In order to improve parameter identifiability in mathematical tumor models, we propose a Bayesian framework using Markov Chain Monte Carlo (MCMC) methods to fit pharmacodynamic parameters to in vitro tumor spheroid data. We conducted cytotoxicity experiments on Brca1-deficient murine mammary tumor cells, measured tumor volume changes via time-lapse fluorescence microscopy, and calibrated a modified tumor growth model to the resulting data using the No-U-Turn Sampler (NUTS) algorithm. Our results demonstrate that MCMC-based inference yields biologically meaningful posterior distributions, even under data uncertainty. We observe trends in parameter estimates across multiple drug concentrations and identify cases where parameter identifiability is limited. This approach offers a robust framework for model calibration and uncertainty quantification, which supports future efforts in therapy optimization based on in vitro experiments.

The future of healthcare increasingly depends on personalized treatments based on accurate modeling of patient-specific tumor dynamics. Tumor growth models play a key role in quantifying responses to chemotherapy. In preclinical studies, data collection is often constrained by ethical and practical limitations, resulting in sparse and heterogeneous measurements. Consequently, it is essential to extract the maximum possible information from the available data by focusing on model-consistent segments and minimizing the impact of measurement noise or biological variability that the model cannot capture. In this study, we estimate the parameters of an in vivo tumor model using nonlinear mixed-effects (NLME) modeling. A major challenge is that the mathematical model cannot describe resistant tumor phases, and NLME assumes inter-individual similarity, which may not hold in heterogeneous populations. Additionally, NLME fitting is sensitive to initial values, complicating the distinction between poor fit and poor initialization. In order to address these issues, we developed a multi-stage estimation workflow. We begin with a global NLME fit, followed by automatic exclusion of resistant segments and re-estimation on the trimmed data. Least squares fits are used to classify individuals into well- and poorly-fitting subgroups. Each group is then refitted using NLME with feedback-based parameter refinement. This approach improves estimation robustness and enables model-driven stratification that may reflect underlying biological heterogeneity.

Chemotherapy optimization based on mathematical models is a promising direction of personalized medicine. Personalizing, thus optimizing treatments, may have multiple advantages, from fewer side effects to lower costs. However, personalization is a complicated process in practice. We discuss a mathematical model of tumor growth and therapy optimization algorithms that can be used to personalize therapies. The therapy generation is based on the concept of keeping the drug level over a specified value. A mixed-effect model is used for parametric identification, and the doses are calculated using a two-compartment model for drug pharmacokinetics, and a nonlinear pharmacodynamics and tumor dynamics model. We propose personalized therapy generation algorithms for having a maximal effect and minimal effective doses. We handle inter-and intra-patient variability for the minimal effective dose therapy. Results from mouse experiments for the personalized therapy are discussed and the algorithms are compared to a generic protocol based on overall survival. The experimental results show that the introduced algorithms significantly increased the overall survival of the mice, demonstrating that by control engineering methods an efficient modality of cancer therapy may be possible.

With the advancement of technology and medicine, personalized therapies arise which may provide a promising solution for the problems of chemotherapy, such as many side effects. Personalized therapies can be applied that meet the individual needs of patients, this can make the healthcare of cancer patients safer and more cost-effective. However, personalized therapy requires a reliable model of tumor dynamics and the effect of the drug applied during the therapy. Examining the effect of certain drugs on in vitro cell cultures helps us to gain understanding of the drug mechanism and create pharmacodynamics models. In vitro experiments provide a more cost-effective, ethical and more controllable way to examine the effect of chemotherapeutic agents. In this work, we carried out parameter identification and validation of several versions of a tumor growth model based on in vitro cytotoxicity measurements in two-dimensional tumor cell cultures. In vitro experiments were carried out on Brcal– / –; p53 mice breast cancer cell line. The chemotherapeutic agents used were Doxil and Doxorubicin at different concentrations. Parameter identification was performed by fitting to data measured at 12 time points in 5 days. We examined how the presence or absence of necrotic rate n and an additional Hill coefficient affect the value of sum square error (SSE). We showed that the models that contain tumor cell necrosis and a general Hill function have the best performance for Doxil.