Diffusion Tensor Analysis
Edge enhanced spatio-temporal constrained reconstruction of undersampled dynamic contrast enhanced radial MRI|
E.V.R. DiBella, T. Tasdizen. In Proceedings of the 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 704--707. 2012.
There are many applications in MRI where it is desirable to have high spatial and high temporal resolution. This can be achieved by undersampling of k-space and requires special techniques for reconstruction. Even if undersampling artifacts are removed, sharpness of the edges can be a problem. We propose a new technique that uses the gradient from a reference image to improve the quality of the edges in the reconstructed image along with a spatio-temporal constraint to reduce aliasing artifacts and noise. The reference is created from undersampled dynamic data by combining several adjacent frames. The method was tested on undersampled radial DCE MRI data with little respiratory motion. The proposed method was compared to reconstruction using the spatio-temporal constrained reconstruction. Sharper edges and an increase in the contrast was observed by using the proposed method.
Differences in subcortical structures in young adolescents at familial risk for schizophrenia: A preliminary study|
M.K. Dougherty, H. Gu, J. Bizzell, S. Ramsey, G. Gerig, D.O. Perkins, A. Belger. In Psychiatry Res., pp. (Epub ahead of print. Nov. 9, 2012.
PubMed ID: 23146250
How Many Templates Does It Take for a Good Segmentation?: Error Analysis in Multiatlas Segmentation as a Function of Database Size|
S.P. Awate, P. Zhu, R.T. Whitaker. In Int. Workshop Multimodal Brain Image Analysis (MBIA) at Int. Conf. MICCAI, Lecture Notes in Computer Science (LNCS), Vol. 2, Note: Recieved Best Paper Award, pp. 103--114. 2012.
PubMed ID: 24501720
PubMed Central ID: PMC3910563
This paper proposes a novel formulation to model and analyze the statistical characteristics of some types of segmentation problems that are based on combining label maps / templates / atlases. Such segmentation-by-example approaches are quite powerful on their own for several clinical applications and they provide prior information, through spatial context, when combined with intensity-based segmentation methods. The proposed formulation models a class of multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of images. The paper presents a systematic analysis of the nonparametric estimation's convergence behavior (i.e. characterizing segmentation error as a function of the size of the multiatlas database) and shows that it has a specific analytic form involving several parameters that are fundamental to the specific segmentation problem (i.e. chosen anatomical structure, imaging modality, registration method, label-fusion algorithm, etc.). We describe how to estimate these parameters and show that several brain anatomical structures exhibit the trends determined analytically. The proposed framework also provides per-voxel confidence measures for the segmentation. We show that the segmentation error for large database sizes can be predicted using small-sized databases. Thus, small databases can be exploited to predict the database sizes required (\"how many templates\") to achieve \"good\" segmentations having errors lower than a specified tolerance. Such cost-benefit analysis is crucial for designing and deploying multiatlas segmentation systems.
Watershed Merge Tree Classification for Electron Microscopy Image Segmentation|
T. Liu, E. Jurrus, M. Seyedhosseini, M. Ellisman, T. Tasdizen. In Proceedings of the 21st International Conference on Pattern Recognition (ICPR), pp. 133--137. 2012.
Automated segmentation of electron microscopy (EM) images is a challenging problem. In this paper, we present a novel method that utilizes a hierarchical structure and boundary classification for 2D neuron segmentation. With a membrane detection probability map, a watershed merge tree is built for the representation of hierarchical region merging from the watershed algorithm. A boundary classifier is learned with non-local image features to predict each potential merge in the tree, upon which merge decisions are made with consistency constraints to acquire the final segmentation. Independent of classifiers and decision strategies, our approach proposes a general framework for efficient hierarchical segmentation with statistical learning. We demonstrate that our method leads to a substantial improvement in segmentation accuracy.
Mixed-Effects Shape Models for Estimating Longitudinal Changes in Anatomy|
M. Datar, P. Muralidharan, A. Kumar, S. Gouttard, J. Piven, G. Gerig, R.T. Whitaker, P.T. Fletcher. In Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, Lecture Notes in Computer Science, Vol. 7570, Springer Berlin / Heidelberg, pp. 76--87. 2012.
In this paper, we propose a new method for longitudinal shape analysis that ts a linear mixed-eects model, while simultaneously optimizing correspondences on a set of anatomical shapes. Shape changes are modeled in a hierarchical fashion, with the global population trend as a xed eect and individual trends as random eects. The statistical signi cance of the estimated trends are evaluated using speci cally designed permutation tests. We also develop a permutation test based on the Hotelling T2 statistic to compare the average shapes trends between two populations. We demonstrate the bene ts of our method on a synthetic example of longitudinal tori and data from a developmental neuroimaging study.
Keywords: Computer Science
Topology Preserving Atlas Construction from Shape Data without Correspondence using Sparse Parameters|
S. Durrleman, M.W. Prastawa, S. Joshi, G. Gerig, A. Trouve. In Proceedings of MICCAI 2012, Lecture Notes in Computer Science (LNCS), pp. 223--230. October, 2012.
Statistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L1-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations.We show an application of our method for comparing anatomical shapes of patients with Down’s syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude.
Analysis of Longitudinal Shape Variability via Subject Specific Growth Modeling|
J. Fishbaugh, M.W. Prastawa, S. Durrleman, G. Gerig. In Medical Image Computing and Computer-Assisted Intervention – Proceedings of MICCAI 2012, Lecture Notes in Computer Science (LNCS), Vol. 7510, pp. 731--738. October, 2012.
Statistical analysis of longitudinal imaging data is crucial for understanding normal anatomical development as well as disease progression. This fundamental task is challenging due to the difficulty in modeling longitudinal changes, such as growth, and comparing changes across different populations. We propose a new approach for analyzing shape variability over time, and for quantifying spatiotemporal population differences. Our approach estimates 4D anatomical growth models for a reference population (an average model) and for individuals in different groups. We define a reference 4D space for our analysis as the average population model and measure shape variability through diffeomorphisms that map the reference to the individuals. Conducting our analysis on this 4D space enables straightforward statistical analysis of deformations as they are parameterized by momenta vectors that are located at homologous locations in space and time. We evaluate our method on a synthetic shape database and clinical data from a study that seeks to quantify growth differences in subjects at risk for autism.
Neuroimaging of Structural Pathology and Connectomics in Traumatic Brain Injury: Toward Personalized Outcome Prediction|
A. Irimia, Bo Wang, S.R. Aylward, M.W. Prastawa, D.F. Pace, G. Gerig, D.A. Hovda, R.Kikinis, P.M. Vespa, J.D. Van Horn. In NeuroImage: Clinical, Vol. 1, No. 1, Elsvier, pp. 1--17. 2012.
Recent contributions to the body of knowledge on traumatic brain injury (TBI) favor the view that multimodal neuroimaging using structural and functional magnetic resonance imaging (MRI and fMRI, respectively) as well as diffusion tensor imaging (DTI) has excellent potential to identify novel biomarkers and predictors of TBI outcome. This is particularly the case when such methods are appropriately combined with volumetric/morphometric analysis of brain structures and with the exploration of TBI]related changes in brain network properties at the level of the connectome. In this context, our present review summarizes recent developments on the roles of these two techniques in the search for novel structural neuroimaging biomarkers that have TBI outcome prognostication value. The themes being explored cover notable trends in this area of research, including (1) the role of advanced MRI processing methods in the analysis of structural pathology, (2) the use of brain connectomics and network analysis to identify outcome biomarkers, and (3) the application of multivariate statistics to predict outcome using neuroimaging metrics. The goal of the review is to draw the communityfs attention to these recent advances on TBI outcome prediction methods and to encourage the development of new methodologies whereby structural neuroimaging can be used to identify biomarkers of TBI outcome.
Fractional Anisotropy Distributions in 2-6 Year-Old Children with Autism|
C. Cascio, M.J. Gribbin, S. Gouttard, R.G. Smith, M. Jomier, S.H. Field, M. Graves, H.C. Hazlett, K. Muller, G. Gerig, J. Piven. In Journal of Intellectual Disability Research (JIDR), pp. (in print). 2012.
Background: Increasing evidence suggests that autism is a disorder of distributed neural networks that may exhibit abnormal developmental trajectories. Characterization of white matter early in the developmental course of the disorder is critical to understanding these aberrant trajectories.
Methods: A cross-sectional study of 2-6 year old children with autism was conducted using diffusion tensor imaging combined with a novel statistical approach employing fractional anisotropy distributions. 58 children aged 18-79 months were imaged: 33 were diagnosed with autism, 8 with general developmental delay (DD), and 17 were typically developing (TD). Fractional anisotropy values within global white matter, cortical lobes, and the cerebellum were measured and transformed to random F distributions for each subject. Each distribution of values for a region was summarized by estimating delta, the estimated mean and standard deviation of the approximating F for each distribution.
Results: The estimated delta parameter, delta-hat, was significantly decreased in individuals with autism compared to the combined control group. This was true in all cortical lobes, as well as in the cerebellum, but differences were strongest in the temporal lobe. Predicted developmental trajectories of delta-hat across the age range in the sample showed patterns that partially distinguished the groups. Exploratory analyses suggested that the variability, rather than the central tendency, component of delta-hat was the driving force behind these results. Conclusions: White matter in young children with autism appears to be abnormally homogeneous, which may reflect poorly organized or differentiated pathways, particularly in the temporal lobe, which is important for social and emotional cognition.
White matter structure assessment from reduced HARDI data using low-rank polynomial approximations|
Y. Gur, F. Jiao, S.X. Zhu, C.R. Johnson. In Proceedings of MICCAI 2012 Workshop on Computational Diffusion MRI (CDMRI12), Nice, France, Lecture Notes in Computer Science (LNCS), pp. 186-197. October, 2012.
Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg- Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions.
Sasaki Metrics for Analysis of Longitudinal Data on Manifolds|
P. Muralidharan, P.T. Fletcher. In Proceedings of the 2012 IEEE conference on Computer Vision and Pattern Recognition (CVPR), pp. 1027--1034. 2012.
Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.
A System for Query Based Analysis and Visualization|
A.R. Sanderson, B. Whitlock, O. Reubel, H. Childs, G.H. Weber, Prabhat, K. Wu. In Proceedings of the Third International Eurovis Workshop on Visual Analytics EuroVA 2012, pp. 25--29. June, 2012.
Today scientists are producing large volumes of data that they wish to explore and visualize. In this paper we describe a system that combines range-based queries with fast lookup to allow a scientist to quickly and efficiently ask \"what if?\" questions. Unique to our system is the ability to perform "cumulative queries" that work on both an intra- and inter-time step basis. The results of such queries are visualized as frequency histograms and are the input for secondary queries, the results of which are then visualized.
Semi-Automated Neuron Boundary Detection and Nonbranching Process Segmentation in Electron Microscopy Images|
E. Jurrus, S. Watanabe, R.J. Giuly, A.R.C. Paiva, M.H. Ellisman, E.M. Jorgensen, T. Tasdizen. In Neuroinformatics, pp. (published online). 2012.
Neuroscientists are developing new imaging techniques and generating large volumes of data in an effort to understand the complex structure of the nervous system. The complexity and size of this data makes human interpretation a labor-intensive task. To aid in the analysis, new segmentation techniques for identifying neurons in these feature rich datasets are required. This paper presents a method for neuron boundary detection and nonbranching process segmentation in electron microscopy images and visualizing them in three dimensions. It combines both automated segmentation techniques with a graphical user interface for correction of mistakes in the automated process. The automated process first uses machine learning and image processing techniques to identify neuron membranes that deliniate the cells in each two-dimensional section. To segment nonbranching processes, the cell regions in each two-dimensional section are connected in 3D using correlation of regions between sections. The combination of this method with a graphical user interface specially designed for this purpose, enables users to quickly segment cellular processes in large volumes.
Biomedical Visual Computing: Case Studies and Challenges|
C.R. Johnson. In IEEE Computing in Science and Engineering, Vol. 14, No. 1, pp. 12--21. 2012.
PubMed ID: 22545005
PubMed Central ID: PMC3336198
Computer simulation and visualization are having a substantial impact on biomedicine and other areas of science and engineering. Advanced simulation and data acquisition techniques allow biomedical researchers to investigate increasingly sophisticated biological function and structure. A continuing trend in all computational science and engineering applications is the increasing size of resulting datasets. This trend is also evident in data acquisition, especially in image acquisition in biology and medical image databases.
For example, in a collaboration between neuroscientist Robert Marc and our research team at the University of Utah's Scientific Computing and Imaging (SCI) Institute (www.sci.utah.edu), we're creating datasets of brain electron microscopy (EM) mosaics that are 16 terabytes in size. However, while there's no foreseeable end to the increase in our ability to produce simulation data or record observational data, our ability to use this data in meaningful ways is inhibited by current data analysis capabilities, which already lag far behind. Indeed, as the NIH-NSF Visualization Research Challenges report notes, to effectively understand and make use of the vast amounts of data researchers are producing is one of the greatest scientific challenges of the 21st century.
Visual data analysis involves creating images that convey salient information about underlying data and processes, enabling the detection and validation of expected results while leading to unexpected discoveries in science. This allows for the validation of new theoretical models, provides comparison between models and datasets, enables quantitative and qualitative querying, improves interpretation of data, and facilitates decision making. Scientists can use visual data analysis systems to explore \"what if\" scenarios, define hypotheses, and examine data under multiple perspectives and assumptions. In addition, they can identify connections between numerous attributes and quantitatively assess the reliability of hypotheses. In essence, visual data analysis is an integral part of scientific problem solving and discovery.
As applied to biomedical systems, visualization plays a crucial role in our ability to comprehend large and complex data-data that, in two, three, or more dimensions, convey insight into many diverse biomedical applications, including understanding neural connectivity within the brain, interpreting bioelectric currents within the heart, characterizing white-matter tracts by diffusion tensor imaging, and understanding morphology differences among different genetic mice phenotypes.
Quantitative Tract-Based White Matter Development from Birth to Age Two Years|
X. Geng, S. Gouttard, A. Sharma, H. Gu, M. Styner, W. Lin, G. Gerig, J.H. Gilmore. In NeuroImage, pp. 1-44. March, 2012.
Few large-scale studies have been done to characterize the normal human brain white matter growth in the first years of life. We investigated white matter maturation patterns in major fiber pathways in a large cohort of healthy young children from birth to age two using diffusion parameters fractional anisotropy (FA), radial diffusivity (RD) and axial diffusivity (RD). Ten fiber pathways, including commissural, association and projection tracts, were examined with tract-based analysis, providing more detailed and continuous spatial developmental patterns compared to conventional ROI based methods. All DTI data sets were transformed to a population specific atlas with a group-wise longitudinal large deformation diffeomorphic registration approach. Diffusion measurements were analyzed along the major fiber tracts obtained in the atlas space. All fiber bundles show increasing FA values and decreasing radial and axial diffusivities during development in the first 2 years of life. The changing rates of the diffusion indices are faster in the first year than the second year for all tracts. RD and FA show larger percentage changes in the first and second years than AD. The gender effects on the diffusion measures are small. Along different spatial locations of fiber tracts, maturation does not always follow the same speed. Temporal and spatial diffusion changes near cortical regions are in general smaller than changes in central regions. Overall developmental patterns revealed in our study confirm the general rules of white matter maturation. This work shows a promising framework to study and analyze white matter maturation in a tract-based fashion. Compared to most previous studies that are ROI-based, our approach has the potential to discover localized development patterns associated with fiber tracts of interest.
3D Tensor Normalization for Improved Accuracy in DTI Registration Methods|
A. Gupta, M. Escolar, C. Dietrich, J. Gilmore, G. Gerig, M. Styne. In Biomedical Image Registration Lecture Notes in Computer Science (LNCS), In Biomedical Image Registration Lecture Notes in Computer Science (LNCS), Vol. 7359, pp. 170--179. 2012.
This paper presents a method for normalization of diffusion tensor images (DTI) to a fixed DTI template, a pre-processing step to improve the performance of full tensor based registration methods. The proposed method maps the individual tensors of the subject image in to the template space based on matching the cumulative distribution function and the fractional anisotrophy values. The method aims to determine a more accurate deformation field from any full tensor registration method by applying the registration algorithm on the normalized DTI rather than the original DTI. The deformation field applied to the original tensor images are compared to the deformed image without normalization for 11 different cases of mapping seven subjects (neonate through 2 years) to two different atlases. The method shows an improvement in DTI registration based on comparing the normalized fractional anisotropy values of major fiber tracts in the brain.
Prenatal isolated mild ventriculomegaly is associated with persistent ventricle enlargement at ages 1 and 2|
A.E. Lyall, S. Woolson, H.M. Wolf, B.D. Goldman, J.S. Reznick, R.M. Hamer, W. Lin, M. Styner, G. Gerig, J.H. Gilmore. In Early Human Development, Elsevier, pp. (in press). 2012.
Background: Enlargement of the lateral ventricles is thought to originate from abnormal prenatal brain development and is associated with neurodevelopmental disorders. Fetal isolated mild ventriculomegaly (MVM) is associated with the enlargement of lateral ventricle volumes in the neonatal period and developmental delays in early childhood. However, little is known about postnatal brain development in these children.
Methods: Twenty-eight children with fetal isolated MVM and 56 matched controls were followed at ages 1 and 2 years with structural imaging on a 3T Siemens scanner and assessment of cognitive development with the Mullen Scales of Early Learning. Lateral ventricle, total gray and white matter volumes, and Mullen cognitive composite scores and subscale scores were compared between groups.
Results: Compared to controls, children with prenatal isolated MVM had significantly larger lateral ventricle volumes at ages 1 and 2 years. Lateral ventricle volume at 1 and 2 years of age was significantly correlated with prenatal ventricle size. Enlargement of the lateral ventricles was associated with increased intracranial volumes and increased gray and white matter volumes. Children with MVM had Mullen composite scores similar to controls, although there was evidence of delay in fine motor and expressive language skills.
Conclusions: Children with prenatal MVM have persistent enlargement of the lateral ventricles through the age of 2 years; this enlargement is associated with increased gray and white matter volumes and some evidence of delay in fine motor and expressive language development. Further study is needed to determine if enlarged lateral ventricles are associated with increased risk for neurodevelopmental disorders.
Brain Volume Findings in Six Month Old Infants at High Familial Risk for Autism|
H.C. Hazlett, H. Gu, R.C. McKinstry, D.W.W. Shaw, K.N. Botteron, S. Dager, M. Styner, C. Vachet, G. Gerig, S. Paterson, R.T. Schultz, A.M. Estes, A.C. Evans, J. Piven. In American Journal of Psychiatry (AJP), pp. (in print). 2012.
Objective: Brain enlargement has been observed in individuals with autism as early as two years of age. Studies using head circumference suggest that brain enlargement is a postnatal event that occurs around the latter part of the first year. To date, no brain imaging studies have systematically examined the period prior to age two. In this study we examine MRI brain volume in six month olds at high familial risk for autism.
Method: The Infant Brain Imaging Study (IBIS) is a longitudinal imaging study of infants at high risk for autism. This cross-sectional analysis examines brain volumes at six months of age, in high risk infants (N=98) in comparison to infants without family members with autism (low risk) (N=36). MRI scans are also examined for radiologic abnormalities.
Results: No group differences were observed for intracranial cerebrum, cerebellum, lateral ventricle volumes, or head circumference.
Conclusions: We did not observe significant group differences for head circumference, brain volume, or abnormalities of radiologic findings in a sample of 6 month old infants at highrisk for autism. We are unable to conclude that these changes are not present in infants who later go on to receive a diagnosis of autism, but rather that they were not detected in a large group at high familial risk. Future longitudinal studies of the IBIS sample will examine whether brain volume may differ in those infants who go onto develop autism, estimating that approximately 20\% of this sample may be diagnosed with an autism spectrum disorder at age two.
|Patient-tailored connectomics visualization for the assessment of white matter atrophy in traumatic brain injury,
A. Irimia, M.C. Chambers, C.M. Torgerson, M. Filippou, D.A. Hovda, J.R. Alger, G. Gerig, A.W. Toga, P.M. Vespa, R. Kikinis, J.D. Van Horn. In Frontiers in Neurotrauma, Note: http://www.frontiersin.org/neurotrauma/10.3389/fneur.2012.00010/abstract, 2012.
Available approaches to the investigation of traumatic brain injury (TBI) are frequently hampered, to some extent, by the unsatisfactory abilities of existing methodologies to efficiently define and represent affected structural connectivity and functional mechanisms underlying TBI-related pathology. In this paper, we describe a patient-tailored framework which allows mapping and characterization of TBI-related structural damage to the brain via multimodal neuroimaging and personalized connectomics. Specifically, we introduce a graphically driven approach for the assessment of trauma-related atrophy of white matter connections between cortical structures, with relevance to the quantification of TBI chronic case evolution. This approach allows one to inform the formulation of graphical neurophysiological and neuropsychological TBI profiles based on the particular structural deficits of the affected patient. In addition, it allows one to relate the findings supplied by our workflow to the existing body of research that focuses on the functional roles of the cortical structures being targeted. Agraphical means for representing patient TBI status is relevant to the emerging field of personalized medicine and to the investigation of neural atrophy.
Statistical Growth Modeling of Longitudinal DT-MRI for Regional Characterization of Early Brain Development|
N. Sadeghi, M.W. Prastawa, P.T. Fletcher, J.H. Gilmore, W. Lin, G. Gerig. In Proceedings of IEEE ISBI 2012, pp. 1507--1510. 2012.
A population growth model that represents the growth trajectories of individual subjects is critical to study and understand neurodevelopment. This paper presents a framework for jointly estimating and modeling individual and population growth trajectories, and determining significant regional differences in growth pattern characteristics applied to longitudinal neuroimaging data. We use non-linear mixed effect modeling where temporal change is modeled by the Gompertz function. The Gompertz function uses intuitive parameters related to delay, rate of change, and expected asymptotic value; all descriptive measures which can answer clinical questions related to growth. Our proposed framework combines nonlinear modeling of individual trajectories, population analysis, and testing for regional differences. We apply this framework to the study of early maturation in white matter regions as measured with diffusion tensor imaging (DTI). Regional differences between anatomical regions of interest that are known to mature differently are analyzed and quantified. Experiments with image data from a large ongoing clinical study show that our framework provides descriptive, quantitative information on growth trajectories that can be directly interpreted by clinicians. To our knowledge, this is the first longitudinal analysis of growth functions to explain the trajectory of early brain maturation as it is represented in DTI.