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We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…
Cancer progression and monotonic accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in computational oncology and virology but also in…
Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the…
Many learning problems require predicting how populations evolve under an unknown transformation. A natural representation for such populations is a probability measure, with point clouds as a key example. In this work, we study the…
Motivation: Driver (epi)genomic alterations underlie the positive selection of cancer subpopulations, which promotes drug resistance and relapse. Even though substantial heterogeneity is witnessed in most cancer types, mutation accumulation…
Paragangliomas are rare, primarily slow-growing tumors for which the underlying growth pattern is unknown. Therefore, determining the best care for a patient is hard. Currently, if no significant tumor growth is observed, treatment is often…
Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…
This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of…
Over 80% of human cancers originate from the epithelium, which covers the outer and inner surfaces of organs and blood vessels. In stratified epithelium, the bottom layers are occupied by stem and stem-like cells that continually divide and…
In this study, we present a stochastic simulation model designed to explicitly incorporate cell cycle length, overcoming limitations associated with classical compartmental models. Our approach employs a delay mechanism to represent the…
Understanding the cross-species behavior of cancer is important for uncovering fundamental mechanisms of carcinogenesis, and for translating results of model systems between species. One of the most famous interspecific considerations of…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
Tomasetti and Vogelstein (2015a) find that the incidence of a set of cancer types is correlated with the total number of normal stem cell divisions. Here, we separate the effects of standing stem cell number (i.e., organ or tissue size) and…
Cancer arises from successive rounds of mutations which generate tumor cells with different genomic variation i.e. clones. For drug responsiveness and therapeutics, it is necessary to identify the clones in tumor sample accurately. Many…
A principal component analysis of the TCGA data for 15 cancer localizations unveils the following qualitative facts about tumors: 1) The state of a tissue in gene expression space may be described by a few variables. In particular, there is…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…
Phenotypic heterogeneity along the epithelial-mesenchymal (E-M) axis contributes to cancer metastasis and drug resistance. Recent experimental efforts have collated detailed time-course data on the emergence and dynamics of E-M…