Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis.

Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results.

Mathematical modeling of tumor growth, drug-resistance, toxicity, and optimal therapy design.

The combination of mathematical modeling and optimal control techniques holds great potential for quantitatively describing tumor progression and optimal treatment planning. Hereby, we use a Gompertz-type growth law and a pharmacokinetic-pharmacodynamic approach for modeling the effects of drugs on tumor progression in tumor bearing mice, and we combine these in order to design optimal therapeutic patterns. Specifically, we describe colon cancer progression in both untreated mice as well as mice treated with widely used anticancer agents. We also present a pharmacokinetic model to describe the kinetics of drugs in the body as well as detailed toxicity models to describe the severity of side effects. Finally, we propose a promising methodology by which cancer progression in mice with drug resistance can be controlled. By using optimal control, we demonstrate that the optimal planning of the frequency and magnitude of treatment interruptions is key to the control of cancer progression in subjects with resistance and should be further investigated in an experimental setting, which is currently underway.

Taking a break from chemotherapy to fight drug-resistance: The cases of cancer and HIV/AIDS.

In this work, we present how optimized treatment interruptions during chemotherapy may be used to control drug-resistance, a major challenge for clinicians worldwide. Specifically, we examine resistance in cancer and HIV/AIDS. For each disease, we use mathematical models alongside real data to represent the respective complex biological phenomena and optimal control algorithms to design optimized treatment schedules aiming at controlling disease progression and patient death. In both diseases, it is shown that the key to controlling resistance is the optimal management of the frequency and magnitude of treatment interruptions as a way to facilitate the interplay between the competitive resistant/sensitive strains.