Data-Driven Discovery of Mathematical and Physical Relations in Oncology Data Using Human-Understandable Machine Learning

For decades, researchers have used the concepts of rate of change and differential equations to model and forecast neoplastic processes. This expressive mathematical apparatus brought significant insights in oncology by describing the unregulated proliferation and host interactions of cancer cells, as well as their response to treatments. Now, these theories have been given a new life and found new applications. With the advent of routine cancer genome sequencing and the resulting abundance of data, oncology now builds an “arsenal” of new modeling and analysis tools. Models describing the governing physical laws of tumor–host–drug interactions can be now challenged with biological data to make predictions about cancer progression. Our study joins the efforts of the mathematical and computational oncology community by introducing a novel machine learning system for data-driven discovery of mathematical and physical relations in oncology. The system utilizes computational mechanisms such as competition, cooperation, and adaptation in neural networks to simultaneously learn the statistics and the governing relations between multiple clinical data covariates. Targeting an easy adoption in clinical oncology, the solutions of our system reveal human-understandable properties and features hidden in the data. As our experiments demonstrate, our system can describe nonlinear conservation laws in cancer kinetics and growth curves, symmetries in tumor’s phenotypic staging transitions, the preoperative spatial tumor distribution, and up to the nonlinear intracellular and extracellular pharmacokinetics of neoadjuvant therapies. The primary goal of our work is to enhance or improve the mechanistic understanding of cancer dynamics by exploiting heterogeneous clinical data. We demonstrate through multiple instantiations that our system is extracting an accurate human-understandable representation of the underlying dynamics of physical interactions central to typical oncology problems. Our results and evaluation demonstrate that, using simple—yet powerful—computational mechanisms, such a machine learning system can support clinical decision-making. To this end, our system is a representative tool of the field of mathematical and computational oncology and offers a bridge between the data, the modeler, the data scientist, and the practicing clinician.

The Multiple Dimensions of Networks in Cancer: A Perspective

This perspective article gathers the latest developments in mathematical and computational oncology tools that exploit network approaches for the mathematical modelling, analysis, and simulation of cancer development and therapy design. It instigates the community to explore new paths and synergies under the umbrella of the Special Issue “Networks in Cancer: From Symmetry Breaking to Targeted Therapy”. The focus of the perspective is to demonstrate how networks can model the physics, analyse the interactions, and predict the evolution of the multiple processes behind tumour-host encounters across multiple scales. From agent-based modelling and mechano-biology to machine learning and predictive modelling, the perspective motivates a methodology well suited to mathematical and computational oncology and suggests approaches that mark a viable path towards adoption in the clinic.

Data-driven Discovery of Mathematical and Physical Relations in Oncology Data using Human-understandable Machine Learning

For decades, researchers have used the concepts of rate of change and differential equations to model and forecast neoplastic processes. This expressive mathematical apparatus brought significant insights in oncology by describing the unregulated proliferation and host interactions of cancer cells, as well as their response to treatments. Now, these theories have been given a new life and found new applications. With the advent of routine cancer genome sequencing and the resulting abundance of data, oncology now builds an "arsenal" of new modeling and analysis tools. Models describing the governing physical laws of tumor-host-drug interactions can be now challenged with biological data to make predictions about cancer progression. Our study joins the efforts of the mathematical and computational oncology community by introducing a novel machine learning system for data-driven discovery of mathematical and physical relations in oncology. The system utilizes computational mechanisms such as competition, cooperation, and adaptation in neural networks to simultaneously learn the statistics and the governing relations between multiple clinical data covariates. Targeting an easy adoption in clinical oncology, the solutions of our system reveal human-understandable properties and features hidden in the data. As our experiments demonstrate, our system can describe nonlinear conservation laws in cancer kinetics and growth curves, symmetries in tumor's phenotypic staging transitions, the pre-operative spatial tumor distribution, and up to the nonlinear intracellular and extracellular pharmacokinetics of neoadjuvant therapies. The primary goal of our work is to enhance or improve the mechanistic understanding of cancer dynamics by exploiting heterogeneous clinical data. We demonstrate through multiple instantiations that our system is extracting an accurate human-understandable representation of the underlying dynamics of physical interactions central to typical oncology problems. Our results and evaluation demonstrate that using simple - yet powerful - computational mechanisms, such a machine learning system can support clinical decision making. To this end, our system is a representative tool of the field of mathematical and computational oncology and offers a bridge between the data, the modeler, the data scientist, and the practising clinician.

The Bourque distances for mutation trees of cancers

Background Mutation trees are rooted trees in which nodes are of arbitrary degree and labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson–Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Results We generalize the Robinson–Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. We show the basic version of the Bourque distance for mutation trees can be computed in linear time. We also make a connection between the Robinson–Foulds distance and the nearest neighbor interchange distance.

The Bourque Distances for Mutation Trees of Cancers

Background: Mutation trees are rooted trees in which nodes are of arbitrary degree are labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson-Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Results: We generalize the Robinson-Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. We show the basic version of the Bourque distance for mutation trees can be computed in linear time. We also make a connection between the Robinson{Foulds distance and the nearest neighbor interchange distance.

Combining Mechanistic Models and Machine Learning for Personalized Chemotherapy and Surgery Sequencing in Breast Cancer

Mathematical and computational oncology has increased the pace of cancer research towards the advancement of personalized therapy. Serving the pressing need to exploit the large amounts of currently underutilized data, such approaches bring a significant clinical advantage in tailoring the therapy. CHIMERA is a novel system that combines mechanistic modelling and machine learning for personalized chemotherapy and surgery sequencing in breast cancer. It optimizes decision-making in personalized breast cancer therapy by connecting tumor growth behaviour and chemotherapy effects through predictive modelling and learning. We demonstrate the capabilities of CHIMERA in learning simultaneously the tumor growth patterns, across several types of breast cancer, and the pharmacokinetics of a typical breast cancer chemotoxic drug. The learnt functions are subsequently used to predict how to sequence the intervention. We demonstrate the versatility of CHIMERA in learning from tumor growth and pharmacokinetics data to provide robust predictions under two, typically used, chemotherapy protocol hypotheses.

The Bourque Distances for Mutation Trees of Cancers

Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson–Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients usually contain different sets of mutation labels. Here, we generalize the Robinson–Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson–Foulds distance and the nearest neighbor interchange distance is also presented.