scholarly journals Assessment of the Efficient Strategies for Applying Antitumor Viral Vaccine Therapy Based On Mathematical Modeling

2019 ◽  
Vol 14 (1) ◽  
pp. 34-53 ◽  
Author(s):  
N.A. Babushkina ◽  
E.A. Kuzina ◽  
A.A. Loos ◽  
E.V. Belyaeva
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Tumor Cells ◽  
Tumor Size ◽  
Single Shot ◽  
Complete Elimination ◽  
Antitumor Therapy ◽  
Viral Vaccine ◽  
Two Stages ◽  
The Mathematical Model

The paper presents the mathematical description of the two stages of tumor cells’ death as a result of immune response after antitumor viral vaccine introduction. This mathematical description is presented by the system of nonlinear equations implemented in the MatLab-Simulink system. As a result of the computing experiment, two strategies for effective application of the antitumor viral vaccine were identified. The first strategy leads to complete elimination of the tumor cells after a single-shot administration of the vaccine. The second strategy makes it possible to stabilize tumor size through the recurrent introductions of the vaccine. Using the mathematical model of antitumor therapy, appropriate dosages were identified based on the number of tumor cells that die at the two stages of immune response. Dynamics of tumor growth for the two strategies of the viral vaccine application was forecasted based on the mathematical model of antitumor therapy with discontinuous trajectories of tumor growth. The computing experiments made it possible to identify initial tumor size at the start of the therapy and the dosages that allow complete elimination of the tumor cells after the single-shot introduction. For the second strategy, dosages and intervals between recurrent vaccine introductions required to stabilize tumor size at the initial level were also identified. The proposed approach to exploring the effectiveness of vaccine therapy may be applied to different types of experimental tumors and antitumor vaccines.

A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2018 ◽  
Vol 9 (3) ◽  
pp. 1-23 ◽  
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

scholarly journals Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

2018 ◽  
Vol 36 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Angela M Jarrett ◽  
Meghan J Bloom ◽  
Wesley Godfrey ◽  
Anum K Syed ◽  
David A Ekrut ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Murine Model ◽  
Tumour Growth ◽  
Experimental Approach ◽  
Her2 Breast Cancer ◽  
The Mathematical Model

Abstract The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

scholarly journals Uptake of cadmium by Pseudokirchneriella supcapitata

2005 ◽  
Vol 48 (6) ◽  
pp. 1027-1034 ◽  
Author(s):  
Magela Paula Casiraghi ◽  
Samuel Luporini ◽  
Eduardo Mendes da Silva
Keyword(s):  
Mathematical Model ◽  
Metal Ions ◽  
Simulation Model ◽  
Kinetic Parameters ◽  
Cellular Membrane ◽  
Surface Absorption ◽  
Fast Absorption ◽  
Passive Adsorption ◽  
Two Stages ◽  
The Mathematical Model

In this work the microalgae Pseudokirchneriella supcapitata was used for the removal of the cadmium in liquids. The accumulations of metal ions by the alga occur in two stages: a very fast absorption (passive adsorption) proceeded by a slower absorption (activate absorption). A mathematical model based on the surface absorption and on the transport into the interior of the cellular membrane was developed. The simulation model kinetic parameters were experimentally obtained. Through the results observed, the mathematical model was shown to be suitable when compared to the experimental results, confirming the validation of the mathematical model.

scholarly journals On Study of Immune Response to Tumor Cells in Prey-Predator System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gurpreet Kaur ◽  
Naseem Ahmad
Keyword(s):  
Immune Response ◽  
Tumor Cells ◽  
Deterministic Model ◽  
Cellular Level ◽  
Resting Cells ◽  
Global Stability Analysis ◽  
System A ◽  
Specific Antigens ◽  
The Mathematical Model ◽  
Predator System

This paper aims to develop the mathematical model that explores the immune response to a tumor system as a prey-predator system. A deterministic model defining the dynamics of tumor growth progression and regression has been analyzed. Our analysis indicates the tumor recurring and dormancy on the cellular level in combination with resting and hunting cells. The model considered in the present study is a generalization of El-Gohary (2008) by introducing the Michaelis-Menten function. This function describes the stimulation process of the resting cells by the tumor cells in the presence of tumor specific antigens. Local and global stability analysis have been performed along with the numerical simulation to support our findings.

Numerical analysis of fractional-order tumor model

2015 ◽  
Vol 08 (05) ◽  
pp. 1550069 ◽  
Author(s):  
Ayesha Sohail ◽  
Sadia Arshad ◽  
Sana Javed ◽  
Khadija Maqbool
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Fractional Order ◽  
Interleukin 2 ◽  
Tumor Model ◽  
Graphical Analysis ◽  
System A ◽  
The Stability ◽  
The Mathematical Model ◽  
Limiting Values

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis–Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass.

A CONTROL THEORY APPROACH TO CANCER REMISSION AIDED BY AN OPTIMAL THERAPY

2010 ◽  
Vol 18 (01) ◽  
pp. 75-91 ◽  
Author(s):  
SIDDHARTHA P. CHAKRABARTY ◽  
SANDIP BANERJEE
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Control Theory ◽  
Malignant Tumors ◽  
Interleukin 2 ◽  
Cellular Immunotherapy ◽  
Theory Approach ◽  
Optimal Therapy ◽  
Cancer Remission ◽  
The Mathematical Model

The mathematical model depicting cancer remission as presented by Banerjee and Sarkar1is reinvestigated here. Mathematical tools from control theory have been used to analyze and determine how an optimal external treatment of Adaptive Cellular Immunotherapy and interleukin-2 can result in more effective remission of malignant tumors while minimizing any adverse affect on the immune response.

scholarly journals Forecasting the Bladder Tumor Size and Immune Response of a Patient Over the Time Using a Dynamic Mathematical Model

2018 ◽  
Author(s):  
Clara Burgos ◽  
Noemí García-Medina ◽  
David Martínez-Rodríguez ◽  
José-Luis Pontones ◽  
David Ramos ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Tumor Size ◽  
Model Calibration ◽  
Bladder Tumor ◽  
Tumor Evolution ◽  
Model Parameters ◽  
Single Patient ◽  
Dynamic Mathematical Model ◽  
Parameter Values

Bladder cancer is one of the most common malignant diseases in the urinary system and a highly aggressive neoplasm. The prognosis is not favourable usually and its evolution for particular patients is very difficult to find out. In this paper we propose a dynamic mathematical model that describes the bladder tumor growth and the immune response evolution. This model is customized for a single patient, determining appropriate model parameter values via model calibration. Due to the uncertainty of the tumor evolution, using the calibrated model parameters, we predict the tumor size and the immune response evolution over the next few months assuming three different scenarios: favourable, neutral and unfavourable. In the former, the cancer disappears; in the second a 5mm tumor is expected around the middle of August 2018; in the worst scenario, a 5mm tumor is expected around the end of May 2018. The patient has been cited around June 15th, 2018, to check the tumor size, if it exists.

scholarly journals Assessing the Effects of Estrogen on the Dynamics of Breast Cancer

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Chipo Mufudza ◽  
Walter Sorofa ◽  
Edward T. Chiyaka
Keyword(s):  
Breast Cancer ◽  
Mathematical Model ◽  
Immune Response ◽  
Risk Factor ◽  
Tumor Cells ◽  
Immune Cells ◽  
Population Model ◽  
Host Cells ◽  
Common Cancer ◽  
General Dynamics

Worldwide, breast cancer has become the second most common cancer in women. The disease has currently been named the most deadly cancer in women but little is known on what causes the disease. We present the effects of estrogen as a risk factor on the dynamics of breast cancer. We develop a deterministic mathematical model showing general dynamics of breast cancer with immune response. This is a four-population model that includes tumor cells, host cells, immune cells, and estrogen. The effects of estrogen are then incorporated in the model. The results show that the presence of extra estrogen increases the risk of developing breast cancer.

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