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.

Despite the increasing availability and reliability of artificial pancreas devices, many people with type 1 diabetes mellitus are still on multiple daily injections therapy consisting of a daily basal insulin injection and mealtime boluses. The use of an insulin bolus advisor may improve glycaemic control as well as reduce the burden of the disease on these patients. This paper investigates the application of an impulsive model predictive controller in a bolus advisor system. The bolus calculator is assessed in closed-loop simulations using different basal insulin scenarios. The simulations show that a model predictive controller can achieve good glycaemic control and may be suitable to give bolus recommendations to people with diabetes. Higher basal insulin levels can result in better times in the target range but also carry a higher risk of hypoglycemia.

Like many physiological systems, the various mathematical models describing the glucose-insulin system can only have non-negative inputs. Thus, the control method — often model predictive control in artificial pancreas systems—must provide a non-negative control signal. Existing solutions include saturation and constrained optimization. In this paper, we propose a dynamic extension of the patient model as a way of ensuring the positivity of the control signal, a method previously applied in tumor growth control. We evaluate the controller in a closed-loop simulation and compare the results with a controller using saturation. Our simulations show that control performance with the extended model can reach or exceed the performance achieved with saturation.

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.

Therapy optimization and personalization in cancer treatment requires reliable mathematical models. A key issue in personalization is the identification of the model parameters. We employ artificial neural networks to identify the model parameters based on few measurements using a priori information about the range of the parameters. The trainig data are generated in silico on known parameter intervals, taking into consideration the experimental setup we use to validate our results. The estimated parameters can be used to track the change of the parameters and can also be used as initial guesses for identification algorithms using local search.

Mathematical modeling of tumor growth dynamics may have great impact on modern medicine. The dynamical model of tumor growth which describes the effect of drugs can be used e.g., for therapy optimization, therapy supervision, drug development. Based on a single drug tumor growth model, we create a model that can be used to describe the effect of two drugs. The extended model is created using formal reaction kinetics analogy, thus the meaning of the equations is interpretable for experts not familiar with differential equations. We carry out parametric identification using nonlinear mixed-effect model, for the identification we use measurements from mice experiments carried out using bevacizumab and fluorouracil treatment. The results of the identification show that the measurements can be reproduced using the model with small error, and the interpatient variability for most of the parameters is relatively low.

A key research domain within self-driving vehicle technology is system safety. Current development efforts target Level 3 autonomy, where the vehicle controls both lateral and transversal motion of the dynamic driving task, while the driver is permitted to divert its attention, as long as s/he is able to react properly to a handover request. Situation awareness, describing the cognitive capabilities of the driver in that given instant, has become a key metric of a safe handover process. This paper proposes an experimental setup for handover studies using the CARLA driving simulator alongside the master console of the da Vinci Surgical System. This surgical master console offers a built-in display in a setup particularly suitable for the analysis of situation awareness, controllers and foot pedals. Steering wheel-like behavior of the arms was achieved using impedance control. The presented solution is open-source, and available at https://github.com/ABC-iRobotics/dvrk_carla.

The advantages of using advanced control techniques related to physiological applications are unquestionable as it was proven in many cases in the recent times. Although, there are several challenges that practitioners need to face. For example, the lack of precise information about the internal state of the patients, i.e. the inter-and intra-patient variabilities which cause uncertainties that need to be tolerated by the applied controllers. In this study an alternative solution is presented for control of tumor growth. Uncertainties and nonlinearities are handled by the applied Linear Parameter Varying (LPV) methodology completed by Tensor Product (TP) model transformation. Linear Matrix Inequalities (LMI) based optimization are used for controller design. The lack of information about the internal state is solved by using Extended Kalman Filter (EKF) to estimate the non-measurable state variables. The developed control structure is able to enforce the controlled system to behave as a predefined reference system. We show that the control framework operates well and reaches the determined aims of the control.

A general approach to solve the inverse kinematics problem of series manipulators, i.e. finding the required joint motions for the desired end effector motions, is based on the linear approximation of the forward kinematics map and discretization of the continuous problem. Due to the linearization, first velocities are calculated, so numerical integration needs to be done to get the joint variables. This general solution is just a numerical approximation, thus improving the tracking performance of the inverse kinematics algorithm is of great importance. The application of several numerical integration techniques (implicit Euler, explicit trapezoid, implicit trapezoid) is analyzed, and a fix point iteration is given that can be used to calculate implicit solutions. The tracking performance of the spatial inverse positioning problem of a spatial manipulator is analyzed by checking the tracking error in the desired direction (i.e. along the derivative of the desired end effector path) and in the plane perpendicular to the desired direction. The application of the explicit and implicit trapezoid methods yielded much better tracking performance in the directions orthogonal to the desired direction when the end effector had to track a linear path, while the tracking performance in the desired direction was similar for all the methods. Simulations showed that the application of implicit and second-order methods in the numerical integration may greatly improve the tracking performance of the closed-loop inverse kinematics algorithm.

In the medical practice, there are several methods to administer anti-cancer drugs. A commonly used method is the intermittent bolus doses (BD) administration when the patient receives drug on given days and the therapy has rest periods between the injections. The amount of bolus doses can be the maximum tolerated dose (MTD) or less. Anti-cancer drug can be administered in low doses over prolonged periods without extended rest periods which is called as low-dose metronomic therapy (LDM). In addition, continuous infusion therapy is applicable within clinical environment, not yet as a portable device. The major disadvantage of these methods is the empiricism associated with determining the optimal biologic dose (OBD). In order to solve the problem, we have designed discrete-time controllers which realize automated optimal treatments.

Tumor growth model identification under antiangiogenic therapy is a very current issue since the existing models in the literature have some limitations and usually they are not clinically validated. We have carried out animal experiments to observe valid data, mice were transplanted with C38 colon Aden carcinoma and they were treated with bevacizumab. Two groups were created, control group was treated according to the protocol, while case group members receive much lower doses daily. We created fixed and mixed models for the groups. Mixed models differs from fixed ones in random effects -- in the case of mixed models both the intercept and the slope are random variables. These models are appropriate when the aim is to model not the concrete subjects in the sample, but rather, to describe the imagined population from which the samples were coming.