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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Harv Rev Psychiatry. Author manuscript; available in PMC 2010 April 13.
Published in final edited form as:
Harv Rev Psychiatry. 2002 Nov–Dec; 10(6): 324–336.
PMCID: PMC2853779
NIHMSID: NIHMS186574

Diffusion Tensor Imaging and Its Application to Neuropsychiatric Disorders

Abstract

Magnetic resonance diffusion tensor imaging (DTI) is a new technique that can be used to visualize and measure the diffusion of water in brain tissue; it is particularly useful for evaluating white matter abnormalities. In this paper, we review research studies that have applied DTI for the purpose of understanding neuropsychiatric disorders. We begin with a discussion of the principles involved in DTI, followed by a historical overview of magnetic resonance diffusion-weighted imaging and DTI and a brief description of several different methods of image acquisition and quantitative analysis. We then review the application of this technique to clinical populations. We include all studies published in English from January 1996 through March 2002 on this topic, located by searching PubMed and Medline on the key words “diffusion tensor imaging” and “MRI.” Finally, we consider potential future uses of DTI, including fiber tracking and surgical planning and follow-up.

Diffusion tensor imaging (DTI) is an exciting recent technique in neuroimaging that affords a unique opportunity to quantify the diffusion of water in brain tissue. It is based upon the phenomenon of water diffusion known as Brownian motion, named after the English botanist Robert Brown, who in 1827 observed the constant movement of minute particles suspended within grains of pollen.* We now know that molecular motion is affected by the properties of the medium in which it occurs and that diffusion within biological tissues reflects both tissue structure and architecture at the microscopic level. Equal, or isotropic, diffusion occurs when a medium does not restrict molecular motion, as would be the case with cerebrospinal fluid. Skewed, or anisotropic, diffusion, seen in crystals and polymer films, is not equal in all directions. DTI measures diffusion properties and consequently allows spatial description of the medium under study.

Taking advantage of the fact that diffusion is not uniform throughout the brain (differing, for example, between gray matter, white matter, and cerebrospinal fluid), researchers can employ DTI to evaluate tissue characteristics. The technique is particularly useful in the study of white matter tracts in the brain since the mobility of water is restricted perpendicular to the axons oriented along the fiber tracts (anisotropic diffusion). This is due to the concentric structure of multiple tightly packed myelin membranes wrapped around the axon fibers. Although myelination is not essential for diffusion anisotropy of nerves (see studies on nonmyelinated garfish olfactory nerves1 and on neonate brains prior to the appearance of myelin2,3), myelin is generally assumed to be the major barrier to diffusion in white matter tracts.

DTI evolved from earlier studies using diffusion-weighted imaging (DWI), a magnetic resonance imaging (MRI) technique in which a single field gradient pulse is applied during image acquisition, allowing quantitative measurement of water diffusion.4 Displacement of water molecules (diffusion) causes randomization of the nuclear magnetic resonance spin phase, which, in turn, results in signal reduction. The amount of reduction provides a quantitative measure of the diffusion in the gradient direction; thus, only diffusion in the direction of this particular gradient can be detected. Since diffusion is a three-dimensional process, three orthogonal measures are needed to calculate the mean diffusivity for each voxel.

DTI was developed for true multidimensional assessment of diffusion data in vivo.5,6 In contrast to DWI, DTI measures at least six different gradient directions. The diffusion data for each voxel, represented as a 3 × 3 matrix, comprise a diffusion tensor (see Figure 1). In isotropic media, where diffusion along the three main axes is equal, the diffusion tensor is symmetrical in all directions and is visualized as a sphere. In anisotropic media, where the diffusion is different along each axis, the diffusion tensor is visualized as an ellipsoid, with its longest axis indicating the greatest of the so-called principal directions of diffusion. The shape of the tensor ellipsoid depends on the strength of the diffusion along the three principal directions (i.e., its eigenvectors). Within myelinated white matter fiber tracts, the greatest principal direction of diffusion will always indicate the axonal trajectory, since perpendicular diffusion is restricted by myelin sheathing. The shape of the tensor ellipsoid therefore provides qualitative and quantitative measures of white matter tracts within the brain.

FIGURE 1
Difference between unrestricted (isotropic) and restricted (anisotropic) diffusion within the brain. The shape of the tensor ellipsoid is determined by the strength of the diffusion along three principal directions (its eigenvectors). In nonrestrictive ...

DWI and its Acquisition in the Brain

DWI was introduced in 1986 by Le Bihan and colleagues.4 From the beginning, however, the widespread application of this technique to clinical studies was greatly impeded by technical constraints, the most important being motion sensitivity, which can cause severe ghosting artifacts or complete signal loss. In attempts to observe molecular displacement in micrometers, it is no surprise that motion of any sort, even unavoidable involuntary head movements or pulsations of blood in the brain tissue, interfere with measurement. The problem is even more serious when scans must be obtained from, for example, a disoriented and confused stroke victim, who may move his or her head excessively. These limitations were a major incentive for the development of faster sequences that are more robust in the face of bulk motion.

The development of diffusion-sensitive pulse sequences followed two basic directions: echo-planar imaging methods,7 which capture a complete image within a single shot, and navigator methods,8 which acquire images in multiple shots, with each shot employing “navigator MR signals” to detect and correct the bulk motion. Although single-shot methods are extremely robust, the elevated sensitivity to magnetic field inhomogeneities inherent in these techniques may lead to image-distortion artifacts, such as susceptibility artifacts, occurring in areas exhibiting large variations in magnetic susceptibility (e.g., interfaces between air, bone, and brain tissue), and chemical shift artifacts, caused by the difference in chemical properties of fat and water. Moreover, spatial resolution is limited, and signal averaging may be necessary. Navigator methods, on the other hand, permit excellent spatial resolution with a minimum of image-distortion artifacts and high signal-to-noise ratio, but they are not as robust and require acquisition times of 10 minutes or more. Furthermore, cardiac gating—that is, synchronization of slice acquisition with heart rate—must be used, which makes the technique less attractive in a routine clinical setting. Recently, researchers have proposed several new techniques (diffusion-weighted radial acquisition of data,9 line-scan diffusion imaging,10 slab-scan diffusion imaging13) that avoid susceptibility and chemical shift artifacts and allow for resolution higher than that obtained with echo-planar imaging.

Quantitative Representation of Diffusion in DWI

As noted previously, the measurement of water diffusion in tissues is based on probing the movement of water molecules within the tissue environment. In pure liquids, such as water, individual molecules are in constant motion in every direction due to random (Brownian) motion. In tissues, however, various tissue components (larger molecules, intracellular organs, membranes, cell walls, and so on) restrict the Brownian motion. In cerebrospinal fluid and many tissues (liver and cerebral gray matter, for example), when averaged over the macroscopic scale of image voxels, this restriction is identical in every direction—the diffusion is isotropic. In some very structured tissues, however, such as muscle or cerebral white matter, cellular arrangement shows a preferred direction of water diffusion that is largely uniform across the entire voxel—the diffusion is anisotropic. The diffusion coefficient is a measure of this molecular motion, and it can be determined by applying consecutive magnetic field gradient pulses and then measuring the change between the images acquired. Each gradient is typically applied for several tens of milliseconds, during which time the average water molecule in brain tissues may migrate 10 or more micrometers in a random direction. The irregularity of the motion entails a signal loss that can be used to quantify the diffusion constant. This MR measurement, however, fails to differentiate diffusion-related motion from blood flow, perfusion, bulk tissue, or tissue pulsation motions. Thus, the diffusion value obtained with this technique is not an actual diffusion coefficient, but only an apparent diffusion coefficient (ADC).

Diffusion Tensor Imaging

The concept of a diffusion tensor was introduced to the field of MR diffusion imaging by Basser and colleagues in 1994.6 It is a construct adapted from physics and engineering, where it is employed to describe tension forces in solid bodies with an array of three-dimensional vectors.

The particular tensors used to describe diffusion can be further conceptualized and visualized as ellipsoids. The three main axes of the ellipsoid describe an orthogonal coordinate system. The directions of the main axes represent the so-called eigenvectors; their length, the so-called eigenvalues of the tensor. In DTI, a tensor that describes diffusion in all spatial directions is calculated for each voxel. The longest main axis of the diffusion ellipsoid represents the value and the direction of maximum diffusion, whereas the shortest axis represents the value and direction of minimum diffusion. If the three eigenvalues are equal, then the diffusion is said to be isotropic, and the diffusion tensor can be visualized as a sphere. If they are unequal, then the diffusion is said to be anisotropic, and the diffusion tensor can be visualized more as an ellipsoid, as would be the case for myelin sheaths (see Figure 1). To estimate the diffusion tensor, at least six measurements (taken from different gradient directions) are needed, in addition to the baseline image data.

White matter fiber tracts consist of a large number of densely packed myelinated axons. Because the movement of water molecules within this myelinated white matter is substantially restricted perpendicular to the longitudinal axes of the axons, the longest main axis of the diffusion ellipsoid is much larger than the other two and coincides with the direction of the fibers. Following Westin and colleagues' geometric classification of the diffusion tensor using linear, planar, and spherical measures,12 this type of anisotropically restricted diffusion is termed “linear diffusion.” “Planar diffusion” refers to diffusion restricted in one direction only and unrestricted in the other two—for example, between layers of tissue.

The above-mentioned basic ellipsoid model is idealized and does not necessarily reflect the true diffusion behavior encountered in real tissues. For example, at nerve-fiber-tract crossings, the ellipsoid tensor model fails, since each fiber tract registers a principal direction of diffusion. Acquisition protocols that measure diffusion in a large number of directions allow for a better description of the complex directional diffusion behavior at fiber-tract crossings and in other heterogeneously organized tissue structures.

Data from DTI can be analyzed in several ways. The most general approach is to characterize the overall displacement of the molecules (average ellipsoid size) by determining mean diffusivity. To do so, the trace of the diffusion tensor,4 which is calculated as the sum of the eigenvalues of the tensor, is employed. This sum is divided by three to calculate mean diffusivity.

Several measures have been introduced to describe anisotropic diffusion. To be useful, such measures must be independent of the orientation of the diffusion ellipsoid and thus provide information relevant to the specific tissue type. The most commonly used measures, proposed by Basser and Pierpaoli,13 are relative anisotropy (RA), a normalized standard deviation representing the ratio of the anisotropic part of the tensor to its isotropic part; fractional anisotropy (FA), a measure of the fraction of the magnitude of the tensor that can be ascribed to the anisotropic diffusion; and volume ratio, a measure representing the ratio of the ellipsoid volume to the volume as a sphere of radius l. These and other anisotropy indices are summarized in Table 1. Such indices measure the diffusion within each voxel (intravoxel diffusion) separately. A second type of anisotropy measure has been introduced to describe the intervoxel coherence of the tensors in the neighboring voxels. The latter measures, summarized in Table 2, better reflect fiber organization and orientation at the macroscopic level.

TABLE 1
Anisotropy Indices Used in Clinical Studies
TABLE 2
Intervoxel Diffusion Indices Describing Local Coherence between Tensors

Like quantifying diffusion tensor anisotropy, displaying tensors in three dimensions also poses a problem. Several methods have been proposed for visualizing the three-dimensional information contained in DTI data. These include using the octahedra in each pixel;14 color maps,15 where different intensities of the three colors indicate the size and the ADC in each of the three Cartesian directions;16 and blue lines to represent the in-plane component of the principal diffusion direction, along with a color-coded out-of-plane component17 (see Figure 2).

FIGURE 2
Visualization of diffusion tensors. The blue lines represent the in-plane component of the principal diffusion direction; the other colors show the magnitude of the out-of-plane component, with orange/red indicating maximal diffusion. The white and green ...

Clinical Applications in Neuropsychiatric Disorders

The phenomenon of restricted diffusion is of particular interest to studies that evaluate the integrity of white matter fiber tracts, as noted above. Based on geometry and the degree of anisotropy loss, white matter tract pathology, such as dislocation, swelling, infiltration, and disruption, can be documented. In addition, the cross-sectional sizes of these pathways yield a quantitative measure of connectivity between different brain regions. For example, disruptions in connectivity—and, in some cases, subsequent reorganization of nerve pathways—resulting from physical trauma or ischemia, brain tumor, multiple sclerosis (MS), infection with human immunodeficiency virus (HIV), schizophrenia, or degenerative or metabolic diseases might be visualized and quantified. A loss of connectivity between brain regions as measured by DTI could indicate developmental pathology, axonal damage, demyelination, and/or disruption of fiber tracts.

Brain ischemia

Evaluation of ischemia is one of the earliest, most important, and most widely used clinical applications of DWI. So far, DWI is the most sensitive in vivo method for detecting acute ischemia.18,19 It also allows for the distinction between old and new strokes19,20 and helps to differentiate early stroke from other focal brain processes mimicking stroke on conventional MRI.21,22 DWI studies2325 show that diffusion parameters decrease in the acute stage, “pseudonormalize” in the subacute phase, and increase in the chronic stage of the stroke. Unfortunately, because DWI does not reflect the spatial organization of the fiber tracts, it fails to detect long-term white matter changes, either in the close vicinity of the lesion or remote from it.

DTI, on the other hand, is more sensitive to the organization and orientation of the fiber tracts, and research26 already shows better correlation between clinical status and anisotropy indices (e.g., diffusion anisotropy remains decreased in the subacute stage, even after diffusion coefficient normalization [between 1 and 3 weeks.]). DTI data are more sensitive to changes in fiber-tract organization (i.e., axonal loss, degeneration, or incomplete remyelination) following a stroke. Moreover, changes in anisotropy can be detected several months after the stroke—and within the fiber tracts remote from the stroke (e.g., in the corticospinal tract)—presumably marking fiber-tract degeneration (wallerian degeneration).27,28

A recent DTI study29 has also demonstrated that ischemic stroke damage in white matter occurs earlier and is more severe than previously inferred from DWI investigations. Table 3 summarizes all clinical DTI studies published through March 2002 on stroke and other neuropsychiatric conditions.

TABLE 3
Clinical Applications of Diffusion Tensor Imaging

Traumatic brain injury

As with stroke, DWI has played a major role in the early detection of brain changes following traumatic injury. The early increase in ADC seen on DWI is usually attributable to vasogenic edema, whereas later decreases in ADC (despite ongoing increase of intracranial pressure) are usually attributable to cytotoxic edema,30 believed to play a major role in posttraumatic brain swelling.31

DTI allows a closer investigation of the specific fiber tracts affected, as well as the ability to monitor the degeneration process following injury. Specifically, DTI performed several months after an internal capsule focal brain injury32 demonstrated full recovery and preservation of the structural integrity and orientation in the posterior capsular limb and disrupted structure in the anterior limb on the injured side, which correlated with the functional motor deficits revealed by the functional MRI. Moreover, in another DTI study33 a patient who had right frontotemporal brain injury and impaired memory revealed increased diffusion traces in right frontal, temporal, and occipital lobes as well as diffusion changes in myelinated structures, including the right optic radiation and the forceps major of the corpus callosum, which corresponded with clinically predictable symptoms. These case studies suggest that DTI is a powerful new technology for investigating functional deficits caused by brain injury, as well as for predicting prognosis.

Brain tumors

DWI has not been particularly useful in brain tumor differentiation, although it is helpful in detecting the cystic components of tumors, early edema around the tumor, and ischemic lesions within the pathological mass. In contrast, DTI can be implemented for modeling fiber-tract disruptions or displacement caused by the tumor34,35 and could be useful for early detection of spine metastases, as well as for detection of corticospinal-tract disruptions or displacement.

Seizure disorders

Compared with its use in the detection and differentiation of early stroke from brain tumor, DWI has so far played only a minor role in routine interictal imaging. In rats, severe, acute focal damage (expressed in animals as cytotoxic edema, which causes a drop in diffusion) after prolonged induced seizures can be detected with DWI, especially within the amygdala and piriform cortex.35 These results have not been replicated in humans, presumably because they show a different mechanism of brain injury (vasogenic edema, which causes an increase in diffusion, coexists with the cytotoxic edema).

A few existing DTI studies already demonstrate higher sensitivity of DTI compared to structural MRI in detecting malformations of cortical development. Such malformations disturb the orientation of the fiber tracts and are a common cause of epilepsy. Rugg-Gunn and colleagues,37 for example, have shown that changes within the white matter of the left temporal lobe can be identified with DTI but not with structural MRI.

Other Conditions Affecting White Matter

DWI has been shown to be superior in detecting white matter abnormalities in MS—abnormalities that are not as readily observed in conventional structural MRI (“normal-appearing white matter”).3840 It is hoped that DTI will be of even greater value in detecting fiber-tract alterations due to demyelination and axonal loss. DTI studies in patients with MS have shown an increase in mean diffusivity and a decrease in diffusion anisotropy within acute lesions,41 as well as within the normal-appearing white matter,42 most likely attributable to edema. In addition, DTI has been found to be useful in differentiating between two types of MS,43 secondary progressive and relapsing-remitting, which have different clinical courses.

Finally, DTI has demonstrated white matter fiber tract pathology in Krabbe's disease,44 HIV infection,45,46 amyotrophic lateral sclerosis,47 cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy,48 leukoencephalopathy,49 and chronic alcohol dependence.50 In such studies, DTI was able to detect and quantify therapeutic responses to treatment that are believed to be the result of decreased edema during the acute phase of inflammation.44,46 The potential of DTI as an exploratory tool is suggested by a study of patients with chronic alcohol dependence50 that revealed a correlation between loss of working memory and attention and a decrease in diffusion anisotropy within the corpus callosum.

Alzheimer's disease

The early to moderate stages of Alzheimer's disease are characterized by impaired cognition with preserved mobility.51 Although the disease is believed mainly to affect gray matter, postmortem studies52,53 have revealed loss of axons and oligodendrocytes within the white matter as well. Of note, a recent DWI study54 has shown reduced diffusion within the splenium and body of the corpus callosum, findings consistent with previous reports of atrophy in the corpus callosum in patients with Alzheimer's disease.55,56 In addition, DTI studies conducted in the early stages of the disease57,58 have revealed significant connectivity disruptions within the association white matter fiber tracts, including the temporal stem (uncinate fasciculus), cingulate fasciculus, corpus callosum, and superior longitudinal fasciculus, as well as the hippocampus. Thus, DTI studies may improve our ability to track progressive changes in Alzheimer's disease and could possibly be used in the future to evaluate changes in response to treatment.

Schizophrenia

Schizophrenia is a disorder of unknown etiology. Although many subtle brain abnormalities have been observed in this disorder (see review in reference 59), no brain lesions have been definitively correlated with many of the functional deficits found in these patients. Of note, however, are several DTI reports of decreased diffusion anisotropy in the white matter of persons with schizophrenia. Loss of orientation and organization of fiber tracts has been detected in the whole white matter60 and in frontal white matter,61 but also in particular fiber tracts such as the corpus callosum62,63 and the uncinate fasciculus.64 Further DTI investigation of white matter fiber-tract abnormalities in schizophrenia may change how we view this disorder, particularly in providing access to in vivo developmental studies across time.

Other possible uses in psychiatric disorders

To date, there are no studies using DTI to investigate white matter abnormalities that have been reported in other psychiatric conditions. MRI has revealed white matter hyperintensities in deep and periventricular white matter in patients with affective disorders;65 it has also shown deep white matter lesions to be correlated with poor outcome in bipolar disorder66 and with degree of residual dysfunction following a severe episode of depression.67 MRI studies in patients with posttraumatic stress disorder have revealed nonspecific white matter lesions, as well as some functional deficits that might be attributed to the disconnection of specific cortical regions (i.e., the amygdala, Broca's region, and the cingulate cortex).68 Correlations between psychiatric symptoms and white matter lesions could be further evaluated using DTI. Such testing might be able to determine the specificity of the particular fiber tracts affected, as well as the extent of their involvement.

Developmental Studies

Developmental DTI studies are only just beginning. Investigation of normal and abnormal brain development, however, should lead to a better understanding of brain maturation. DWI has, in fact, already revealed greater water diffusion in neonates than in adults,69,70 and there is evidence to suggest that anisotropic diffusion is higher in full-term neonates than in preterm neonates,3 a difference most likely due to the myelination of white matter fiber tracts. Such findings suggest that diffusion-imaging techniques can detect an increase in myelination during normal development.

In addition, anisotropic diffusion has been observed to decline as a result of age-related degenerative processes involving white matter fibers and myelin sheaths.71 Whether this change is due to normal aging or pathological aging remains to be determined. Table 4 summarizes all neurodevelopmental studies utilizing DTI published through March 2002.

TABLE 4
Neurodevelopmental Studies Utilizing DTI

Diffusion imaging offers the opportunity to evaluate both normal and pathological changes in white matter and brain connectivity over the life span. Such changes may be important for understanding not only normal development but also differences in cognitive abilities over time.

Future Applications

Potential future applications of DTI include visualization of the anatomical connections among different parts of the brain. Diffusion tensor tractography (see Figure 3), proposed by several authors,7275 uses the principal diffusion direction measured with DTI to compute the pathways of complete nerve fiber tracts. The tracing is performed by first defining regions of interest. Then, starting from points (“seed points”) selected within this region and following the spatially interpolated direction of maximum diffusion in neighboring voxels, the path of fibers within a fiber tract is defined. Such tracking, which is done repetitively with multiple seed points, creates a contiguous path that defines the fiber tract of interest.

FIGURE 3
Three-dimensional tractography of a normal subject, showing the anterior (white) and posterior (blue) portions of the corpus callosum as well as the left and right (yellow and green) corticospinal tracts. These tracts pass through an axial section of ...

Visualization is then performed in three dimensions to depict the white matter fiber tract. Progressing from an examination of anisotropy to a more elaborate analysis of the relationship between neighboring diffusion ellipsoids opens the possibility for assessing, in vivo, axonal fiber connectivity and functional links among brain regions.

A slightly different approach to tensor tractography, described by Westin and colleagues,14 attempts to reduce problems encountered when tracing fibers in complex regions (such as where fiber tracts merge, branch, or cross within a voxel) by defining the direction of the trace path in a novel way. Rather than following the direction of the maximum diffusivity (the direction of the major axis of the diffusion ellipsoid), this approach “bends” the trace with a strong bias toward this direction. Another approach regularizes the trace path based on its curvature—that is, fixes the curve according to a predefined parameter.

Diffusion tensor tractography, combined with information from conventional and functional MR imaging, can provide a powerful tool for neurosurgical planning, especially when surgery occurs in the vicinity of vital nerve fiber tracts. Tracing and mapping the passage of functionally relevant fiber tracts along the tumors is as important as mapping cortical functions adjacent to tumors. The information gathered with these complementary techniques helps the neurosurgeon to decide where tumor tissue can be excised without permanent neurological consequences.

In addition, DTI, as mentioned above, can be used to follow up surgical and neurological treatment (by assessing the regeneration and/or remyelination of the affected fiber tracts), as well as to monitor the effects of medication. Finally, in disorders such as schizophrenia, where gross brain abnormalities are not evident, DTI may offer an opportunity to evaluate subtle changes in white matter fiber tracts that are related to neurocognitive abnormalities observed in this disorder. Such information might further our knowledge of brain-connectivity abnormalities and lead to more-targeted pharmacological treatments as well as to a better understanding of brain-behavior links in this devastating disorder.

In summary, DTI has opened up new research possibilities in areas that previously relied largely upon postmortem studies. For the first time, the intricate connective architecture of the most complex human organ can be studied noninvasively. Other potentially important applications for this technique, such as characterization of cardiac muscle tissue architecture, diagnosis of liver disease, mapping of tissue temperature, and diffusion spectroscopy, are beyond the scope of this article. It is clear that DTI could revolutionize what is known in many different domains of medicine and disease. The ability to visualize white matter fiber tracts in the human brain, in vivo, will likely be critical to a new understanding of brain structure and function, both in normal individuals and in those with a neuropsychiatric disorder.

The authors would like to thank Marie Fairbanks for her administrative assistance.

Acknowledgments

This work was supported, in part, by grants from the National Alliance for Research on Schizophrenia and Depression (Drs. Kubicki and Frumin), the Grable Foundation (Dr. Kubicki), the National Institutes of Health (K02 MH 01110 and R01 MH 50747 to Dr. Shenton, R01 NS 39335 to Dr. Maier, R01 MH 40799 to Dr. McCarley), and the National Center for Research Resources (R01 RR 11747 to Dr. Kikinis, P41 RR 13218 to Drs. Jolesz and Westin); Department of Veterans Affairs Merit Awards (Drs. Shenton and McCarley); and a VA Psychiatry/Neuroscience Research Fellowship Award (Dr. Frumin).

Footnotes

*It was long thought that Brown observed the movement of pollen grains suspended in water. Many now believe that he observed the movement of particles suspended within the grains of pollen. See, for example, BJ Ford, Brownian movement in Clarkia pollen: a reprise of the first observations. The Microscope 1992;40:235–41 (available on the World Wide Web at: http://www.sciences.demon.co.uk/wbbrowna.htm).

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