Download specific aims

Paul’s things for the Tumor Imaging Grant
SPECIFIC AIMS
…..
Specific Aim 2. (a) Mapping Patterns of Tumor Growth in 4D.
We will develop novel image analysis strategies
to map detailed patterns of growth in brain tumors, as they evolve over time. Detailed 3D maps will be created visualizing
the rates, principal directions, and quantitative statistics of growth. Specialized image matching algorithms will be
developed, allowing us to analyze and visualize tumor changes with unprecedented spatial and temporal sensitivity.
(b) Data Fusion for Correlation with Intraoperative Biopsy. We will develop, refine, and validate nonlinear image
registration tools, which will allow the digital overlay of pre-operative tumor maps and intra-operative imaging data. We
will use 3D elastic matching techniques to align maps of growth rates, preoperative diffusion imaging and parametric
MRI data with intraoperative image volumes. Stereotaxic mapping of biopsy sites will enable 3D correlation of pathologic
markers, genetic measures, and immunohistochemical data with dynamic maps and measures of tumor growth and
composition in the living patient.
(insert the next bit later in Experimental Design).
Mapping Tumor Growth in 4D. We will develop new computational strategies for mapping dynamic (4D) profiles of
tumor growth in individual patients. The goal will be to create detailed 3D models of brain tumors, visualizing the rates,
principal directions, and quantitative statistics of growth. Since tumor growth is typically quantified using simple area or
caliper measures (or in some cases, volumes), these maps of tumor growth (Fig. 1) will offer previously unobtainable
sensitivity in capturing the local details of the disease process. They will also allow the digital mapping of growth rates in
3 dimensional space. The resulting 3D images of growth will be aligned (Specific Aim 2(b)), using nonlinear registration,
with intraoperative images. This will allow direct comparison between growth in vivo and ex vivo molecular and
pathologic data.
Tumor Modeling.
Growth maps will be generated based on detailed 3D models of tumor geometry. These models
will be based on longitudinal series of images acquired from the same patient across several time points (at least two for
patients undergoing their first resection, and three for patients undergoing repeat surgery). As in our published work and
preliminary data (Haney et al., 2000, 2001a,b; Thompson et al., 2000), we will build detailed volumetric maps of tumor
components including contrast enhancement, necrosis, edema, cystic compartments and prior resection cavities (if
present). As in our prior work, we will use co-registered T1 contrast-enhanced and T2 MRI volumes to generate detailed
3D voxel maps of each of these tissue classes (Fig. 1). A Gaussian mixture tissue classifier will be used to estimate the
intensity mean and variance of each tissue class from 120 manually tagged points in the tissue volume. Having evaluated
unsupervised approaches, EM classifiers, and RBF neural network segmentation approaches in many brain imaging
studies, we prefer this approach as it is fast, reliable, and is also applicable to single-channel MR data (Sowell et al., 1999;
Thompson et al., 2001a,b). It has been extensively cross-validated by ourselves and others against manual data (Sowell et
al., 1999), and 3D parametric surface models derived by contouring the lesion classes in every image section (Haney et
al., 2000). The Bayesian maximum a posteriori (MAP) classification, which corresponds to the most likely segmentation
of the data, will be represented as an integer-valued image volume which is easily edited by digital overlay with the
patient’s co-registered multi-modality MR volumes. This classification is able to resove fine-scale details of tumor growth
not appreciable from the single time-point MR data (Fig. 2).
Surface Parameterization.
As in our on-going brain mapping and anatomical modeling projects (Thompson et al.,
1996a,b, 1997, 2000; Zhou et al., 1999), the surfaces of each tissue class will then be converted into 3D parametric mesh
format. This is a tiled polygonal data format that allows quantitative measures of tumor geometry, complexity, and surface
morphology to be generated. In simple cases (Thompson et al., 1996; Haney et al., 2000, 2001a), a single curvilinear mesh
will be imposed on the tissue elements (Fig. 3). If the geometry is more complex (i.e., multiple disconnected elements of
the same tissue in a single section), we will employ our recently developed voxel-coding approach to recover the surface
geometry (Zhou et al., 1999, 2000).
Tracking Change. The imposition of a regular parametric grid of the same type in each scan allows the association of
points on different surface models as they evolve dynamically over time. As in our prior studies tracking brain change in
development (Thompson et al., Nature, 2000), Alzheimer’s Disease (Thompson et al., 2001) and schizophrenia
(Thompson et al., 2001; Vidal et al., 2001), and initial tumor modeling experiments (Frew et al., 2000; Haney et al.,
2001b), we will build models of the tumor itself and adjacent anatomical structures. Depending on the adjacent anatomy
in the vicinity of the tumor, these will include the cerebral cortex, 3D parametric models of gyral/sulcal patterns,
hippocampus, lateral and/or 3rd ventricles, basal ganglia and diencephalon. These surfaces will then be used to generate a
model of brain change as follows.
Dense Maps of Deformational Change in Tumor and Surrounding Brain Tissues.
Brain change will be tracked
by formulated the evolution of anatomy across time as a 3D elastic matching problem, in which a complex 3D
deformation field is computed that matches large numbers of surface, curve, and point landmarks in the two brains to be
matched (see Thompson et al., 2000 for details, and a review of similar methods by other groups). This approach was
originally developed to map growth patterns in the brains of developing children with higher sensitivity than previous
studies (Thompson et al., 2000; Fig. 4). The process is also visualized in Fig. 5, where the profile of dynamic changes in a
patient with a recurrent glioblastoma multiforme are localized using 3D vector maps (Fig. 5). These maps illustrate the
magnitude and direction of tumor growth in an individual patient over time. To generate these maps, parametric mesh
models of brain structures will be used to drive a 3D deformation field u(x) which is derived from the Navier-Stokes
equilibrium equations for linear elasticity:
2u + (+)(Tu(x)) + F(x) = 0, xR
(1).
Here R is a discrete lattice representation of the scan to be transformed, Tu(x)=uj/xj is the divergence, or
cubical dilation of the medium, 2 is the Laplacian operator, F(x) is the internal force vector, and Lamé’s coefficients 
and  refer to the elastic properties of the medium. Matching of cortical surfaces across time, and tumor surfaces in which
curved and point landmarks are identifiable, requires a specialized approach. A parameterization-invariant variational
formulation will be used to minimize metric distortion when mapping one surface to another. If P and Q are cortical
surfaces with metric tensors gjk(ui) and hjk() in local coordinates ui and  (i, =1,2), the Dirichlet energy of the
mapping (u) is defined as:
E() =

P
e()(u) dP, where e()(u) = gij(u) (u)/ui (u)/uj h((u)),
(2)
and dP=(det[gij])du1du2. The Euler equations, whose solution (u) minimizes the mapping energy, are:
0 = L(i) = m=1 to 2 /um [(det[gru]) l=1 to 2 gmlur i/ul ] (i=1,2), (3)
(Thompson et al., 2000). The resulting (harmonic) map (1) minimizes the irregularity of the transformation from one
surface to the other, and (2) is again independent of the parameterizations (spherical or planar) used to represent each
surface computationally. By applying local operators to the deformation fields, tensor maps will be created to reflect the
magnitude and principal directions of tissue dilation or contraction, and the local rates, divergence and gradients of the
degenerative processes detected in the dynamically changing brain.
As shown in Figure 6, detailed maps and visualizations of growth rates, patterns of tissue shearing, dilation, contraction,
shape change, and morphometric statistics will be used to chart the disease process in individual subjects, for visualization
and subsequent pathologic correlation.
(b) Data Fusion with Intraoperative Image Volumes, for Pathology Correlation.
We will develop, refine, and
validate methods for 3D elastic image registration, or warping strategies, to compare and digitally overlay images and
maps of brain change with imaging data acquired intraoperatively. We have many years of experience in developing these
algorithms (Thompson et al., 1996, 1997a,b, 1998, 1999, 2000a,b,c, 2001; Fig. 7), although we have not previously
evaluated them in an intraoperative setting. The resulting fused maps of brain change will be represented in a coordinate
space that allows stereotaxically sampled biopsy data to be digitally correlated with maps of growth. Image matching
algorithms will be applied to recover deformational changes due to intraoperative brain shift and mechanical alterations in
tissue geometry during resection.
Retrospective Registration.
The initial goal is to perfect this registration off-line, i.e. retrospectively, allowing
detailed matching of anatomical boundaries. Subsequent improvements in nonlinear registration techniques will enable
real-time deformation correction, but in Phase I of the project our goal is maximal registration accuracy. The exact spatial
registration of biopsy samples and pre-operative growth mapping data for is paramount for tissue correlation, and for
accurate data fusion. The proposed data fusion technique aims to shed light on the relation between tissue growth and
pathologic markers, to elucidate the genetics and timing of tumor growth, and to help understand their evolution in a
dynamic framework.
{**continue with intraoperative methods, INSERT 6 figures**}
Figures:
1. Gaussian Mixture Classification 2. Dynamic Changes in 3D Tissue Maps 3. Parametric Mesh Modeling (a), (b) 4. Mapping Caudate Growth in a 7-11 year old Child
5. Tumor Vector Maps
6. Genetic Correlation 7. Elastic Matching Image, 3D MR data.