Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology.
Immune responses against conserved and variable viral epitopes.
Immune responses and viral phenotype: Do replication rate and cytopathogenicity influence virus load?
Immunological barrier for infectious diseases
A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.
Immunotherapy with interleukin-2: A study based on mathematical modeling
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation
Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn...
Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis
Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin...
Improving EWMA plans for detecting unusual increases in Poisson counts.
Inbuilt mechanisms for overcoming functional problems inherent in hepatic microlobular structure.
Individual Cell-Based Model for In-Vitro Mesothelial Invasion of Ovarian Cancer
In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular matrix and...
Inferences for joint modelling of repeated ordinal scores and time to event data.
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
Intensified Doxorubicin-Based Regimen Efficacy in Residual Non-Hodgkin's Lymphoma Disease: Towards a Computationally Supported Treatment Improvement
Despite recent advances, treatment of patients with aggressive Non-Hodgkin's lymphoma (NHL2) has yet to be optimally designed. Notwithstanding the contribution of molecular treatments, intensification of chemotherapeutic regimens may still be beneficial. Hoping to aid in the design of intensified chemotherapy, we put forward a mathematical and computational model that analyses the effect of Doxorubicin on NHL over a wide range of patho-physiological conditions. The model represents tumour growth...
Interdependence between CHD risk factors examined using linear models with and without transformation of data
Intracellular Modelling of Cell-Matrix Adhesion during Cancer Cell Invasion
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from neighbouring cells, degrade the basement membrane, and migrate through the extracellular matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix adhesion. In this paper we present a mathematical model of an intracellular pathway for the interactions between a cancer cell and the extracellular matrix. Cancer cells use similar...
Invariant subspaces for grasping internal forces and non-interacting force-motion control in robotic manipulation
This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural...
Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell proliferation and motility rates. The interplay of proliferation and migration dynamics plays an important role in the invasion of these malignant tumors. We analyze the regulation of proliferation and migration processes with a lattice-gas cellular automaton (LGCA). We study and characterize the influence of the migration/proliferation dichotomy (also known...
Irregular and semi-regular polyhedral models for Rous sarcoma virus cores.
Is the skin an excitable medium? Pattern formation in erythema gyratum repens.