Growth patterns in the developing brain detected by using continuum mechanical tensor maps

Abstract

The dynamic nature of growth and degenerative disease processes requires the design of sensitive strategies to detect, track and quantify structural change in the brain in its full spatial and temporal complexity. Although volumes of brain substructures are known to change during development, detailed maps of these dynamic growth processes have been unavailable. Here we report the creation of spatially complex, four-dimensional quantitative maps of growth patterns in the developing human brain, detected using a tensor mapping strategy with greater spatial detail and sensitivity than previously obtainable. By repeatedly scanning children (aged 3-15 years) across time spans of up to four years, a rostro-caudal wave of growth was detected at the corpus callosum, a fibre system that relays information between brain hemispheres. Peak growth rates, in fibres innervating association and language cortices, were attenuated after puberty, and contrasted sharply with a severe, spatially localized loss of subcortical grey matter. Conversely, at ages 3-6 years, the fastest growth rates occurred in frontal networks that regulate the planning of new actions. Local rates, profiles, and principal directions of growth were visualized in each individual child.

Full text

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Acknowledgements
This work was supported by the NIH, the NSF and the Alfred P. Sloan Foundation. We
thank J. DiCarlo, M. Usher and S. Yantis for discussions and J. Lane for technical support.
Correspondence and requests for materials should be addressed to E.N.
(e-mail: niebur@jhu.edu).
letters to nature
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Growth patterns in the developing
brain detected by using
continuum mechanical tensor maps
Paul M. Thompson*, Jay N. Giedd², Roger P. Woods*, David MacDonald³,
Alan C. Evans³& Arthur W. Toga*
*Laboratory of Neuro Imaging, Department of Neurology, Division of Brain
Mapping, UCLA School of Medicine, 710 Westwood Plaza, Los Angeles,
California 90095-1769, USA
²Child Psychiatry Branch, National Institute of Mental Health, NIH,
10 Center Drive, MSC 1600, Bethesda 20982-1600, Maryland, USA
³Montreal Neurological Institute, McGill University, 3801 University Street,
Montreal, Que
Âbec, Canada H3A 2B4
..............................................................................................................................................
The dynamic nature of growth and degenerative disease processes
requires the design of sensitive strategies to detect, track and
quantify structural change in the brain in its full spatial and
temporal complexity1. Although volumes of brain substructures
are known to change during development2, detailed maps of these
dynamic growth processes have been unavailable. Here we report
the creation of spatially complex, four-dimensional quantitative
maps of growth patterns in the developing human brain, detected
using a tensor mapping strategy with greater spatial detail and
sensitivity than previously obtainable. By repeatedly scanning
children (aged 3± 15 years) across time spans of up to four years, a
rostro-caudal wave of growth was detected at the corpus callosum,
a ®bre system that relays information between brain hemispheres.
Peak growth rates, in ®bres innervating association and language
cortices, were attenuated after puberty, and contrasted sharply
with a severe, spatially localized loss of subcortical grey matter.
Conversely, at ages 3 ±6 years, the fastest growth rates occurred in
frontal networks that regulate the planning of new actions. Local
rates, pro®les, and principal directions of growth were visualized
in each individual child.
Time series of high-resolution three-dimensional magnetic reso-
nance imaging (MRI) scans were acquired across large time spans
from young normal subjects (aged 3±6, 6±7, 7 ±11, 8±12, 9 ±13 and
11± 15 years) at intervals ranging from two weeks to four years.
Growth patterns were recovered by computing a three-dimensional
elastic deformation ®eld, which recon®gures the anatomy at the
earlier time point into the shape of the anatomy of the later scan.
Maps of local growth rates (Figs 1±4) revealed the complexity and
regional heterogeneity of the tissue growth, pruning and maturation
processes of late brain development. In subjects aged 6±15 years, the
Figure 1 Growth patterns in the developing human brain detected at ages 3 ±15 years.
A rostro-caudal wave of peak growth rates is detected in young normal subjects scanned
repeatedly across time spans of up to four years. Between ages 3 and 6 years, peak
growth rates (red colours; 60± 80% locally) were detected in the frontal circuits of the
corpus callosum, which sustain mental vigilance and regulate the planning of new actions.
Older children displayed fastest growth at the callosal isthmus, which innervates temporo-
parietal systems supporting spatial association and language function. Between ages
11± 15 years, growth rates still peak at the isthmus, but are attenuated.
Figure 2 Mapping dynamic patterns of brain development: four-dimensional growth
maps. Strikingly similar growth rates were detected in the corpus callosum of ®ve young
normal subjects scanned repeatedly aged 6± 13 years. Peak values throughout the
posterior midbody (red colours) were attenuated after puberty (11 ±15 years). By contrast,
near-zero maps of change were observed between scans acquired over a two-week
interval. Between ages 3± 6 years, extreme growth rates were found in the anterior
interhemispheric ®bre systems that transfer information to sustain mental vigilance and
organize new actions. Tensor maps identify the principal directions of growth rates,
revealing an outward radial tissue expansion in frontal regions.
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highest growth rates were consistently attained in temporo-parietal
systems which are functionally specialized for language, and for
understanding spatial relations (Fig. 2). In contrast to the near-zero
maps of change recovered at short time intervals (`Two-week
interval' in Fig. 2), growth maps spanning large time intervals
showed complex and heterogeneous patterns of change. Between
ages 7 and 11 years (Fig. 2), comparative stability of the splenial and
rostral ®bre systems of the corpus callosum contrasted sharply with
rapid focal growth at the callosal isthmus (up to 80%). Although
global measurements indicated an overall 22.4% increase in mid-
sagittal callosal area during the four-year time span (from
527.6 mm
2
to 645.6 mm
2
), these global values disguise the complex-
ity of local growth patterns. Local growth is as high as 80% (Fig. 2), a
feature which may not be apparent with conventional volumetric
descriptors.
Although some individual variation was expected, this focus of
extreme growth at the callosal isthmus was detected consistently in
all subjects tracked between 6 and 15 years (Fig. 2), suggesting that
cortico-cortical networks supporting rapid associative relay and
language functions may myelinate more extensively3and over
longer periods than rostral ®bre systems. In a girl scanned twice
exactly one year apart at ages 6 and 7 years, extreme growth (up to
85%) at the callosal isthmus contrasted with a comparatively
quiescent region in the more rostral systems that innervate frontal
and pre-frontal cortices. When a four-year growth map was gener-
ated for a slightly older child (11± 15 years, Fig. 2), growth rates were
correspondingly reduced in every region. Nonetheless, growth
patterns at the isthmus and splenium (commonly de®ned as the
posterior ®fth of the callosum) were still more rapid (20±25%
locally) than in the more anterior rostrum and genu (near-zero
change). In an analysis of grey matter at the cortex4, we recently
observed a localized grey matter loss in frontal cortex that persists in
normal subjects throughout adolescence even into adulthood. The
gradual quiescence of growth at the rostral callosum around pub-
erty may therefore be a precursor to a prolonged regressive process
of grey matter loss through adolescence into adulthood in the
frontal circuits it innervates.
Several near-zero maps of change were recovered at short time
intervals. Figure 2 shows a typical map from a subject scanned at age
8 years, exactly four years later at age 12 years, and again two weeks
later. Negligible change at short time intervals (`Two-week interval'
in Fig. 2) contrasted with a highly heterogeneous map of growth
across the four-year time span. Growth rates again achieved their
highest rates in the associative and linguistic networks that cross at
the callosal isthmus.
Figure 3 Patterns of cerebral growth. a, In a subject scanned at age 7 years and again
exactly four years later at age 11 years, dramatic growth is found in temporo-parietal
regions (red colours). b, All brain regions are stable in a control experiment (blue colours)
analysing scans acquired two weeks apart. c, Between ages 9± 13 years, growth is also
most pronounced in temporo-parietal regions. d, This was con®rmed by digitally
overlaying models of the cerebral cortex at each time point (arrows 9 and 13). Growth at
the callosal isthmus in subjects aged 7± 11 and 9± 13 years (Fig. 2) is therefore
accompanied by diffuse growth in its (temporo-parietal) lobar projection zones.
Figure 4 Detecting three-dimensional patterns of deep nuclear tissue loss. a,b, Tensor
maps distinguish local growth or brain tissue loss from global displacements (b) of the
adjacent ventricular anatomy, modelled here (a) at ages 7 years (red) and 11 years
(yellow). c,d, Between ages 7 and 11 years, three-dimensional displacement vector
maps show the deformation required to recon®gure earlier models of the caudate head
into their later shape. The caudate tail is stable (blue colours, d). e,f, Local growth (e) and
anatomical displacement (d) of the caudate head are independently recovered, with 50%
tissue loss detected locally (e,f), adjacent to a region of 20± 30% growth throughout the
internal capsule.
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A subject scanned at ages 3 and 6 years exhibited a focus of peak
growth rates (60±80% locally) throughout the anterior corpus
callosum, in frontal circuits that help to sustain a vigilant mental
state and regulate the organization and planning of new actions. The
extremely rapid rates of local growth are consistent with metabolic
studies using positron emission tomography5, which show an
extraordinary doubling of the rates of glucose metabolism in the
frontal cortex between ages 2 and 4 years, with frontal metabolic
rates remaining at 199% of their adult values throughout the age
range of 3± 8 years. Between ages 3 and 6 years, when language
function and associative thinking are not yet fully developed,
growth rates at the isthmus were more quiescent (Fig. 2; 0± 20%
growth). Later growth foci in the isthmus, found consistently in all
subjects aged 6± 15 years, may re¯ect ®ne tuning of language
functions known to occur late in childhood.
Regressive processes (tissue loss) were also detected at the same
time as rapid growth. In the 7± 11 and 9±13 year old subjects (Fig.
3), maps of lobar growth revealed pronounced (2±6 mm) temporo-
parietal and pre-frontal enlargement. Somatosensory, motor and
occipital brain regions were comparatively stable, with near-zero
change in all brain regions at short time intervals (Fig. 3b). Up to
50% loss of tissue volume was detected at the caudate head (Fig. 4e
and f). This tissue loss was highly localized, and contrasted with a
20± 30% growth of the adjacent internal capsule (for which a
separate surface model was made) and a 5±10% dilation of the
superior ventricular horn (Fig. 4a). Gross volumetric measures
con®rmed an overall 60 mm
3
tissue loss at the caudate head,
although these global measures disguise the regional complexity
of the change. This example helps illustrate how tensor maps
distinguish local growth patterns (Fig. 4e) from bulk shifts, such
as global displacements of the adjacent cerebral ventricles (Fig. 4a
and b). Three-dimensional vector displacement maps (Fig. 4b and
d) emphasize that both global and local displacements are required
to match modelled anatomical elements across time. The three-
dimensional deformation ®eld, however, encodes the patterns of
local anatomical dilation and contraction, and its values are
unaffected by global displacements. Maps of local three-dimen-
sional growth are therefore not critically dependent on how well
scans are initially aligned, and can de®ne growth at arbitrary three-
dimensional points in the local anatomy (Fig. 4e). Figure 4f
indicates the anatomical context and regional complexity of these
growth and regressive processes. The foci of tissue loss corroborate
the hypothesis that pruning processes occur during this develop-
mental stage2, suggesting that these processes can be tracked in an
individual child.
We detected striking, spatially complex patterns of growth and
tissue loss in the developing human brain. A rostro-caudal wave of
peak growth rates (Fig. 1) was identi®ed in the corpus callosum.
Fibre systems that mediate language function and associative
thinking grew more rapidly than surrounding regions across time
spans before and during puberty (6±13 years), with growth attenu-
ated shortly afterwards (11±15 years). This temporal pattern coin-
cides with the ending of a well-known critical period for learning
language, consistently noted in studies of second-language acquisi-
tion, including sign language, and in isolated children not exposed
to language during early development6. The ability to learn new
languages declines rapidly after the age of 12 years, as does the
ability to recover language function if linguistic areas in one brain
hemisphere are surgically resected. Peak growth rates in linguistic
callosal regions, as well as their attenuation around puberty, may
re¯ect the conclusion of the critical period for learning language and
for accelerating signal transduction in networks that support both
associative reasoning and language function. We recently found that
the same temporo-parietal ®bre system, crossing at the callosal
isthmus, degenerates fastest in early Alzheimer's disease7, when
progressive neuronal loss and perfusion de®cits begin to occur in
temporo-parietal association cortices and their commissural pro-
jection systems. The sensitivity of the approach may therefore offer
advantages in tracking ®ne-scale effects of therapeutic interventions
in dementia and oncology, mapping the local complexities of
disease processes using dynamic rather than static criteria. M
Methods
Magnetic resonance imaging and pre-processing
Three-dimensional (256
2
´124 ´0.97 mm ´0.97 mm ´1.5 mm resolution) T
1
-weighted
fast SPGR (spoiled GRASS (gradient-recalled acquisition in the steady state)) MRI
volumes were acquired from young normal subjects (mean age 8.6 63.1 years) at inter vals
ranging from two weeks to four years. For each scan pair, a radio-frequency bias ®eld
correction algorithm8was applied to both scans to eliminate intensity drifts caused by
scanner ®eld inhomogeneity. The initial scan was then rigidly registered to the target using
automated image registration software9and resampled using chirp-Z (in-plane) and linear
(out-of-plane) interpolation. Registered scans were histogram-matched (that is, their
intensity distributions were equalized) and a preliminary map of differences in MRI signal
intensities between the two scans was constructed1,10. Tensor models of structural change
were then used to calculate rates of tissue dilation, contraction and shearing, mapping
local patterns of change in three dimensions.
Image analysis
A high-resolution surface model of the cortex was automatically extracted11 from each
scan pair, and three-dimensional digital anatomical models, based on parametric surface
meshes12,13, were generated to represent a comprehensive set of deep sulcal, callosal,
caudate and ventricular surfaces at each time point14. Surface models based on manually
digitized data were averaged across multiple trials (N= 6) to minimize error15. These
model surfaces provided anatomic constraints for an elastic image registration
algorithm12,14. For each subject, this algorithm calculated a three-dimensional elastic
deformation vector ®eld, with 384
2
´256 ´3<0.1 billion degrees of freedom,
recon®guring the anatomy at the earlier time point into the shape of the anatomy of the
later scan. Surface deformations were used to derive a volumetric deformation ®eld from
which local measures of three-dimensional tissue dilation or contraction were quanti®ed.
Landmark points, surfaces, and curved anatomic interfaces were matched up in the pair of
three-dimensional image sets, and the biological validity of the resulting anatomical
transformation was guaranteed by forcing a large system of anatomical surface boundaries
to match exactly. These included multiple structural, functional, and tissue type bound-
aries in three dimensions, including the callosum, caudate, cortex and ventricles. The
deformation ®eld driving the earlier onto the later anatomy was extended to the full
volume using a continuum-mechanical model based on the Cauchy± Navier operator of
linear elasticity14,16±18. The resulting system of 0.1 billion second-order elliptic partial
differential equations was solved by successive over-relaxation methods, with multi-grid
acceleration12,14, on a standard radiologic workstation. Potential artefactual differences due
to differences in how surfaces were parametrized in each scan were compensated for, using
a ®eld of Christoffel symbols to modify the surface differential operators during the
anatomical transformation14.
Tensor map computation
From this transformation, local rates of tissue dilation, contraction and shearing were
calculated. Deformation processes recovered by the image-matching algorithm were
analysed mathematically with vector ®eld operators 14 to produce a variety of tensor maps.
These maps re¯ect the magnitude and principal directions of tissue dilation or contrac-
tion, and the local rates, divergence and gradients of the growth processes detected in the
dynamically changing brain.
Received 27 August 1999; accepted 21 January 2000.
1. Fox, N. C., Freeborough, P. A. & Rossor, M. N. Visualisation and quanti®cation of rates ofatrophy in
Alzheimer's disease. Lancet 348, 94±97 (1996).
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Cereb. Cortex 6, 551±560 (1996).
3. Yakovlev, P. I. & Lecours, A. R. in Regional Development of the Brain in Early Life (ed. Minkowski, A.)
3±70 (Davis, Philadelphia, 1967).
4. Sowell, E. R., Thompson, P. M.,Holmes, C. J., Jernigan, T. L. & Toga, A. W. In vivo evidence for post-
adolescent brain maturation frontal and striatal regions. Nature Neurosci. 2, 859± 861 (1999).
5. Chugani, H. T., Phelps, M. E. & Mazziotta, J. C. Positronemission tomography study of human brain
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adolescence: evidence for a critical period for verbal language development. Brain Lang. 63, 237±255
(1998).
7. Thompson, P. M. et al. Cortical variability and asymmetry in normal aging and Alzheimer's disease.
Cereb. Cortex 8, 492±509 (1998).
8. Zijdenbos, A. P.& Dawant, B. M. Brain segmentation and white matter lesion detection in MR images.
Crit. Rev. Biomed. Eng. 22, 401±465 (1994).
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12. Thompson, P. M. & Toga, A. W. A surface-based technique for warping 3-dimensional imagesof the
brain. IEEE Trans. Med. Imag. 15, 471±489 (1996).
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structure with a deformable probabilistic brain atlas based on random vector ®eld transformations.
Med. Image Anal. 1, 271±294 (1997).
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1998).
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variability in the human brain. J. Neurosci. 16, 4261±4274 (1996).
16. Thompson, P. M. et al. Detection and mapping of abnormal brain structure with a probabilistic atlas
of cortical surfaces. J. Comp. Assist. Tomogr. 21, 567 ±581 (1997).
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Correspondence and requests for materials should be addressed to P.M.T. (e-mail:
thompson@loni.ucla.edu).
Acknowledgements
We thank E. Sowell, M. Mega and J. Mazziotta for their advice and support. P.M.T. was
supported by the Howard Hughes Medical Institute, the US Information Agency, and the
US± UK Fulbright Commission. Additional research support was provided by a Human
Brain Project grant to the International Consortium for Brain Mapping, funded jointly by
NIMH and NIDA, by National Institutes of Health intramural funding (J.N.G.), and by
the National Library of Medicine, National Science Foundation, and the NCRR.
.................................................................
A clonogenic common myeloid
progenitor that gives rise
to all myeloid lineages
Koichi Akashi*², David Traver*, Toshihiro Miyamoto
& Irving L. Weissman
Departments of Pathology and Developmental Biology, Stanford University School
of Medicine, Stanford, California 94305, USA
*These authors contributed equally to this work
..............................................................................................................................................
Haematopoietic stem cells give rise to progeny that progressively
lose self-renewal capacity and become restricted to one lineage1,2.
The points at which haematopoietic stem cell-derived progenitors
commit to each of the various lineages remain mostly unknown.
We have identi®ed a clonogenic common lymphoid progenitor
that can differentiate into T, B and natural killer cells but not
myeloid cells3. Here we report the prospective identi®cation,
puri®cation and characterization, using cell-surface markers
and ¯ow cytometry, of a complementary clonogenic common
myeloid progenitor that gives rise to all myeloid lineages.
Common myeloid progenitors give rise to either megakaryo-
cyte/erythrocyte or granulocyte/macrophage progenitors. Puri-
®ed progenitors were used to provide a ®rst-pass expression
pro®le of various haematopoiesis-related genes. We propose
that the common lymphoid progenitor and common myeloid
progenitor populations re¯ect the earliest branch points between
the lymphoid and myeloid lineages, and that the commitment of
common myeloid progenitors to either the megakaryocyte/
erythrocyte or the granulocyte/macrophage lineages are mutually
exclusive events.
The existence of clonal common lymphoid progenitors (CLPs)3
suggests that complementary progenitors common to all myeloid
cells may also exist. Because the expression of the interleukin-7
receptor a-chain (IL-7Ra) marks the CLPs and other downstream
lymphoid progenitors3,4, we searched the IL-7Ra
-
fraction of
²Present address: Department of Cancer Immunology and AIDS, Dana-Farber Cancer Institute,
44 Binney Street, Boston, Massachusetts 02115, USA.
murine bone marrow for primitive myeloid progenitor populations.
In steady-state mouse bone marrow, myeloerythroid colony-
forming unit (CFU) activity was found almost exclusively in the
IL-7Ra
-
Lin
-
c-Kit
+
fraction (data not shown). Within this popula-
tion, Sca-1
+
cells are highly enriched for haematopoietic stem cells
(HSCs)3,5±7. To remove HSCs, Sca-1
+
cells were excluded. The
IL-7Ra
-
Lin
-
c-Kit
+
Sca-1
-
fraction was further divided into three
subpopulations according to the expression pro®les of the Fcg
receptor-II/III (FcgR), an important marker for myelomonocytic
cells and a progenitor marker in fetal liver haematopoiesis8, and
CD34, which marks a fraction of haematopoietic stem cells and
progenitors6: the FcgR
lo
CD34
+
,FcgR
lo
CD34
-
, and FcgR
hi
CD34
+
populations (Fig. 1a).
Each of the above populations were cleanly isolatable (Fig. 1b)
and gave rise to distinct colony types in methylcellulose CFU
assays (Figs 1c and 2). In the presence of steel factor (Slf), Flt-3
ligand (FL), IL-11, IL-3, granulocyte/macrophage-colony stimulat-
ing factor (GM-CSF), erythropoietin (Epo) and thrombopoietin
(Tpo), ,80% of single multipotent HSCs randomly committed to
myeloid lineages9, giving rise to various types of myeloid colonies
including CFU-Mix10, burst-forming units-erythroid (BFU-E),
Figure 1 Identi®cation of myeloid progenitors in mouse bone marrow. a, The IL-7Ra
-
Lin
-
Sca-1
-
c-Kit
+
fraction was subdivided into FcgR
lo
CD34
+
,FcgR
lo
CD34
-
, and FcgR
hi
CD34
+
populations (a, b, c respectively as indicated in the right-hand panel). Percentages of each
population relative to whole bone marrow are shown next to each sort gate. b, Re-analysis
of the sorted FcgR
lo
CD34
+
,FcgR
lo
CD34
-
and FcgR
hi
CD34
+
populations. c, Clonogenic
myeloid colony formation in methylcellulose. From each sorted progenitor population, 288
wells receiving a single cell each were scored. FcgR
lo
CD34
+
cells and HSCs formed various
myeloid colonies including CFU-Mix, whereas the FcgR
lo
CD34
-
and FcgR
hi
CD34
+
populations
gave rise only to MegE and GM colonies, respectively (left). Megakaryocyte/erythroid colony
formation from the FcgR
lo
fractions was dependent upon Epo and/or Tpo (right).
© 2000 Macmillan Magazines Ltd