# Dissertation/Thesis Abstract

Circulating Tumor Cells: Mathematical Theory of Detectability with Simulations and Experimental Results in a Model System
by Futia, Gregory Louis, Ph.D., University of Colorado at Denver, 2017, 171; 10682544
Abstract (Summary)

Circulating tumor cells (CTCs) are nucleated objects that are shed from a primary tumor into the blood stream. Effective identification of CTCs holds promise for improving early detection and disease monitoring of cancer but is difficult due to the rarity of CTCs compared to background blood cells.

In this dissertation, I develop mathematics describing how the rarity of cell that an assay can detect is limited by the sensitivity and specificity of the assay’s identifying biomarker to that cell. I refer to the rarity of cell that an assay can detect as detectable rarity. I show that depending on the distribution of disease positive and disease negative populations on an identifying biomarker there can be a maximum in detectable rarity as a function of the test positive-test negative cutoff position on that biomarker. Most CTC assays consist of 2 stages which are an enrichment stage followed by an image cytometry stage. I present mathematics describing how the sensitivity, specificity, and detectable rarity of a multistage tests relates to the sensitivity, specificity, and detectable rarity of the individual test stages.

The enriched output fraction typically contains between 1,000–10,000 cells. Difficulties in processing this cell fraction for image cytometry lies in (1) preventing cell loss in the numerous handling steps involved in labeling and mounting the cells and (2) controlling the area of the resulting cell field such that is neither too sparse or too dense. I present technology I have engineered that addresses point (1) by confining cells during the labeling process using a filter and addresses point (2) by allowing the size of the cell field to be set using standard o-rings and with diameters interchangeable using variable low cost alignment plates.

I assess the identification performance of adding lipid imaging to the standard DAPI, Cytokeratin, CD45 panel used to identify CTCs. I assess the identification performance of adding metrics of spatial second moment, spatial-frequency second moment, the product of spatial second moment and spatial-frequency second moment to simple total content metric. To perform this assessment, I use technology I engineered to prepare samples for image cytometry with fluorescent staining and antibody labeling DAPI, Bodipy (lipids), Cytokeratin and CD45. I perform this analysis in a model system of disease negative white blood cells and disease positive MCF7 cancer cells.

In this model system, I present my analysis of the four spatial features calculated on each of the four labels, providing a total of 16 biomarkers. The best performing of the 16 biomarkers produced an average separation of 3 standard deviations between disease positive (D+) and disease negative (D) populations and an average detectable rarity of ~1 in 200. I performed multivariable regression and feature selection to combine multiple biomarkers for increased performance and showed an average separation of 7 standard deviations between the D+ and D populations giving an average detectable rarity of ~1 in 480. Histograms and receiver operating characteristics (ROC) for these biomarker features and regressions are presented. I show methods to optimize for the maximum detectable rarity as a function of test positive-test negative cutoff position and apply this method for all biomarkers measured.

Indexing (document details)
 Advisor: Gibson, Emily A., Benninger, Richard KP Commitee: Behbakht, Kian, Schlaepfer, Isabel, Shandas, Robin School: University of Colorado at Denver Department: Bioengineering School Location: United States -- Colorado Source: DAI-B 79/03(E), Dissertation Abstracts International Source Type: DISSERTATION Subjects: Bioengineering, Optics, Immunology Keywords: Biomarkers, Circulating tumor cells, Image cyotmetry, Lipids, Microsocpy, Receiver operating characteristics (ROC) Publication Number: 10682544 ISBN: 978-0-355-51120-8