Conference Agenda

Tumor spheroids are pre-clinical cell culture systems for assessing the impact of combinatorial radio(chemo)therapy. In contrast to 2D-in-vitro-experiments, they exhibit therapeutically relevant in-vivo-like characteristics, from three-dimensional (3D) cell-cell and cell-matrix interactions to radial pathophysiological gradients related to proliferative activity and nutrient/oxygen supply, all altering cellular radioresponse. The analysis of 3D tumor spheroid assays comprises of reading out the growth kinetics from brightfield microscopy images taken every second day and of classifing the therapeutic outcome into the cases ,,controlled’’ (no growth recurrence) and ,,relapse’’ (growth recurrence). To assist in the required evaluation of up to several thousands of microscopy images per treatment arm and to give support in evaluating the effect mechanisms, we develop a (semi-) automated spheroid analysis pipeline. It integrates automated spheroid segmentation as well as classification of the therapeutic outcome based on statistical and machine learning algorithms with knowledge-driven mechanistic modelling. We present an efficient mathematical model for three-dimensional multicellular tumor spheroids, capable to explain experimental tumor spheroid growth data of several cell lines with and without radiotherapy, which facilitates efficient parameter calibration. The latter is accomplished since we effectively reduce computational cost by exploiting radial symmetry. We further demonstrate how this model can be integrated into a pipeline for automated 3D tumor spheroid analysis.

[1] Franke F, Michlikova S, Aland S, Kunz-Schughart LA, Voss-Böhme A, Lange S. Efficient Radial-Shell Model for 3D Tumor Spheroid Dynamics with Radiotherapy. Cancers 2023; 15(23):5645 doi:10.3390/cancers15235645

[2] Streller M, Michlikova S, Ciecior W, Lönnecke K, Kunz-Schughart LA, Lange S, Voss-Böhme A. Image segmentation of treated and untreated tumor spheroids by Fully Convolutional Networks. arXiv:2405.01105

Structural equation modeling (SEM) is a popular and widely applied method that predominantly models latent variables by means of common factor models. Yet, in recent years, the composite model has gained increasing research attention. In contrast to common factor models, approaches to estimate composite models are limited. We contribute a full-information maximum likelihood (ML) estimator for composite models. We present the general composite model including its model-implied variance-covariance matrix and derive a full-information ML approach to estimate the parameters of composite models. Moreover, a test is provided to assess the overall fit of composite models. To demonstrate the performance of the ML estimator and to compare it to its closest contender, i.e., partial least squares path modeling (PLS-PM), in finite samples, a Monte Carlo simulation is conducted. The Monte Carlo simulation reveals that, overall, the ML estimator performs well and is similar to PLS-PM in finite samples. Hence, under the considered conditions, the proposed estimator is a valid alternative with known superior statistical properties.

Linear models commonly employed in longitudinal data analysis often assume a multivariate normal distribution. However, the presence of outliers can introduce bias in estimating the mean parameter within these models. In response to this challenge, alternative linear models have been proposed, assuming either a multivariate t distribution or a multivariate Laplace distribution, known for their robustness in mean parameter estimation. This paper conducts a comprehensive review of existing multivariate linear models and introduces multivariate Laplace linear models tailored for analyzing multivariate longitudinal data in the presence of outliers. Additionally, we present methodologies for addressing the covariance matrix or scale matrix, utilizing modified Cholesky decomposition and hyperspace decomposition. The comparison of these models is facilitated through simulations and examples, aiming to provide insights into their appropriate utilization.