Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

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Three important special cases are worthy of attention, which are most

clearly illustrated in the coordinate system determined by the eigen-

vectors e

. First, for k

¼ k

we have a axially symmetric bipolar dis-

tribution, with density function

ð yj kÞ¼

F ðk Þ

exp k cos



sin y; for k  0 ; (Eq. 12)

(see (Eq. 19) of Statistical methods for paleomagnetic vector

analysis .) The angle y is defined by the directional datum

x and

the principal axis determined by the eigenvector with the largest

eigenvalue e

cos y ¼

x  e

; (Eq. 13)

normalization is given by

F ð kÞ¼

i¼ 0

Gð i þ

: (Eq. 14)

Second, for k

< k

¼ 0 the distribution is a axially symmetric gir-

dle, with density function (Dimroth 1962; Watson 1965)

ð yj kÞ¼

F ð kÞ

exp k cos



sin y ; for k  0 (Eq. 15)

The angle y is defined by the directional datum

x and the principal axis

determined by the eigenvector with the smallest eigenvalue e

cos y ¼

x  e

: (Eq. 16)

These two special cases of the more general Bingham distribution are

useful for describing the dispersion (Eq. 12) of bipolar data about

some mean pole, and the dispersion (Eq. 15) of bipol ar data

about some mean plane. And, finally, the third symmetric distribution

is uniform, obtained for k

¼ k

¼ 0. In spherical coordinates this

is just

ð yj kÞ¼ sin y; for k ¼ 0 : (Eq. 17)

The uniform distribution has no preferred direction and so y can be

measured from an arbitrary axis. Of course, if we now allow k to be

positive or negative (or zero), then the full range of axially symmetric

density functions is available (Mardia, 1972, p. 234):

1; 3

ðy jk Þ¼

F ðk Þ

exp k cos



sin y; for 1 k 1:

(Eq. 18)

The off-axis angle y is then defined by the axis of symmetry of the dis-

tribution. Symmetric density functions, ranging from bipolar to girdle,

obtained for a variety of values of k , are illustrated in Figure B11.

Maximum -likelihoo d estima tion

In fitting a Bingham distribution to paleomagnetic directional data a

convenient method is that of maximum-likelihood; for a general

review see Stuart et al. (1999). With this formalism, the likelihood

function is constructed from the joint probability-density function for

the existing data set. Using the general form of the Bingham density

function (Eq. 8) the likelihood for N data is just

L ðk

; k

; e

Þ¼

j ¼1

pb I

; D

j k

; k

; e



: (Eq. 19)

Maximizing L is accomplished numerically (Press et al ., 1992), an

exercise yielding a pair of eigenvectors e

and e

and their correspond-

ing concentration parameters k

and k

. The third eigenvector e

determined by orthogonality and its concentration parameter by

convention (Eq. 7) is zero. Some investigators (e.g., Onstott, 1980;

Tanaka, 1999) prefer a two-step estimation method, where the

eigenvectors are determined by principal component analysis, but

these vectors are identical to those found by maximizing (Eq. 19).

In any case, obtaining the eigenvalues of the data set through prin-

cipal component analysis is still required for establishing confidence

limits.

Confi dence limi ts

It is unfortunate that the relatio nship between the concentration para-

meters k

, determined (usually) by maximum likelihood, and the

eigenvalues of the covariance matrix l

, determined (usually) by prin-

cipal component analysis, is very complicated. This fact makes the

establishment of confidence limits on the eigenvectors difficult. How-

ever, Bingham (1974 , p. 1220) has discovered an approximate formula

for the confidence limit valid under certain circumstances. The confi-

dence ellipse, within which a specified percentage (%) of estimated

eigenvectors e

can be expected to be realized from a statistically

identical data set, is given by the elliptical axes

2N D



1=2

; (Eq. 20)

for

¼ðk

 k

Þðl

 l

Þ1 ; and N !1; (Eq. 21)

Figure B11 Examples of the axially symmetric Bingham

probability density function p

1; 3

ð y Þ, (Eq. 18) for a variety of k

concentration parameters: 0; 1; 4; 16. Note that as jkj is

increased the dispersion decreases.

46 BINGHAM STATISTICS

and where w

is the usual chi-squared value for two degrees of

freedom. Alternative methods have been proposed for establishing

confidence limits, most notably the bootstrap method popularized

within paleomagnetism by Tauxe (1998).

Using the mixed-polarities directional from Hawaii covering the

past 5 Ma (see Principal component analysis), in Table B1 we sum-

marize the statistical parameters, and in Figure B12 we show the

95% confidence limit a

about the eigenvector defining the mean

bipolar direction (e

). Note that the confidence limit is much smaller

than the variance of the data.

Jeffrey J. Love

Bibliography

Abramowitz, M., and Stegun, I.A., 1965. Handbook of Mathematical

Functions. New York: Dover.

Bingham, C., 1964. Distributions on the sphere and on the projective

plane, PhD Dissertation, Yale University, New Haven, CT.

Bingham, C., 1974. An antipodally symmetric distribution on the

sphere. Annals of Statistics, 2 : 1201 –1225.

Collins, R., and Weiss, R., 1990. Vanishing point calculation as a sta-

tistical inference on the unit sphere. International Conference on

Computer Vision, December, pp. 400–403.

Dimroth, E., 1962. Untersuchungen zum Mechanismus von Blastesis

und syntexis in Phylliten und Hornfelsen des südwestlichen Fich-

telgebirges I. Die statistische Auswertung einfacher Gürteldia-

gramme. Tscherm. Min. Petr. Mitt., 8: 248–274.

Mardia, K.V., 1972. Statistics of Directional Data. New York: Aca-

demic Press.

Onstott, T.C., 1980. Application of the Bingham distribution function

in paleomagnetic studies. Journal of Geophysical Research, 85:

1500–1510.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P.,

1992. Numerical Recipes. Cambridge: Cambridge University

Press.

Stuart, A., Ord, K., and Arnold, S., 1999. Kendall’s advanced theory of

statistics, Classical Inference and the Linear Model. Volume 2A,

London: Arnold.

Tanaka, H., 1999. Circular asymmetry of the paleomagnetic directions

observed at low latitude volcanic sites. Earth, Planets, and Space,

51: 1279–1286.

Tauxe, L., 1998. Paleomagnetic Principles and Practice. Dordrecht:

Kluwer Academic.

Watson, G.S., 1965. Equatorial distributions on a sphere. Biometrika,

52: 193–201.

Cross-references

Fisher Statistics

Principal Component Analysis in Paleomagnetism

Statistical Methods for Paleo Vector Analysis

Table B1 Principal component and maximum likelihood analysis of the Hawaiian paleomagnetic directional data recording a mixture of

normal and reverse polarities over the past 5 Ma

Eigenvalue

Eigen direction

Bingham κ

Confidence axes

I(o) D(o) a

0.0304 14.6 87.6 9.8749 >1 0.0765

0.0601 58.9 48.4 9.3490 >1 0.0801

0.9088 31.1 1.5 0.0000 0.0765 0.0801

Figure B12 Equal-area projection of Hawaiian directional data,

defined in (a) geographic coordinates and (b) eigen coordinates.

Also shown are the projections of the variance minor ellipse,

defined by l

and l

, and, inside of that, the a

confidence

ellipse. As is conventional, the azimuthal coordinate is

declination (clockwise positive, 0



to 360



), and the radial

coordinate is inclination (from 90



in the center to 0



on the

circular edge).

BINGHAM STATISTICS 47

BIOMAGNETISM

Biomagnetism has emerged from a somewhat checkered earlier his-

tory. Indeed it has the dubious honor through Dr. Mesmer of contribut-

ing the verb mesmerize to the language and to have been the butt of

Da Ponte and Mozart’s humor in Così fan Tutte. However, it has sur-

vived to become a mature science covering a wide range of areas

including animal navigation and orientation, possible harmful effects

of magnetic fields, and searches for mechanisms explaining these phe-

nomena are underway. In addition, electromagnetic instrumentation

plays a major role in medicine and synthetic magnetic particles have

been used to measure viscosity in cells and to transport chemicals

within the human body, Here we discuss biological sensitivity to mag-

netic fields, the biogenic synthesis of magnetite, and its possible role

in neurodegenerative diseases in humans. We leave the major areas

of electromagnetically based medical instrumentation techniques, such

as magnetocardiagrams, magnetoencephalograms, and the uses of

nanoparticles of magnetite for other reviews.

Sensitivity to magnetic fields

The most readily demonstrated sensitivity to magnetic fields is that of

magnetotactic bacteria. Several discussions of the phenomena are

given in “Magnetite Biomineralization and Magnetoreception in

Organisms” by Kirschvink et al. (1985), which provides an excellent

source for work in this research area up to that time. As is well known,

the bacteria are flagellum driven and the presence of a linear chain of

magnetite particles results in their motion being constrained to move

along, but not across magnetic lines of force. However, the sense of

motion with respect to the field is more complicated than originally

recognized and can in some cases change during the course of the

day. The simple chain enables the bacterium to navigate between oxy-

genated and anoxic conditions at different depths in the water column

as it swims.

Use of the geomagnetic field as a navigational cue

A wide variety of animals have been shown to sense the geomagnetic

field and to use it as a navigational cue, e.g., salmon (Quin, 1980) hon-

eybees (Gould et al. 1978), robins (Wiltschkow and Wiltschkow,

1972), homing pigeons (Walcott, 1977, 1978, 1996), field mice

(Mather and Baker, 1981) and it has been suggested that human beings

can also sense the geomagnetic field (Baker, 1980). There is no longer

any doubt that certain animals can sense the magnetic field and indeed

detect small changes in that field (e.g., Walker and Bitterman, 1989).

The homing pigeons appear to use the gradient of the field (Walker,

1998, 1999), although this work remains controversial. The geomag-

netic field intensity is of the order of tens of microteslas and typical

gradients are a few nanoteslas per kilometer. To detect the necessary

changes in the field to establish the gradients over distances of kilo-

meters would therefore require sensitivity to field differences of the

order of nanoteslas. Yet, pigeons appear to be able to do this (Windsor,

1975; Walker, 1998). It has long been thought that a magnetite-based

sensory receptor makes this possible.

The nature of the magnetic sense organ has proved elusive, but an

example of a magnetite based sensor has been exquisitely demon-

strated in the rainbow trout by Walker et al. (1997). Behavioral studies

established that the animal could discriminate between the presence

and the absence of a field comparable to the geomagnetic field. In-

tracellular magnetite was discovered in its nose. Magnetic force

microscopy observations of the magnetite were consistent with the mag-

netic behavior of single domain magnetite particles (Diebel et al., 2000).

Finally, neural signal responses to field changes were recorded in nerves

from this region. Other detailed demonstrations of magneto-reception

are likely to emerge as various animals, known to be capable of sensing

the field, are examined by similar techniques. Indeed demonstrations of

changes in firing rates in response to small magnetic field variations

have been reported for some time (Figure B13) (for example, see Semm

and Beason, 1990; Schiff, 1991). Magnetite in the bee abdomen has

been implicated in the orientation of honeybees during their “dance”

with a sensitivity to local magnetic field variations many times smaller

than the geomagnetic field (Kirschvink et al., 1997).

Having established that certain animals can sense the geomagnetic

field, the next question is “how is the sensing used in navigation?”

One of the most extensively investigated topics is avian navigation,

which has recently been reviewed (Wiltschkow and Wiltschkow,

2003). Here we restrict the discussion to the pigeon (for which some

of the most convincing evidence of a magnetic compass is available),

although as noted above, the topic remains controversial (e.g., Walcott,

1977, 1978, 1996; Walker, 1998, 1999; Walraff, 1999; Reilly, 2002).

Kramer’s map and compass model (e.g., Kramer, 1961) is the starting

point of most interpretations. In such magnetic navigational systems

the two necessary requirements are: (1) some means whereby the ani-

mal can locate itself in relation to its loft and (2) some form of com-

pass whereby it can set and maintain a course for its target. These

require sensing of the magnetic field and of relatively small changes

in the field, as we noted above.

How exactly the ability to sense the field is used to provide a map or

compass, remains obscure and may well differ from species to species.

A particularly important clue has emerged in the case of the homing

pigeon from studies of the direction flown immediately after release

(Windsor, 1975; Walker, 1998). This is illustrated in Figure B14,in

which we see that initial departure directions are symmetrical about the

local field gradient, which is indicated by the heavy solid NW/SE line.

If birds are released close to this line, the errors are small, but they

increase as release sites depart from it. Moreover, if the birds are released

to the SW of the gradient line, the starting direction errs to the SW, and

conversely if they are released from the site to the NE they err to the

NE. Walker (1998) proposed a vector summation model to account for

the directions and final return to the loft. It is clear that the chosen direc-

tions for the most part take the bird up or down the local gradient in the

appropriate sense to move toward the loft. When the release site is close

to the local gradient leading to the loft, errors are small, but when the site

is away from this line flying down the gradient gives rise to large errors.

Figure B13 Observation of enhanced firing rates in response to

magnetic field changes in the Bobolink. The response of a single

ganglion cell to field intensity changes—(a) spontaneous activity,

(b) response to 200 nT change, (c) response to 5000 nT change,

(d) response to 15000 nT change, (e) response to 25000 nT

change, and (f) response to 100000 nT change. Note the

geomagnetic field is of the order of 10000 nT, or gammas, or tens

of microteslas. The stimulus is indicated by the horizontal heavy

line. The vertical bar indicates 2 mV and the horizontal bar 50 ms

(From Semm and Beason. 1990).

48 BIOMAGNETISM

Indeed, some of the birds released due west of the loft appear to set

off in completely the wrong direction. The overall pattern of direc-

tions demonstrates that the birds are able to determine the local field

gradient and have a memory of whether the field is higher or lower at

the release site than at the loft. The birds appear to use the gradient

of the field in their navigation, which is a long standing idea in

homing noted by Wiltschkow and Wiltschkow (2003), but it is not clear

whether they use nonmagnetic clues or a more sophisticated vector

summation magnetic model, such as that suggested by Walker (1998)

to complete their return to the loft. These ideas have been strongly criti-

cized by Wallraff (1999) and Reilly (2002), but given the observation of

the relation of initial flight directions to the field gradient (Windsor,

1975; Walker, 1998), it is hard to avoid the interpretation that the pigeon

is able to sense and follow the field gradient.

Many other animals are able to sense the geomagnetic field. There

are examples demonstrating determination of the direction of the

horizontal component and of the inclination of the total field vector

field. Beason (1989) demonstrated sensitivity to the sign of the

vertical component of a magnetic field in the Bobolink (Dolichonyx

orzivorous), which is a nocturnal migratory species. The experiments

were carried out in a planetarium and the initial departure directions

were found to reverse with the reversal of the vertical component of

the field. The experiment provided convincing evidence of an inclina-

tion based compass because the direction of horizontal component of

the field was maintained when the vertical component was reversed

and yet the initial departure directions reversed. Particularly convin-

cing evidence of the ability to sense the direction of the horizontal

component of the field comes from species which orient themselves,

e.g., resting termites (Roonwal, 1958) or structures they build, e.g., ter-

mite galleries (Becker, 1975), and honey bee hives (Lindauer and

Martin, 1972). These and other examples are presented in an excellent

review of orientation in Arthropods (Lehrer, 1997). With all the many

examples of sensitivity to the geomagnetic field in animals, it is nat-

ural to ask whether human beings are sensitive to the Earth’s field

and claims that we are indeed able to sense the field have been made

(Baker, 1980), but the results have not been replicated. A review of

human magnetoreception is given in Kirschvink et al. (1985).

In addition to useful magnetic field sensing in relation to navigation,

there is a broader issue of field sensitivity including possible harmful

effects of magnetic fields. Such effects are not likely to be related to

the normal field strength of the geomagnetic field because animals have

evolved in the presence of this field. Rather, it is the absence of the geo-

magnetic field, or the presence of much stronger fields that may prove

harmful. During the period of low field intensity associated with field

reversals, when the simple geometry of the field is also lost, animals

relying on the field for navigation will presumably experience difficulty.

In a more direct test of the importance of the geomagnetic field,

Shibab et al. (1987) reported impairment of axonal ensheathment and

myelination of peripheral nerves of newborn rats kept in 10 nT and

0.5 mT environments compared with controls.

Sensitivity to ac fields and dc fields larger than the

geomagnetic field

Studies of effects of alternating magnetic fields and static fields that

are stronger than the geomagnetic field have also tested sensitivity of

the nervous system to these fields, but the main emphasis of the stu-

dies is on possible harmful effects, such as carcinogenesis, mutagen-

esis, and developmental effects. Much of this work has been

stimulated by epidemiological studies such as that of Feychting and

Ahlbom (1995), which suggested links between power line exposure

and cancer in children. This has generated an enormous literature,

but no conclusive evidence of cause and effect has emerged.

As an example of an effect of a static field only marginally larger

than the geomagnetic field, Bell et al. (1992) reported changes in elec-

trical activity in the human brain on exposure to fields of 0.78 G, or

78 mT. Power spectra of electroencephalograms (EEG) were found to

be modified in all but one case, and in most cases an increase was

observed. Interictal (between seizure) firing rates in the hippocampus

of epileptic patients are increased by fields of the order of milliteslas.

Such fields are some 20 times larger than the geomagnetic field (Dob-

son et al., 1995; Fuller et al., 1995, 2003). The procedure had some

clinical value in the preoperative evaluation of patients with

drug resistant epilepsy. In contrast to the generally observed increases

in activity, activity was inhibited when the field was applied during

periods of strong activity (Dobson et al., 1998). Work on hippocampal

slices by Wieraszko (2000) showed a complicated response pattern,

with initial inhibition of firing followed by an amplification phase

after the field was removed. The amplification was modulated by dan-

trolene, which is an inhibitor of intracellular calcium channels. In con-

trast, to the observations of neural responses to field changes observed

in animals that use the field sensitivity for navigation, these responses

were on a relatively long timescale of seconds and increased firing rates

persisted in some case for tens of minutes. This suggests that these

phenomena are very different from the magnetite sensor-mediated

responses discussed above in the trout and the Bobolink. In those cases,

the response took place within milliseconds of the field change and was

completed within seconds.

Wikswo and Barach (1980) showed that very large fields of 24 T

would be needed to bring about a 10% difference in conduction, in

the discussion of the direct effect of magnetic fields on nerve transmis-

sion. In this, they noted that they had specifically ignored “micro-

scopic chemical effects as well as those due to induced fields.” It is

evidently through these more subtle effects that weak magnetic fields

affect biological systems.

The direct effect of magnetic fields on the rate of recombination of

free radicals is an example of a mechanism that could play a role in

field sensitivity. Moreover, given the importance of free radicals in

biological systems this could be a significant effect. It arises because

the probability of recombination of free radicals depends upon their

spin state, which in turn can be affected by a dc field (McLauchlan,

1989) and possibly by ac fields (Hamilton et al., 1988).

Figure B14 Initial departure directions of pigeons released at

various distance and azimuthal direction from their loft. Note that

the departure directions are symmetrical about the local field

gradient indicated by the heavy NW/SE line (From Windsor, 1975

and Walker, 1998).

BIOMAGNETISM 49

Whereas the sensitivity of the trout to the geomagnetic field is

clearly through the intermediary of a magnetite based sensory receptor,

it may well be that there are also direct effects of magnetic fields on

the nervous system. Indeed, it seems that the effects on the epileptic

patients are very different from the process in the trout and may result

from direct effects on cell processes.

Biogenic magnetite

Biogenic magnetite clearly plays a central role in the sensitivity of the

trout to magnetic fields and probably in many other animals. Biogenic

magnetite was first discovered in organisms as a capping on the radula

(teeth) of the chiton—a marine mollusk (Lowenstam, 1962). Since that

time it has been found in many organisms ranging from bacteria to

humans. In some species it has been demonstrated to form a part of

a geomagnetic field receptor system (e.g., Frankel, 1984; Walker

et al., 1997; Wiltschko and Wiltschko, 2002; Kirschvink and Walker,

1995; Lohmann and Lohmann, 1996), but in most it is not obviously

linked to magnetic orientation/navigation and its role is unclear.

Magnetite is ferrimagnetic because of the imbalance of Fe

2þ

, which

is confined to one of the two opposed sub-lattices, i.e., on the octa-

hedral sites. It has a saturation magnetization of 4.71  10

1

at room temperature, a Curie (Néel) point of 578



C and a high density

of 5.2 g cm

3

. It is presumably the high density and hardness that

account for its presence in the radula of Chiton. In magnetotactic bac-

teria and in species that sense the magnetic field, it plays a role in

detecting the field. However, magnetite is also a source of ferrous iron,

which can generate potentially harmful free radicals. Here we will dis-

cuss the synthesis of magnetite, its occurrence in organisms including

human beings and its possible role in neurodegenerative diseases.

Synthesis and occurrence of biogenic magnetite

Perhaps the best understood example of biogenic magnetite occurs in

the various species of magnetotactic bacteria. These motile, gram-

negative bacteria synthesize chains of highly pure and crystallographi-

cally perfect magnetite nanoparticles for use as a navigational aid—a

phenomenon known as “magnetotaxis” (Blakemore, 1975; Frankel,

1984). The morphology of these particles is characteristic of the var-

ious species, however, in all cases, the size of the particles is generally

just above the superparamagnetic limit such that they are magnetically

blocked. This enables the chain to experience a torque when the

geomagnetic field is at an angle to the long axis of the chain.

Recent work from Bertani and others (2001) has led to the identifi-

cation of genes, which are involved in the synthesis of magnetite in

magnetotactic bacteria. Though this gives an indication of the pro-

cesses involved in magnetite synthesis, the mechanism employed

by the bacteria to form perfect crystals of very specific size has

remained difficult to identify. Work published recently, however,

characterized proteins associated with biogenic magnetite crystals

from the bacterium M. magnetotacticum, which are believed to regu-

late crystal growth (Arakakai et al., 2003). The authors were able to

use these proteins to direct the synthesis of magnetite nanoparticles

in the laboratory with sizes and shapes very similar to those found in

M. magnetotacticum.

Biogenic magnetite in organisms

Biogenic magnetite is found in many organisms; however, its physio-

logical role in most of these is not well understood (Webb et al., 1990).

The mineral is also found in human tissue. Biogenic magnetite, along

with maghemite (g Fe

—an oxidation product of magnetite), was

first reported in humans in 1992 by a group at the California Institute

of Technology led by Joseph Kirschvink (Kirschvink et al., 1992). In

that study, the group examined human brain tissue samples taken from

cadavers and this work proved somewhat controversial.

In order to allay this controversy and to examine the possibility of

contamination and postmortem changes in brain iron chemistry, a series

of studies on tissue removed from the human hippocampus was under-

taken. The analyses were performed on tissue resected during amygda-

lohippocampectomies (a surgical procedure in which the damaged

hippocampus of focal epilepsy patients is removed) as well as from

cadaver tissue. Thus it was possible to control post mortem artifacts,

which may have complicated the interpretation of Kirschvink’s earlier

results. These studies demonstrated clearly that biogenic magnetite

is present in human brain tissue and confirm the results of the Cal

Tech group (Dunn et al., 1995; Dobson and Grassi, 1996; Schultheiss-

Grassi and Dobson, 1999). In addition, recent results appear to

demonstrate that biogenic magnetite concentration increases with age

in males; however, this relationship is not seen in female subjects (Dob-

son, 2002).

While initial analysis of human brain tissue focused on magnetome-

try studies and the identification of biogenic magnetite by proxy,

particles of this material also have been extracted, imaged, and charac-

terized using transmission electron microscopy (TEM) (Kirschvink

et al., 1992; Schultheiss-Grassi et al., 1999) (Figure B15). The parti-

cles are generally smaller than 200 nm and, in most cases, are on the

order of a few tens of nanometers. While some particles exhibit disso-

lution edges, others preserve pristine crystal faces, and all particles

examined thus far are chemically pure (this is common in biogenic

magnetite). Morphologically, many of the particles are similar to those

observed in magnetotactic bacteria (Schultheiss-Grassi et al., 1999)

though other particles are more irregularly shaped. A particularly intri-

guing transmission electron image has suggested that the iron oxide

present in some hippocampal tissue may be concentrated in or near

the cell membrane (Dobson, et al., 2001) (Figure B16). Whether this

location is related to cell membrane transport, or simply iron storage,

is not known. However, the high concentration of iron oxide in this

cell suggests a degree of specialization because such a concentration

in all hippocampal tissue would give an unrealistically high concentra-

tion in this tissue. Unfortunately, magnetic particles have, for the most

part, only been observed in tissue extracts, and work is currently

underway to develop new techniques for imaging the particles in tissue

slices and mapping their distribution to tissue structures.

Biogenic magnetite also has been found in the human heart, spleen,

and liver. Again, this was determined by magnetometry studies, and

calculation of magnetite concentrations showed that the heart has the

highest levels of all organs examined thus far (Schultheiss-Grassi

et al., 1997). These investigations are continuing with the aim of deter-

mining the origin and role of biogenic magnetite in the human body.

Figure B15 Transmission electron micrograph of biogenic

magnetite extracted from the human hippocampus. Inset shows

an electron diffraction pattern confirming the presence of

magnetite. (From Schultheiss-Grassi et al., 1999).

50 BIOMAGNETISM

Biogenic magnetite and neurological disorders

Though the physiological role of magnetite in humans is not yet known,

recent studies have demonstrated a tentative link between magnetite bio-

genesis and neurodegenerative disorders such as Alzheimer’s disease

(AD) (Dobson, 2001, 2004; Hautot et al. , 2003). It has been known for

50 years that neurodegenerative diseases are associated with elevated

levels of iron (Goodman, 1953). However, since that discovery, very lit-

tle progress has been made in identifying the iron compounds present,

their role, and their origin until this recent work.

Magnetite was first reported in AD tissue in the original study of

human brain tissue by Kirschvink et al. (1992). These results did not

demonstrate any correlation between elevated levels of biogenic mag-

netite and AD. Although the results were negative, it appears that this

may have been due to the particular measurement technique rather

than the absence of a correlation altogether. The isothermal remanent

magnetization (IRM) of the tissue was measured using the supercon-

ducting quantum interference device (SQUID) magnetometry. One of

the drawbacks of this method is that the contribution of very fine

(superparamagnetic) particles (less than 50 nm) is lost from the signal,

particularly when measured at 0



C as was the case in this first study. In

this case, any concentration which is calculated from the data depends

on making some assumptions— one assumption being that the signal is

due to particles which are large enough to contribute to the remanent

magnetization (i.e., blocked). In this study, that may not have been a true

picture of all the biogenic magnetite in the tissue samples.

Recently, Hautot et al. (2003) have developed methods for measur-

ing the total biogenic magnetite signal. This is done by measuring the

magnetization vs. applied field and then modeling the contributions

from material such as the diamagnetic tissue, ferritin, and heme iron.

In this way, the total concentration of magnetite—regardless of grain

size—can be determined. Using this method, preliminary evidence of

a correlation between biogenic magnetite concentration has been

demonstrated in female AD patients.

By measuring other parameters, such as magnetic interactions

between groups of magnetite particles, it has also been shown that

there is preliminary evidence of a correlation between particle packing

geometry and focal epilepsy. There was no demonstrable correlation

between biogenic magnetite concentration and epileptic tissue, but

again, these results are from measurements of remanent magnetization.

New studies using microfocused synchroton x-ray sources have now

enabled iron compounds in brain tissue to be located and characterized

in situ with subcellular resolution (Mikhaylova et al., 2005; Colling-

wood et al., 2005). This breakthrough allows, for the first time, the map-

ping of specific iron compounds including magnetite, to structures and

cells within neurodegenerative tissue. Magnetite-rich iron anomalies

have been unequivocally identified in AD tissue using this method,

and it shows great promise for furthering our understanding of the role

of magnetite and other iron compounds in neurological disorders.

Conclusion

Biomagnetism is now a major research area with a healthy mix of biol-

ogists, physicists, and chemists involved. We can safely conclude that

many organisms sense the geomagnetic field and use it as a naviga-

tional cue, or for other purposes, such as nest alignment. Again it is

clear that strong magnetic fields can produce mutagenic effects and

produce harmful developmental effects in the several animals investi-

gated. It is much less clear how much damage the relatively weak

fields of power lines, mobile phones, and other electrical devices of

modern society actually harm human beings. Magnetite is synthesized

by many organisms and is involved in field detection in some. It is

however present in many organisms in which its role is unclear.

Indeed, as we noted, magnetite may be harmful as a source of free

radicals. Presently, the possibility that magnetite may play a role in

neurodegenerative diseases, such as Alzheimer’s, Parkinson’s, or

Huntington’s, is being investigated and may explain the association

of iron enrichment and these diseases.

Mike Fuller and Jon Dobson

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Magnetization, Isothermal Remanent

Rock Magnetism

52 BIOMAGNETISM

BLACKETT, PATRICK MAYNARD STUART,

BARON OF CHELSEA (1887–1974)

Blackett (Figure B17) came to geophysics late in a remarkable career.

He had been educated at Osborne Naval College and Dartmouth and

joined the Royal Navy, seeing action at the Battles of Jutland and of

the Falklands in the Great War, as it was then known. After the war,

he resigned from the navy, went to Cambridge to Magdalene College,

and read for the Natural Science Tripos. He joined Lord Rutherford’s

group at the Cavendish as a graduate student in 1921, where he worked

on transmutation of atoms using cloud chambers, carrying out in the

succeeding two decades much of the work for which he was eventually

awarded a Nobel Prize in Physics in 1948.

In 1933 he became professor of physics at Birkbeck College,

London and in 1937 he moved to Manchester University as the

Langworthy Professor of Physics. Prior to the Second World War, he

had been brought into the Air Defense Committee and with the advent

of the war was involved in many technical projects and made notable

contributions in operations research. After the Second World War, he

returned to Manchester and to research and was instrumental in estab-

lishing the first chair in radioastronomy and in the development of the

Jodrell Bank Research Station that would lead to the famous steerable

radio telescope. Meanwhile he became interested in magnetic fields in

stars and planets, which led to his research in geophysics. In 1953, he

was appointed professor and head of the physics department at Imper-

ial College and built up an influential group in rock magnetism and

paleomagnetism. Professor Blackett was elected president of the Royal

Society in 1965 and made a life peer in 1969. He died in 1974.

Blackett was a member of the heroic generation of physicists, most

of whom were European, who revolutionized physics between the two

world wars. As one of Lord Rutherford’s students, he was assigned to

study the disintegration of elements using the cloud chamber, which

had been invented by C.T.R. Wilson at Cambridge nearly a quarter

of a century earlier. With it, Wilson had demonstrated the tracks of

ionizing alpha particles emitted from a small radioactive source. In

his initial studies of thousands of photographs using such a source

and with the cloud chamber containing nitrogen, Blackett found just

eight, in which something remarkable was recorded. As Figure B18

shows, most of the alpha particles from the radioactive source below

the chamber pass through it, not striking the atoms of nitrogen gas

in the chamber. However, on the left a track shows that an alpha par-

ticle has hit a nitrogen atom. This has yielded a heavy oxygen isotope

and a proton that leaves to the right of the original track. The heavy

oxygen leaves to the left with a stronger track and is seen to collide

again. Blackett had trapped a nuclear transmutation on film! He went

on to establish the nature of the scattering of alpha particles from a

number of nuclei of varying mass.

A major problem with the cloud chamber used in Blackett’s early

experiments was that thousands of photographs were needed to have

a good chance of seeing an interesting transmutation. This problem

became all the more daunting when the cloud chambers were turned

to the analysis of cosmic rays. It was then a matter of chance, whether

a cosmic ray crossed the chamber close to the time of expansion.

The problem was solved by Blackett and a young Italian physicist

Giuseppe Occhialini. Occhialini had studied with Rossi at Florence

and brought with him knowledge of the work on coincident signals

from Geiger counters. Blackett and Occhialini’s solution was to place

a Geiger counter above and below the cloud chamber so that a simul-

taneous signal from the two could be used to detect a cosmic ray par-

ticle and fire the cloud chamber. Of course by that time, the cosmic ray

particle was long gone, but the ionization trail was still there and pro-

duced the necessary condensation for a track to be formed when the

chamber was expanded. Although Anderson was the first to detect

Dirac’s antielectron, or positron as it has become known, Blackett and

Occhialini confirmed its existence with their technique and demon-

strated the produ ction of positrons. To do this they had placed a copper

plate above the cloud chamber, which produced gamma rays from the

interaction of energetic cosmic ray electrons with the copper. Within

the chamber numerous symmetrically divergent tracks were formed,

as the particles with opposite electric charge formed and responded to

the strong magnetic field imposed. These divergent tracks recorded

the generation of matter, in the form of electrons and positrons, from

energy, in the form of gamma rays, as predicted by Einstein. The citation

for Blackett’s 1948 Noble Prize was “for his development of the Wilson

cloud chamber method and his discoveries therewith in the fields of

nuclear physics and cosmic radiation.”

Blackett’s Nobel acceptance speech in 1948 reveals his social sensi-

tivity. After expressing his personal feelings of satisfaction in the

award, he remarked that he saw the Nobel Prize “as a tribute to the

vital school of European Experimental Physics.” He then went on to

address the problem of avoiding the catastrophe of nuclear war, noting

that “technological progress and pure science are but different facets

of the same growing mastery by man over the force of nature. It is

Figure B17 P.M.S. Blackett.

Figure B18 Cloud chamber photograph showing alpha particles

traversing the chamber and an example on the left of a collision

between an alpha particle and a nitrogen atom, yielding a heavy

oxygen isotope and a proton. The proton leaves to the right of the

initial track (after Close et al., 1987).

BLACKETT, PATRICK MAYNARD STUART, BARON OF CHELSEA (1887–1974) 53

our task as scientists and citizens to ensure these forces are used for the

good of men and not their destruction.” In 1948 he published more on

these ideas in the book Military and Political Consequences of Atomic

Energy. His socialist political thought caused difficulty with the

America of that time, but his recognition of the dangers of a world

divided into very poor and very rich countries remains all too relevant

to this day.

Blackett was clearly an excellent experimentalist and it was this

ability that led him into the development of a sensitive magnetometer

that opened up the field of paleomagnetism of the weakly magnetized

sediments. Blackett had very skillfully constructed a sensitive magnet-

ometer to test a theory of his about magnetic fields and the rotation of

massive bodies. The idea was in relation to the origin of the magnetic

fields of stars and of the Earth as a fundamental property of their rota-

tion. The work developing this system and the negative result were

described in a famous paper by Blackett entitled “A Negative Experi-

ment Relating to Magnetism and the Earth’s Rotation” and published

in the Transactions of the Royal Society. There used to be a reprint

of this paper in the geophysics library at Madingly Rise, Cambridge,

with a note from Blackett, apologizing for the mistaken theoretical

basis for the experiment. However, his instrument provided the means

of measuring the weak magnetization of sediments, which was essen-

tial to test the idea of continental drift. This was one mistake that had a

substantial silver lining!

Blackett’s rock magnetism group worked initially at Manchester and

then moved with him to Imperial College. His laboratory at Imperial

College, with its orderly arrangement of instruments and polished

wooden floors, was reminiscent of the quarterdeck of a Royal Navy

battleship, presumably a legacy of his naval days. Important work

was done both in fundamental rock magnetism and in paleomagnet-

ism. Leng and Wilson demonstrated the reality of geomagnetic field

reversals. Haigh made critical contributions to the understanding of

magnetization acquired by magnetic materials as they grow in a mag-

netic field. Everi tt studied the acquisition of magnetization as magnetic

particles cooled in a magnetic field and developed the baked contact

test—one of the standard paleomagnetic field tests. The paper by

Blackett, Clegg, and Stubbs (1961) was one of the most convincing

early demonstrations by paleomagnetism of the veracity of the idea

of continental drift. Blackett’s lectures on rock magnetism taken from

his Second Weizman Memorial Lectures of 1954 is a little gem, com-

bining insight on the grand scale, but also reflecting the pleasure of

experimental work (Blackett 1956).

Blackett’s main contributions were outside of geophysics. One

immediately thinks of his experimental skills and the insights that

came from the cloud chamber work; his leadership during World

War II; his contributions to the development of radioastronomy. In

addition to all this, his experimental skills played an important role

in the development of rock magnetism and paleomagnetism. The way

in which his group operated was in a direct lineage from Rutherford’s

Cavendish, which was brought to our field. We were lucky that our

subject was touched by Blackett.

Michael D. Fuller

Bibliography

Blackett, P.M.S., 1952. A negative experiment relating to magnetism

and the Earth’s rotation, Philosophical Transactions of the Royal

Society of London, Series A, A245: 309–370.

Blackett, P.M.S., 1954. Lectures on Rock Magnetism. Jerusalem: The

Weizmann Science Press of Israel.

Blackett, P.M.S., Clegg, J.A., and Stubbs, P.H.S., 1960. An analysis of

rock magnetic data, Proceedings of the Royal Society of London,

256: 291–322.

Close, F., Marten, M., and Sutton, C., 1987. The Particle Explosion.

Cambridge: Oxford University Press.

BULLARD, EDWARD CRISP (1907–1980)

Edward Crisp Bullard, known to everyone as Teddy, was the greatest

geophysicist working in the United Kingdom in the second half of

the 20th century (Figure B19). He made seminal contributions to the

theory of the origin of the magnetic field, to the analysis of the westward

drift and secular variation, and to studies of electromagnetic induc-

tion. He championed a number of developments in the theory of plate

tectonics, and placed his department at the centre of the plate tectonic

revolution of the 1960s. His full biography is in McKenzie (1987).

Teddy was born in Norwich into a wealthy family of brewers. The

building that housed the brewery still stands in an attractive part of

Norwich, but the business was taken over in the 1960s and Bullard’s

beer can no longer be found; the name enjoyed a revival in the early

days of the campaign for Real Ale and won a prize at the 1974

Cambridge beer festival. The young Bullard was educated at Repton

School where his physics teacher, A.W. Barton, initiated his interest

in physics. He studied physics in Cambridge, where he found the lec-

tures dull with the exception of J. Larmor (q.v.), Rutherford, and Pars,

and proceeded to research in Rutherford’s laboratory. He was in fact

supervised by P.M.S. Blackett (q.v.), although Rutherford was probably

the greater influence. His Ph.D. project was on electron scattering, but

on taking up a position in the Department of Geodesy and Geophysics

he began work on the measurement of gravity with pendulums and

made observations with them in East Africa. His Ph.D. thesis, only

26 pages long, includes both the electron scattering and gravity work.

He was elected a fellow of the Royal Society in 1941; the citation

includes work on seismics, heat flow, and gravity: everything, in fact,

except geomagnetism.

On the outbreak of the Second World War he joined the Admiralty

Research Laboratory and set to work on reducing the magnetic fields

around ships. The Germans had laid magnetic mines in shallow waters

around Britain, which sank 60 ships in the “phoney war” in December

1939. The “degaussing” was successful (Bullard, 1946). He subse-

quently joined Blackett to work on what later became known as opera-

tional research. The degaussing of ships was his first work on

magnetism, the only previous reference being to the effect of the

Earth’s magnetic field on the period of invar pendulums (Bullard,

1933), but during his war work he read Chapman and Bartels

(1940), and this probably stimulated him to work on geomagnetism

after the war was over.

Postwar Cambridge offered little for an ambitious researcher, parti-

cularly in geophysics, and Teddy moved to Toronto. There followed

the most produ ctive period of his career. He used his knowledge of

Figure B19 “Teddy” as the author knew him in about 1970.

54 BULLARD, EDWARD CRISP (1907–1980)

heat flow to develop the convection theory for the dynamo (Bullard,

1950) and analyzed global observations for secular variation and the

westward drift (Bullard et al., 1950). Both these studies remain sub-

stantially correct today, although his theory for westward drift, that

the magnetic field acted on the lower mantle to drive it eastwards by

an electric motor effect, is no longer believed because the electrical

conductivity of the mantle is thought to be too small.

W.M. Elsasser (q.v.) also began working on the origin of the Earth’s

magnetic field at this time, but he concentrated on the mechanism

by which a magnetic field could be generated by flow in the core,

whereas Bullard had worked with the observations and on the heat

sources driving the convection. Elsasser derived some fundamental

results in dynamo theory and constructed a formalism for solving the

equations, but did not attempt to solve them. This was a very formid-

able problem for that time— indeed, it is still a very difficult problem

with today’s computers. Bullard and a research student at Toronto,

H. Gellman, attempted to find a solution with the tools at hand (see

Bullard-Gellman dynamo). In 1950 Bullard moved back to the United

Kingdom as director of the National Physical Laboratory, where he

had access to one of the most powerful computers of the day.

Although Bullard and Gellman (1954) is one of the most influential

papers ever published in dynamo theory, their solutions had not con-

verged and their claim to have found a working dynamo was sub-

sequently proved incorrect (Gibson and Roberts, 1969). Nonetheless,

it was a brave and very early effort to carry out a numerical solution of

a partial differential equation governing a problem in fluid mechanics.

The dynamo failed because they chose a fluid flow that lacked helicity.

It is clear that they intended to design a flow with helicity because

their paper contains a discussion of magnetic field lines being pulled

and twisted to reinforce the dipole field, but they were restricted by

numerical considerations to a very simple flow. Bullard was undoubt-

edly influenced by Elsasser’s ideas, which were later developed by

E.N. Parker into what is now known as an a-effect dynamo (Parker,

1955). Kumar and Roberts (1975) eventually found a working dynamo

using the Bullard-Gellman formalism and a more complicated

fluid flow.

Bullard desperately wanted to return to Cambridge. Eventually a

post became available when S.K. Runcorn (q.v.) moved to Newcastle,

and Bullard accepted a very junior position, lower than the one he

occupied before the war. He was eventually promoted as reader then

professor in 1964, over 20 years since his election to fellowship of

the Royal Society and 10 years after his knighthood.

On the question of polarity reversals he sat on the fence, much to

Runcorn’s annoyance, remaining sceptical because of the discovery

of self-reversal in certain minerals. He was finally won over by the

classic work of Cox et al. (1963), and when Harry Hess visited Cam-

bridge in 1962 and talked about his ideas on seafloor spreading he

encouraged Fred Vine, then a research student, to pursue his interpre-

tation of reversely magnetized seafloor in terms of Hess’ model. The

result is now known as the Vine-Matthews-Morley hypothesis (q.v.).

In later years he had a succession of successful research students

working on electromagnetic induction, among them Bob Parker, Nigel

Edwards, and Dick Bailey. He put his name to very few scientific

papers written during this period, but his influence was everywhere, both

on the group as a whole and on individual students. Bullard worked to the

end, finishing his last paper on historical measurements at London with

Stuart Malin (Malin and Bullard, 1981) shortly before he died.

David Gubbins

Bibliography

Bullard, E.C., 1933. The effect of a magnetic field on relative gravity

determinations by means of an invar pendulum. Proceedings of the

Cambridge Philosopjical Society, 29: 288–296.

Bullard, E.C., 1946. The protection of ships from magnetic mines.

Proceedings of the Royal Institution of Great Britain, 33: 554–566.

Bullard, E.C., 1950. The transfer of heat from the core of the Earth.

Monthly Notices of the Royal Astronomical Society, 6:36–41.

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Cross-references

Blackett, Patrick Maynard Stuart, Baron of Chelsea (1897–1974)

Bullard-Gellman dynamo

Dynamo, Bullard-Gellman

Dynamos, Kinematic

Elsasser, Walter M. (?–1991)

Geomagnetic Polarity Reversals, Observations

Geomagnetic Secular Variation

Larmor, Joseph (1857–1942)

Mantle, Electrical Conductivity, Mineralogy

Runcorn, S. Keith (1922–1995)

Transient EM Induction

Vine-Matthews-Morley Hypothesis

Westward Drift

BULLARD, EDWARD CRISP (1907–1980) 55