An integrative transcranial magnetic stimulation mapping technique using non-linear curve fitting

The aim of this study is to develop a new simple method for analyzing one-dimensional transcranial magnetic stimulation (TMS) mapping studies in humans. Motor evoked potentials (MEP) were recorded from the abductor pollicis brevis (APB) muscle during stimulation at nine different positions on the scalp along a line passing through the APB hot spot and the vertex. Non-linear curve fitting according to the Levenberg-Marquardt algorithm was performed on the averaged amplitude values obtained at all points to find the best-fitting symmetrical and asymmetrical peak functions. Several peak functions could be fitted to the experimental data. Across all subjects, a symmetric, bell-shaped curve, the complementary error function (erfc) gave the best results. This function is characterized by three parameters giving its amplitude, position, and width. None of the mathematical functions tested with less or more than three parameters fitted better. The amplitude and position parameters of the erfc were highly correlated with the amplitude at the hot spot and with the location of the center of gravity of the TMS curve. In conclusion, non-linear curve fitting is an accurate method for the mathematical characterization of one-dimensional TMS curves. This is the first method that provides information on amplitude, position and width simultaneously.

Classification and selection of biomarkers in genomic data using LASSO

High-throughput gene expression technologies such as microarrays have been utilized in a variety of scientific applications. Most of the work has been on assessing univariate associations between gene expression with clinical outcome (variable selection) or on developing classification procedures with gene expression data (supervised learning). We consider a hybrid variable selection/classification approach that is based on linear combinations of the gene expression profiles that maximize an accuracy measure summarized using the receiver operating characteristic curve. Under a specific probability model, this leads to consideration of linear discriminant functions. We incorporate an automated variable selection approach using LASSO. An equivalence between LASSO estimation with support vector machines allows for model fitting using standard software. We apply the proposed method to simulated data as well as data from a recently published prostate cancer study.

Fitting of Mixtures with Unspecified Number of Components Using Cross Validation Distance Estimate

Estimation of the number of mixture components (k) is an unsolved problem. Available methods for estimation of k include bootstrapping the likelihood ratio test statistics and optimizing a variety of validity functionals such as AIC, BIC/MDL, and ICOMP. We investigate the minimization of distance between fitted mixture model and the true density as a method for estimating k. The distances considered are Kullback-Leibler (KL) and “L sub 2”. We estimate these distances using cross validation. A reliable estimate of k is obtained by voting of B estimates of k corresponding to B cross validation estimates of distance. This estimation methods with KL distance is very similar to Monte Carlo cross validated likelihood methods discussed by Smyth (2000). With focus on univariate normal mixtures, we present simulation studies that compare the cross validated distance method with AIC, BIC/MDL, and ICOMP. We also apply the cross validation estimate of distance approach along with AIC, BIC/MDL and ICOMP approach, to data from an osteoporosis drug trial in order to find groups that differentially respond to treatment.

Fitting ACE Structural Equation Models to Case-Control Family Data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). To this end, we describe a ACE model for binary family data and then introduce an approach to fitting the model to case-control family data. The structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. Our likelihood-based approach to fitting involves conditioning on the proband’s disease status, as well as setting prevalence equal to a pre-specified value that can be estimated from the data themselves if necessary. Simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly-made assumptions hold. These assumptions include: the usual assumptions for the classic ACE and liability-threshold models; assumptions about shared family environment for relative pairs; and assumptions about the case-control family sampling, including single ascertainment. When our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Local targeting of malignant gliomas by the diffusible peptidic vector 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid-substance p

PURPOSE: Malignant glial brain tumors consistently overexpress neurokinin type 1 receptors. In classic seed-based brachytherapy, one to several rigid (125)I seeds are inserted, mainly for the treatment of small low-grade gliomas. The complex geometry of rapidly proliferating high-grade gliomas requires a diffusible system targeting tumor-associated surface structures to saturate the tumor, including its margins. EXPERIMENTAL DESIGN: We developed a new targeting vector by conjugating the chelator 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid to Arg(1) of substance P, generating a radiopharmaceutical with a molecular weight of 1,806 Da and an IC(50) of 0.88 +/- 0.34 nmol/L. Cell biological studies were done with glioblastoma cell lines. neurokinin type-1 receptor (NK1R) autoradiography was done with 58 tumor biopsies. For labeling, (90)Y was mostly used. To reduce the "cross-fire effect" in critically located tumors, (177)Lut and (213)Bi were used instead. In a pilot study, we assessed feasibility, biodistribution, and early and long-term toxicity following i.t. injection of radiolabeled 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid substance P in 14 glioblastoma and six glioma patients of WHO grades 2 to 3. RESULTS: Autoradiography disclosed overexpression of NK1R in 55 of 58 gliomas of WHO grades 2 to 4. Internalization of the peptidic vector was found to be specific. Clinically, the radiopharmeutical was distributed according to tumor geometry. Only transient toxicity was seen as symptomatic radiogenic edema in one patient (observation period, 7-66 months). Disease stabilization and/or improved neurologic status was observed in 13 of 20 patients. Secondary resection disclosed widespread radiation necrosis with improved demarcation. CONCLUSIONS: Targeted radiotherapy using diffusible peptidic vectors represents an innovative strategy for local control of malignant gliomas, which will be further assessed as a neoadjuvant approach.

NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).