Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method - a generalized cubic spline that can be used to model coordinate transformations - to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool - the Chip Invasion and Contour Analysis (ChICA) - to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.