, 395- 492-496 396, 452 Sulcus, of cortex, 357, 405 receiver operating superconducting transformer, characteristics, 380- 191 381 superconductivity on single neurons, 378-383 Josephson effects, 73-74 single-unit vs. Meissner effect, 72 psychophysical, 380- quantum state, 73 382 zero resistance, 72 single-unit vs. evoked superconductor potential, 382-383 diamagnetism of, 30 Tidal volume of lung, 537 transtion temperature, 43 and particle deposition, 539- superinsulation, 56-57 540 superparamagnetism, 510 Time constant, 48 of worker bee, 530 L/R, 48, 152 susceptibility Tonotopic representation, 438- in vivo measurements 441 ---ac technique, 488-489 Torque, on compass, 102 dc technique, 487-489, 494- Transformer 497 electrical analysis, 192-194 SQUID moment magnetometer, Translocation in the lung, 567 518-520 Transmembrane conductance, 147 Synapses gates, 148, 213 chemical, 143 determination, 186 Systeme International, 18 Transmembrane current Systole, 162 of action potential, 179 theory, 186 Tabs, superconducting Transmembrane potential Tacconis oscillations, 53-54 resting, 146 Tachycardia, 221 (~ also Action potential) Tesla, Nicola, 23 Trigger, electronic unit of flux density, 23, 26 template, 594 Thalassemia, 483, 497 threshold, 595 Thermal conductivity, 50 Tumor Thermal noise, 49 associated field, 479-482 Thermal oscillations, 53 Tunnelling, 73 Thermal radiation, 46, 51 2-D system, 330-332 Theta rhythm, 475 Thomson, William, see Kelvin Unblocking field, 526-530 Threshold Unipolar leads, 217 of excitable cell, 143, 149 Unipositional lead system, 261 Threshold measures, 375-383 Units of measure, 20 and noise, 377 parallel channels, Vacuum techniques, 57 390 Vapor-cooled shield, 56 706 INDEX

Variometer, 36 Visual system, 359-362 vector cardiography, 259-261 cortex, 357-358, 360-362, electric heart vector, 248, 372-374 263, 313 lateral geniculate nucleus, magnetic heart vector, 260, 359, 371 263, 313 lateral inhibition, 366-367 vector potential, magnetic 111 parallel pathways, 371, 390 of current dipole, 111 photoreceptors of magnetic dipole, 113 noise, 368 ventilation of lungs, 537 receptive field, 365 ventricular hypertrophy, 287- response to light, 36 290 spatio-contrast sensitivity, Viscosity, magnetic, 553-554 368-370 Visual cortex Volt, unit of potential, 25 cruciform model, 443 Volta, Alesandro, 25 cytoarchitecture, 357-358 voltage clamp method, 147 various projections, 360- Volume conductor 362 effect on field, 11 functional specialization, homogeneous medium, 119 372-374 inhomogeneous medium, 121 disparity detection, 387 Volume current, 106 feature detection, 390-391 Vortex field, 317 retinotopic representation, Vorticity, 119 443-448 Visual evoked field, 444-459 watt, James, 50 compared with potential, 454, unit of power, 50 456-459 Weak link, 73 functional properties Weber, Wilhelm, 24 luminance coding, 453-455 unit of flux, 24, 26 spatio-contrast Welders sensitivity, 444-452, lung contamination, 560-565 454 welding fumes latency, 450-452 magnetic properties, 561 retinotopic representation, Wenckebach phenomenon, 232 445-448 White noise, 36 source Window function, 612-613 multiple, 445, 447 Windowing technique, 612-613, single 619-622 strength, 454-455 Wolf-Parkinson-White syndrome orientation, 455 magnetic studies, 294 Visual evoked potential compared with field, 454, 456-459