Dániel András Drexler

Model-based angiogenic inhibition of tumor growth using modern robust control method

Cancer is one of the most destructive and lethal illnesses of the modern civilization. In the last decades, clinical cancer research shifted toward molecular targeted therapies which have limited side effects in comparison to conventional chemotherapy and radiation therapy. Antiangiogenic therapy is one of the most promising cancer treatment methods. The dynamical model for tumor growth under angiogenic stimulator/inhibitor control was posed by Hahnfeldt et al. in 1999; it was investigated and partly modified many times. In this paper, a modified version of the originally published model is used to describe a continuous infusion therapy. In order to generalize individualized therapies a robust control method is proposed using H(∞) methodology. Uncertainty weighting functions are determined based on the real pathophysiological case and simulations are performed on different tumor volumes to demonstrate the robustness of the proposed method.

Model-Based Analysis and Synthesis of Tumor Growth under Angiogenic Inhibition: A Case Study

Abstract Anti-angiogenic therapy is a promising method to fight cancer, however the special therapeutic drugs applied are quite expensive. The aim of this paper is to define simple therapeutical guidelines for sufficient treatment with the usage of the least amount of drugs possible with the help of control theory. We analyze a nonlinear tumor growth model, and use optimal control to design Linear Quadratic controller for offline simulations. The linear model is gained by working point linearization, after the examination of the possible operation points.

Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy

Background Bevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol. Materials and Methods We have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis. Results In the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model. Conclusion Our results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration.

Flat control of tumor growth with angiogenic inhibition

Cancer represents nowadays one of the most destructive and lethal illnesses of our civilization. In the last decades, clinical cancer research shifted towards molecular targeted therapies which have limited side effects in comparison to conventional chemotherapy and radiation therapy. Antiangiogenic therapy is proved to be one of the most promising cancer treatment methods. This paper concerns on the model-based control of tumor growth under angiogenic inhibition. The tumor growth model is nonlinear, augmented with a linear model representing the pharmacokinetics of the applied inhibitor in tumor treatment. The control strategy is based on feedback linearization and path tracking. The result are compared with other, basically linear control strategies which were previously published by our group.

Modeling and optimal control strategies of diseases with high public health impact

This paper summarizes the results of research tasks in the field of physiological modeling and control of diseases with high public health impact carried out by the Biomedical Engineering Laboratory of the Budapest University of Technology and Economics. The developed and presented optimal algorithms and strategies focus on three diseases with high public health impact diabetes (the question of artificial pancreas), obesity (predicting obesity-related risks) and cancer (antiangiogenic chemotherapy). The studies are done together with different Hungarian hospitals, from where measurement data were obtained.

Model-Based Angiogenic Inhibition of Tumor Growth Using Modern Robust Control Method

Abstract Cancer is one of the most destructive and lethal illnesses of the modern civilization. In the last decades, clinical cancer research shifted towards molecular targeted therapies which have limited side effects in comparison to conventional chemotherapy and radiation therapy. Anti-angiogenic therapy is one of the most promising cancer treatment methods. The dynamical model for tumor growth under angiogenic stimulator/inhibitor control was posed by Hahnfeldt et al. (1999), and it was investigated and partly modified many times. In this paper, a modified version of the originally published model is used in order to describe a continuous infusion therapy. To generalize individualized therapies a robust control method is proposed using ℋ ∞ methodology. Uncertainty weighting functions are determined based on the real pathophysiological case and simulations are performed on different tumor volumes to demonstrate the robustness of the proposed method.

Global controllability of chemical reactions

Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global controllability properties of chemical reactions are analyzed here based on the Lie-algebra of the vector fields associated to the reaction steps. A chemical reaction is controllable almost everywhere if all the reaction rate coefficients can be used as control inputs. The problem where one can not control all the reaction rate coefficients is also analyzed. The reaction steps whose reaction rate coefficients need to be control inputs are identified. A general definition of consecutive reactions is given, and it turns out that they are controllable almost everywhere by using the reaction rate coefficient of only one reaction step as control input.

Tumor growth model identification and analysis in case of C38 colon adenocarcinoma and B16 melanoma

Cancer fighting treatments are expanding, and a promising type, targeted molecular therapies have a new approach. The aim of these therapies is not to eliminate the whole tumor, but to control the tumor into a given state and keep it there. Explicit knowledge of tumor growth dynamics and the effects of targeted molecular therapies is crucial in tumor treatment development. We show the results of mouse experiments where tumor growth was investigated in case of C38 colon adenocarcinoma and B16 melanoma. Several curves were fitted and tumor growth dynamics was examined. Three attributes of tumor were measured: tumor volume, tumor mass and vascularization; and tumor growth dynamics was examined. Tumor volume was measured with digital caliper, vascularization was investigated with CD31 antibody immunohistochemistry staining on frozen sections. The relationship between these tumor attributes were examined with linear regression analysis. The dynamics of tumor growth was identified as a second order linear system.

Regularized Jacobian for the differential inverse positioning problem of serial revolute joint manipulators

Singular configurations arise in the kinematics of revolute joint manipulators, and cause problems in solving the inverse kinematics problem. General inverse kinematics schemes are based on the Jacobian of the forward kinematics map of the manipulator, that becomes ill-conditioned in singular configurations, causing numerical instability and loss of direction of motion. This work proposes a method, that regularizes the Jacobian in the case of singularities in the inverse positioning problem. The Jacobian regularization is based on transforming the acting point of the motion generators of the robot. The existance of a regularizing vector is proved for a 2 degrees of freedom planar subassembly, and the effect of regularization is analyzed.

Model-based angiogenic inhibition of tumor growth using feedback linearization

In the last decades beside conventional cancer treatment methods, molecular targeted therapies show prosperous results. These therapies have limited side-effects, and in comparison to chemotherapy, tumorous cells show lower tendency of becoming resistant to the applied antiangiogenic drugs. In clinical research, antiangiogenic therapy is one of the most promising cancer treatment methods. Using a simplified model of the reference dynamical model for tumor growth under angiogenic inhibition from the literature, exact linearization is performed in the paper to handle the nonlinear behavior of the model. Two different control methods are applied on the linearized model: flat control and switching control. Simulations are performed on the nonlinear model to show the characteristics of the therapies carried out using the presented control methods.