Applications of Deep Learning to Differential Equation Models in Oncology

The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly differential equation-based models, have had great success in various biological applications, including modelling bacterial growth, disease propagation, and tumour spread. However, these approaches can be somewhat limited due to their reliance on known parameter values, initial conditions, and boundary conditions, which can dull their applicability. Furthermore, their forms are directly tied to mechanistic phenomena, making these models highly explainable, but also requiring a comprehensive understanding of the underlying dynamics before modelling the system. On the other hand, machine learning models typically require less prior knowledge of the system but require a significant amount of data for training. Although machine learning models can be more flexible, they tend to be black boxes, making them difficult to interpret. Hybrid models, which combine conventional and machine learning approaches, have the potential to achieve the best of both worlds. These models can provide explainable outcomes while relying on minimal assumptions or data. An example of this is physics-informed neural networks, a novel deep learning approach that incorporates information from partial differential equations into the optimization of a neural network. This hybrid approach offers significant potential in various contexts where differential equation models are known, but data is scarce or challenging to work with. Precision oncology is one such field. This thesis employs hybrid conventional/machine learning models to address problems in cancer medicine, specifically aiming to advance personalized medicine approaches. It contains three projects. In the first, a hybrid approach is used to make patient-specific characterizations of brain tumours using medical imaging data. In the second project, a hybrid approach is employed to create subject-specific projections of drug-carrying cancer nanoparticle accumulation and intratumoral interstitial fluid pressure. In the final project, a hybrid approach is utilized to optimize radiation therapy scheduling for tumours with heterogeneous cell populations and cancer stem cells. Overall, this thesis showcases several examples of how quantitative tools, particularly those involving both conventional and machine learning approaches, can be employed to tackle challenges in oncology. It further supports the notion that the continued integration of quantitative tools in medicine is a key strategy in addressing problems and open questions in healthcare

Robust network calibration and therapy design in systems biology

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 115-123).Mathematical modeling of biological networks is under active research, receiving attention for its ability to quantitatively represent the modeler's systems-level understanding of network functionalities. Computational methods that enhance the usefulness of mathematical models are thus being increasingly sought after, as they face a variety of difficulties that originate from limitations in model accuracy and experimental precision. This thesis explores robust optimization as a tool to counter the effects of these uncertainty-based difficulties in calibrating biological network models and in designing protocols for cancer immunotherapy. The robust approach to network calibration and therapy design aims to account for the worst-case uncertainty scenario that could threaten successful determination of network parameters or therapeutic protocols, by explicitly identifying and sampling the region of potential uncertainties corresponding to worst-case. Through designating individual numerical ranges that uncertain model parameters are each expected to lie within, the region of uncertainties is defined as a hypercube that encompasses a particular uncertainty range along each of its dimensions. For investigating its applicability to parameter estimation, the performance of the optimization method that embodies this robust approach is examined in the context of a model of a unit belonging to the mitogen-activated protein kinase pathway. For its significance in therapeutic design, the method is applied to both a canonical mathematical model of the tumor-immune system and a model specific to treating superficial bladder cancer with Bacillus Calmette-Guirin, which have both been selected to examine the plausibility of applying the method to either discrete-dose or continuous-dose administrations of immunotherapeutic agents. The robust optimization method is evaluated against a standard optimization method by comparing the relative robustness of their respective estimated parameters or designed therapies. Further analysis of the results obtained using the robust method points to properties and limitations, and in turn directions for improvement, of existing models and design frameworks for applying the robust method to network calibration and protocol design. An alternative mathematical formulation to solving the worst-case optimization problem is also studied, one that replaces the sampling process of the previous method with a linearization of the objective function's parameter space over the region of uncertainties. This formulation's relative computational efficiency additionally gives rise to a novel approach to experimental guidance directed at improving modeling efforts under uncertainties, which may potentially further fuel the advancement of quantitative systems biological research.by Bo S. Kim.Ph.D

Personalized Decision Modeling for Intervention and Prevention of Cancers

Personalized medicine has been utilized in all stages of cancer care in recent years, including the prevention, diagnosis, treatment and follow-up. Since prevention and early intervention are particularly crucial in reducing cancer mortalities, personalizing the corresponding strategies and decisions so as to provide the most appropriate or optimal medical services for different patients can greatly improve the current cancer control practices. This dissertation research performs an in-depth exploration of personalized decision modeling of cancer intervention and prevention problems. We investigate the patient-specific screening and vaccination strategies for breast cancer and the cancers related to human papillomavirus (HPV), representatively. Three popular healthcare analytics techniques, Markov models, regression-based predictive models, and discrete-event simulation, are developed in the context of personalized cancer medicine. We discuss multiple possibilities of incorporating patient-specific risk into personalized cancer prevention strategies and showcase three practical examples. The first study builds a Markov decision process model to optimize biopsy referral decisions for women who receives abnormal breast cancer screening results. The second study directly optimizes the annual breast cancer screening using a regression-based adaptive decision model. The study also proposes a novel model selection method for logistic regression with a large number of candidate variables. The third study addresses the personalized HPV vaccination strategies and develops a hybrid model combining discrete-event simulation with regression-based risk estimation. Our findings suggest that personalized screening and vaccination benefit patients by maximizing life expectancies and minimizing the possibilities of dying from cancer. Preventive screening and vaccination programs for other cancers or diseases, which have clearly identified risk factors and measurable risk, may all benefit from patient-specific policies

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Mathematical analysis for tumor growth model of ordinary differential equations

Special functions occur quite frequently in mathematical analysis and lend itself rather frequently in physical and engineering applications. Among the special functions, gamma function seemed to be widely used. The purpose of this thesis is to analyse the various properties of gamma function and use these properties and its definition to derive and tackle some integration problem which occur quite frequently in applications. It should be noted that if elementary techniques such as substitution and integration by parts were used to tackle most of the integration problems, then we will end up with frustration. Due to this, importance of gamma function cannot be denied

Healthcare Logistics: the art of balance

Healthcare management is a very complex and demanding business. The pro - cesses involved – operational, tactical and strategic – are extremely divers, sophisticated, and we see medical-technological advancements following on each other’s heels at breathtaking speed. And then there is the constant great pressure exerted from many sides: ever-increasing needs and demands from patients and society, thinking about organizations, growing competition, necessity to incorporate these rapidly succeeding medical-technological advancements into the organization, strict cost containment, growing demand for healthcare, and a constant tightening of budgets. These developments force healthcare managers in the individual organizations to find a balance between said developments, the feasibilities of organization in question, and the desired healthcare outcomes in an ever-changing world. The search for individual organizational balances requires that the world of professional competencies, i.e. the clinicians, and the world of healthcare managers should speak the same language when weighing the various developments and translating the outcomes into organizational choices. For the clinicians to make the right choices they must be facilitated to appraise the effects of their choices on organizational outcomes. Likewise, the healthcare managers’ decision- making process should include the effects on the medical policies pursued by the individual clinicians in the own organization. This thesis places a focus on developing methods for allocation of hospital resources within a framework that enables clinicians and healthcare managers to balance the developments on the various levels, thus providing a basis for policymaking

Telemedicine

Telemedicine is a rapidly evolving field as new technologies are implemented for example for the development of wireless sensors, quality data transmission. Using the Internet applications such as counseling, clinical consultation support and home care monitoring and management are more and more realized, which improves access to high level medical care in underserved areas. The 23 chapters of this book present manifold examples of telemedicine treating both theoretical and practical foundations and application scenarios