Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Brain fiber tract plasticity in experimental spinal cord injury: diffusion tensor imaging.

Diffusion tensor imaging (DTI) and immunohistochemistry were performed in spinal cord injured rats to understand the basis for activation of multiple regions in the brain observed in functional magnetic resonance imaging (fMRI) studies. The measured fractional anisotropy (FA), a scalar measure of diffusion anisotropy, along the region encompassing corticospinal tracts (CST) indicates significant differences between control and injured groups in the 3 to 4 mm area posterior to bregma that correspond to internal capsule and cerebral peduncle. Additionally, DTI-based tractography in injured animals showed increased number of fibers that extend towards the cortex terminating in the regions that were activated in fMRI. Both the internal capsule and cerebral peduncle demonstrated an increase in GFAP-immunoreactivity compared to control animals. GAP-43 expression also indicates plasticity in the internal capsule. These studies suggest that the previously observed multiple regions of activation in spinal cord injury are, at least in part, due to the formation of new fibers.

The design and evaluation of a 2D dose verification system for intensity modulated radiotherapy

The usage of intensity modulated radiotherapy (IMRT) treatments necessitates a significant amount of patient-specific quality assurance (QA). This research has investigated the precision and accuracy of Kodak EDR2 film measurements for IMRT verifications, the use of comparisons between 2D dose calculations and measurements to improve treatment plan beam models, and the dosimetric impact of delivery errors. New measurement techniques and software were developed and used clinically at M. D. Anderson Cancer Center. The software implemented two new dose comparison parameters, the 2D normalized agreement test (NAT) and the scalar NAT index. A single-film calibration technique using multileaf collimator (MLC) delivery was developed. EDR2 film's optical density response was found to be sensitive to several factors: radiation time, length of time between exposure and processing, and phantom material. Precision of EDR2 film measurements was found to be better than 1%. For IMRT verification, EDR2 film measurements agreed with ion chamber results to 2%/2mm accuracy for single-beam fluence map verifications and to 5%/2mm for transverse plane measurements of complete plan dose distributions. The same system was used to quantitatively optimize the radiation field offset and MLC transmission beam modeling parameters for Varian MLCs. While scalar dose comparison metrics can work well for optimization purposes, the influence of external parameters on the dose discrepancies must be minimized. The ability of 2D verifications to detect delivery errors was tested with simulated data. The dosimetric characteristics of delivery errors were compared to patient-specific clinical IMRT verifications. For the clinical verifications, the NAT index and percent of pixels failing the gamma index were exponentially distributed and dependent upon the measurement phantom but not the treatment site. Delivery errors affecting all beams in the treatment plan were flagged by the NAT index, although delivery errors impacting only one beam could not be differentiated from routine clinical verification discrepancies. Clinical use of this system will flag outliers, allow physicists to examine their causes, and perhaps improve the level of agreement between radiation dose distribution measurements and calculations. The principles used to design and evaluate this system are extensible to future multidimensional dose measurements and comparisons. ^

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^