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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - Tamed Cancer (Personalized Cancer Therapy by Model-based Optimal Robust Control Algorithm)

Teaser

Summary

Medical treatment of diseases includes drug therapies that are specified by protocols. These protocols define the dosage of the drug. Optimized protocols can lead to reduced drug usage which eventuate cheaper therapies and less side effects, and can also lead to reduced recovery time. In the case of diseases where no cure is known, but the disease can be treated, optimized and automated treatments can greatly increase the quality of life of the patient. Automation can reduce human costs, side effects and the burden caused by treatment.
Our societies current, advanced technology is based on acquiring deeper knowledge about our world by mathematical modeling and using these mathematical models to create automated algorithms that can substitute and outperform human operators at many applications. Our ancestors envisaged that this technology may lead to social catastrophe since machines would take away jobs from humans, however, it turned out that these new technologies greatly improved the quality of life of humans, created many new jobs and fields, and also improved the efficiency of human workflows. Time proved that this technology can not replace the intuitive capabilities of the human mind, but it can efficiently complete human labor by solving highly complex (mostly mathematical) problems that are not adequate for the human thinking; moreover, it increased the knowledge level and education system of society as well. Our research focuses on using these techniques in medicine to create optimized therapies, focusing on tumor treatment. Such techniques can be applied either as a medical decision support system that gives recommendations about the doses to the oncologists based on the available data of a specific patient, or can be used in stand-alone devices like an insulin pump to continuously treat patients, thus eliminating the need of frequent visits to doctors or managing self-injections.
Our project contains three objectives which support to reach our long-term goals. Our first objective is to create a tumor growth model that describes the effect of the drug on the growth of the tumor. Creating a reliable tumor growth model is fundamental for the creation of optimal therapies, since all the algorithms are based on this model. In order to be sure we find the most suitable physiological model both for algorithm design and medical therapy, we develop more than one models by using different physiological, mathematical and mixed approaches. The model creation is carried out by collecting knowledge from experts and converting this knowledge into mathematical equations, and the results are validated by mice experiments. We carry out experiments only when they are unavoidable and do everything to minimize the suffering of the animals during these experiments.
Our second objective is to create optimal treatments that can be used globally as new optimized therapies (e.g., recommend a treatment protocol for a specific drug), or these treatments can be implemented in clinical decision support devices that provide patient specific recommendation of the doses. The underlying engineering problem is called discrete-time impulsive control, which is a relatively new field of engineering as well. Thus, this objective greatly contributes to the medical and engineering fields as well.
Our third objective is to create algorithms that can control stand-alone, wearable devices like an insulin pump that can provide continuous, unsupervised treatment of the patient. The engineering background of this problem is more grounded than that of the previous objective, however, there are some engineering problems specific to the treatment problem that are open research areas of control engineering science as well. The main problems are the positivity of the input, which is the result of the fact that we can only inject drug, but can not take it out from the patient; moreover, the differences between the patients and each specific cases must also be han

Work performed

We have developed tumor growth models for various applications. We created complex models that specify the development of the different regions of a tumor and the development of the blood vessels providing the tumor with nutrients. We have created a model with this level of specificity since our research focuses on drugs that inhibit the growth of the blood vessels that support the tumor. We have tested these models using the results from animal experiments and they proved to describe the effect of the drug sufficiently.
We have created general, minimal models as well that describe the most important phenomena and model the volume of the living and dead tumor cells and the level of the drug, not focusing on specific phenomena like the development of blood vessels. Our general model was tested based on experimental results with the drug inhibiting blood vessel formation (called bevacizumab) and also a chemotherapeutic drug (called Doxorubicin), and showed sufficient modeling capabilities for both therapies.
We have carried out experiments with the drug inhibiting blood vessel formation and the combination of this drug with chemotherapeutic drugs. We have applied the protocols used currently for human treatments (the dosages were converted from human to animal dosage), and compared them with protocols with reduced doses. The protocols with reduced doses showed good results with small tumor volume, however, the original protocol caused serious side effects. We have created an algorithm that can generate recommended dosage by using a mathematical model of the tumor growth. The medical doctor is able to specify the desired tumor volume for the next treatment occasion, and the algorithm calculates the optimal amount of drug required to reach the desired volume in the future. The algorithm is the first step towards a clinical support decision software, and will be further developed in the second part of the project by analyzing the effect of tumor-, patient- and drug specific parameters on the therapy.
We have developed control algorithms for the continuous control problem that can be used to control a wearable device. Our control algorithms focus on handling the differences among the patients. We are continuously developing these techniques to increase their efficiency. During drug delivery, the input can only be positive, i.e., we can not take out drug from the patient, only inject drug into the patient. Thus, we have elaborated a method which is able to incorporate this constraint into the mathematical equations, enabling us to design control algorithms that can handle positivity of the input efficiently.

Final results

Our models can describe the growth of tumor and also incorporate the pharmacodynamics of the drug. Most models in the literature describe the effect of the drug as linear, i.e., twice the amount of the drug has twice the effect on the tumor. However, in reality, this is only true for small drug levels; for high doses, the effect of the drug has a maximum (plateau). This phenomenon is described by the pharmacodynamics of the drug, which is incorporated into our models as well. Moreover, our general model can describe the effect of multiple drugs with significantly different mechanism.
Due to the best of our knowledge, our discrete-time therapy optimization algorithm is currently the only one in the literature. At the end of the project, it will be a well established technique with many supporting test cases. This algorithm creates optimal discrete-time impulsive control using a model. The algorithm proved to be efficient for medical protocol generation. In the second part of the project, we will develop this algorithm further to get better therapies.
In the continuous control problem we have developed a method that incorporates the positivity of the input into the modeling process, which is a novel technique in the control literature. We have also applied novel control methodologies for the tumor control problem. We are working on developing new techniques and combining existing ones to find the optimal algorithm for the tumor volume regulation problem.