Tumor growth models are important to create an engineering background for cancer treatment either by using the models for simulations and evaluation of treatment protocols or, if combined with control engineering, by designing treatment protocols. A well-defined tumor growth model must describe the physiological processes and the measurements as well. Growing tumors are composed of dead tumor cells (forming the necrotic part) and living, proliferating tumor cells (forming the proliferating part); when tumor volume is measured, these parts are measured together. Most of the known tumor growth models do not consider the modeling of the necrotic part. Starting from a minimal model of the tumor growth under bevacizumab treatment, the aim of the current research is to extend it incorporating the volume and dynamics of the necrotic part and the pharmacodynamics and mixed-order pharmacokinetics of the applied drug. The extended model is validated using measurements with mice as hosts, colon adenocarcinoma as tumor, and bevacizumab as the drug used for treatment. The results show that the extended model can describe the important physiological phenomena and shows a good fit to the average of the measurements.

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.

One challenging aspect of therapy optimization and application of control algorithms in the field of tumor growth modeling is the limited number of measurable physiological signals—state variables—and the knowledge of model parameters. A possible solution to provide such information is the application of observer or state estimator. One of the most widely applied estimators for nonlinear problems is the extended Kalman filter (EKF). In this study, a moving horizon estimation (MHE)-based observer is developed and compared to an optimized EKF. The observers utilize a third-order tumor growth model. The performance of the observers is tested on measurements gathered from a laboratory mice trial using chemotherapeutic drug. The proposed MHE is designed to be suitable for closed-loop applications and yields simultaneous state and parameter estimation.

Joint Constrained Differential Inverse Kinematics Algorithm for Serial Manipulators

Cancer prevention and treatment is one of the most significant public health challenges of the 21st century. Cancer is a serious health problem, and it is the second leading cause of death following cardiovascular diseases. This requires a reliable virtual patient model, which is usually created based on animal studies that precede human studies. Preclinical drug testing often involves mouse experiments, where tumors are implanted under the skin. Up until now, the most widespread tumor measurement method is caliper measurement, which involves a large measurement error, especially if the tumor is small. We present a noise model that can be used to model the measurement noise in animal experiments where tumor size is measured with calipers. Accurate in silico measurement is essential, as animal studies are costly, time-consuming, and strictly regulated. By incorporating a noise model, in silico experiments can better reflect real-world measurement uncertainties, improving experimental reproducibility and the reliability of virtual patient modeling. In order to model the noise, we use data from preclinical experiments measured using MRI and digital calipers, and we use a nonlinear transformation to whiten the noise. Finally, based on the Anderson-Darling test, we find the distributions that fit the noise best. We show that virtually generated measurements based on the noise model produce similar results to the original measurement noise, thus the noise model can be used to create virtual patients and model realistic experimental setups for in silico experiments.