相关论文: Mathematical Discovery of Natural Laws in Biomedic…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…
Metastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
Despite internal complexity, tumor growth kinetics follow relatively simple macroscopic laws that have been quantified by mathematical models. To resolve this further, quantitative and discriminant analyses were performed for the purpose of…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
Clinical management of cancer has continuously evolved for several decades. Biochemical, molecular and genomics approaches have brought and still bring numerous insights into cancerous diseases. It is now accepted that some phenomena,…
Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Mathematical oncology is a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. Tumor-immune interactions play a…
Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where…
Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer…
We introduce a superstatistical model for the progression statistics of malignant cancer cells. The metastatic cascade is modeled as a complex nonequilibrium system with several macroscopic pathways and inverse-chi-square distributed…