Towards Personalized Prostate Cancer Therapy Using Delta-Reachability Analysis

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ $\delta$-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for personalized cancer therapy.Comment: HSCC 201

An evolutionary-type model for tumor immunotherapy

In this paper we propose a new dynamical model for describing the interactions between immune and tumor cells. This model captures the effects of the tumor cells on the immune system and viceversa, through predator-prey competition terms. Additionally, it incorporates the immune system's mechanism to produce hunting immune cells, which makes the model suitable for immunotherapy strategies analysis and design. Consequently, we propose an approach based on Lyapunov functions in order to compute domains of attraction of equilibria of interes

A Systems Biology Approach in Therapeutic Response Study for Different Dosing Regimens—a Modeling Study of Drug Effects on Tumor Growth using Hybrid Systems

Motivated by the frustration of translation of research advances in the molecular and cellular biology of cancer into treatment, this study calls for cross-disciplinary efforts and proposes a methodology of incorporating drug pharmacology information into drug therapeutic response modeling using a computational systems biology approach. The objectives are two fold. The first one is to involve effective mathematical modeling in the drug development stage to incorporate preclinical and clinical data in order to decrease costs of drug development and increase pipeline productivity, since it is extremely expensive and difficult to get the optimal compromise of dosage and schedule through empirical testing. The second objective is to provide valuable suggestions to adjust individual drug dosing regimens to improve therapeutic effects considering most anticancer agents have wide inter-individual pharmacokinetic variability and a narrow therapeutic index. A dynamic hybrid systems model is proposed to study drug antitumor effect from the perspective of tumor growth dynamics, specifically the dosing and schedule of the periodic drug intake, and a drug’s pharmacokinetics and pharmacodynamics information are linked together in the proposed model using a state-space approach. It is proved analytically that there exists an optimal drug dosage and interval administration point, and demonstrated through simulation study

Topics in perturbation analysis for stochastic hybrid systems

Control and optimization of Stochastic Hybrid Systems (SHS) constitute increasingly active fields of research. However, the size and complexity of SHS frequently render the use of exhaustive verification techniques prohibitive. In this context, Perturbation Analysis techniques, and in particular Infinitesimal Perturbation Analysis (IPA), have proven to be particularly useful for this class of systems. This work focuses on applying IPA to two different problems: Traffic Light Control (TLC) and control of cancer progression, both of which are viewed as dynamic optimization problems in an SHS environment. The first part of this thesis addresses the TLC problem for a single intersection modeled as a SHS. A quasi-dynamic control policy is proposed based on partial state information defined by detecting whether vehicle backlogs are above or below certain controllable threshold values. At first, the threshold parameters are controlled while assuming fixed cycle lengths and online gradient estimates of a cost metric with respect to these controllable parameters are derived using IPA techniques. These estimators are subsequently used to iteratively adjust the threshold values so as to improve overall system performance. This quasi-dynamic analysis of the TLC\ problem is subsequently extended to parameterize the control policy by green and red cycle lengths as well as queue content thresholds. IPA estimators necessary to simultaneously control the light cycles and thresholds are rederived and thereafter incorporated into a standard gradient based scheme in order to further ameliorate system performance. In the second part of this thesis, the problem of controlling cancer progression is formulated within a Stochastic Hybrid Automaton (SHA) framework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, an integrative closed-loop framework is proposed for describing the progressive development of cancer and determining optimal personalized therapies. First, the problem of cancer heterogeneity is addressed through a novel Mixed Integer Linear Programming (MILP) formulation that integrates somatic mutation and gene expression data to infer the temporal sequence of events from cross-sectional data. This formulation is tested using both simulated data and real breast cancer data with matched somatic mutation and gene expression measurements from The Cancer Genome Atlas (TCGA). Second, the use of basic IPA techniques for optimal personalized cancer therapy design is introduced and a methodology applicable to stochastic models of cancer progression is developed. A case study of optimal therapy design for advanced prostate cancer is performed. Given the importance of accurate modeling in conjunction with optimal therapy design, an ensuing analysis is performed in which sensitivity estimates with respect to several model parameters are evaluated and critical parameters are identified. Finally, the tradeoff between system optimality and robustness (or, equivalently, fragility) is explored so as to generate valuable insights on modeling and control of cancer progression

Hybrid Modeling of Cancer Drug Resistance Mechanisms

Cancer is a multi-scale disease and its overwhelming complexity depends upon the multiple interwind events occurring at both molecular and cellular levels, making it very difficult for therapeutic advancements in cancer research. The resistance to cancer drugs is a significant challenge faced by scientists nowadays. The roots of the problem reside not only at the molecular level, due to multiple type of mutations in a single tumor, but also at the cellular level of drug interactions with the tumor. Tumor heterogeneity is the term used by oncologists for the involvement of multiple mutations in the development of a tumor at the sub-cellular level. The mechanisms for tumor heterogeneity are rigorously being explored as a reason for drug resistance in cancer patients. It is important to observe cell interactions not only at intra-tumoral level, but it is also essential to study the drug and tumor cell interactions at cellular level to have a complete picture of the mechanisms underlying drug resistance. The multi-scale nature of cancer drug resistance problem require modeling approaches that can capture all the multiple sub-cellular and cellular interaction factors with respect to dierent scales for time and space. Hybrid modeling offers a way to integrate both discrete and continuous dynamics to overcome this challenge. This research work is focused on the development of hybrid models to understand the drug resistance behaviors in colorectal and lung cancers. The common thing about the two types of cancer is that they both have dierent mutations at epidermal growth factor receptors (EGFRs) and they are normally treated with anti-EGFR drugs, to which they develop resistances with the passage of time. The acquiring of resistance is the sign of relapse in both kind of tumors. The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb). A hybrid model is proposed for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. The colorectal tumor hybrid model is represented as a single state automata, which shows tumor progression and evolution by means of mathematical equations for tumor sub-populations, immune system components and drugs for the treatment. The drug introduction is managed as a discrete step in this model. To evaluate the drug performance on a tumor, equations for two types of tumors cells are developed, i.e KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It is observed that even a minimal initial concentration of KRAS mutated cells before the treatment has the ability to make the tumor refractory to the treatment. Moreover, a small population of KRAS mutated cells has a strong influence on a large number of wild-type cells by making them resistant to chemotherapy. Patient's immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them. Lung cancer is more complicated then colorectal cancer because of acquiring of multiple resistances to anti-EGFR drugs. The appearance of EGFR T790M and KRAS mutations makes tumor resistant to a geftinib and AZD9291 drugs, respectively. The hybrid model for lung cancer consists of two non-resistant and resistant states of tumor. The non-resistant state is treated with geftinib drug until resistance to this drug makes tumor regrowth leading towards the resistant state. The resistant state is treated with AZD9291 drug for recovery. In this model the complete resistant state due to KRAS mutations is ignored because of the unavailability of parameter information and patient data. Each tumor state is evaluated by mathematical differential equations for tumor growth and progression. The tumor model consists of four tumor sub-population equations depending upon the type of mutations. The drug administration in this model is also managed as a discrete step for exact scheduling and dosages. The parameter values for the model are obtained by experiments performed in the laboratory. The experimental data is only available for the tumor progression along with the geftinib drug. The model is then fine tuned for obtaining the exact tumor growth patterns as observed in clinic, only for the geftinib drug. The growth rate for EGFR T790M tumor sub-population is changed to obtain the same tumor progression patterns as observed in real patients. The growth rate of mutations largely depends upon the immune system strength and by manipulating the growth rates for different tumor populations, it is possible to capture the factor of immune strength of the patient. The fine tuned model is then used to analyze the effect of AZD9291 drug on geftinib resistant state of the tumor. It is observed that AZD9291 could be the best candidate for the treatment of the EGFR T790M tumor sub-population. Hybrid modeling helps to understand the tumor drug resistance along with tumor progression due to multiple mutations, in a more realistic way and it also provides a way for personalized therapy by managing the drug administration in a strict pattern that avoid the growth of resistant sub-populations as well as target other populations at the same time. The only key to avoid relapse in cancer is the personalized therapy and the proposed hybrid models promises to do that

Applications of Boolean modelling to study and stratify dynamics of a complex disease

Interpretation of omics data is needed to form meaningful hypotheses about disease mechanisms. Pathway databases give an overview of disease-related processes, while mathematical models give qualitative and quantitative insights into their complexity. Similarly to pathway databases, mathematical models are stored and shared on dedicated platforms. Moreover, community-driven initiatives such as disease maps encode disease-specific mechanisms in both computable and diagrammatic form using dedicated tools for diagram biocuration and visualisation. To investigate the dynamic properties of complex disease mechanisms, computationally readable content can be used as a scaffold for building dynamic models in an automated fashion. The dynamic properties of a disease are extremely complex. Therefore, more research is required to better understand the complexity of molecular mechanisms, which may advance personalized medicine in the future. In this study, Parkinson’s disease (PD) is analyzed as an example of a complex disorder. PD is associated with complex genetic, environmental causes and comorbidities that need to be analysed in a systematic way to better understand the progression of different disease subtypes. Studying PD as a multifactorial disease requires deconvoluting the multiple and overlapping changes to identify the driving neurodegenerative mechanisms. Integrated systems analysis and modelling can enable us to study different aspects of a disease such as progression, diagnosis, and response to therapeutics. Therefore, more research is required to better understand the complexity of molecular mechanisms, which may advance personalized medicine in the future. Modelling such complex processes depends on the scope and it may vary depending on the nature of the process (e.g. signalling vs metabolic). Experimental design and the resulting data also influence model structure and analysis. Boolean modelling is proposed to analyse the complexity of PD mechanisms. Boolean models (BMs) are qualitative rather than quantitative and do not require detailed kinetic information such as Petri nets or Ordinary Differential equations (ODEs). Boolean modelling represents a logical formalism where available variables have binary values of one (ON) or zero (OFF), making it a plausible approach in cases where quantitative details and kinetic parameters 9 are not available. Boolean modelling is well validated in clinical and translational medicine research. In this project, the PD map was translated into BMs in an automated fashion using different methods. Therefore, the complexity of disease pathways can be analysed by simulating the effect of genomic burden on omics data. In order to make sure that BMs accurately represent the biological system, validation was performed by simulating models at different scales of complexity. The behaviour of the models was compared with expected behavior based on validated biological knowledge. The TCA cycle was used as an example of a well-studied simple network. Different scales of complex signalling networks were used including the Wnt-PI3k/AKT pathway, and T-cell differentiation models. As a result, matched and mismatched behaviours were identified, allowing the models to be modified to better represent disease mechanisms. The BMs were stratified by integrating omics data from multiple disease cohorts. The miRNA datasets from the Parkinson’s Progression Markers Initiative study (PPMI) were analysed. PPMI provides an important resource for the investigation of potential biomarkers and therapeutic targets for PD. Such stratification allowed studying disease heterogeneity and specific responses to molecular perturbations. The results can support research hypotheses, diagnose a condition, and maximize the benefit of a treatment. Furthermore, the challenges and limitations associated with Boolean modelling in general were discussed, as well as those specific to the current study. Based on the results, there are different ways to improve Boolean modelling applications. Modellers can perform exploratory investigations, gathering the associated information about the model from literature and data resources. The missing details can be inferred by integrating omics data, which identifies missing components and optimises model accuracy. Accurate and computable models improve the efficiency of simulations and the resulting analysis of their controllability. In parallel, the maintenance of model repositories and the sharing of models in easily interoperable formats are also important