Related papers: Adaptive tumor growth forecasting via neural & uni…
Oral cancer presents a formidable challenge in oncology, necessitating early diagnosis and accurate prognosis to enhance patient survival rates. Recent advancements in machine learning and data mining have revolutionized traditional…
A macroscopic model of the tumor Gompertzian growth is proposed. This approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors.…
Adaptive therapy is a dynamic cancer treatment protocol that updates (or "adapts") treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of…
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…
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using…
Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
Tumor growth prediction, a highly challenging task, has long been viewed as a mathematical modeling problem, where the tumor growth pattern is personalized based on imaging and clinical data of a target patient. Though mathematical models…
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…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
Intratumour phenotypic heterogeneity is nowadays understood to play a critical role in disease progression and treatment failure. Accordingly, there has been increasing interest in the development of mathematical models capable of capturing…
Quantifying the dynamics of tumor burden reveals useful information about cancer evolution concerning treatment effects and drug resistance, which play a crucial role in advancing model-informed drug developments (MIDD) towards personalized…
We propose a new model of cancer growth based on nonextensive entropy. The evolution equation depends on the nonextensive parameter q. The exponential, the logistic, and the Gompertz growth laws are particular cases of the generalized…
Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…