Mathematical Modeling and Computer Simulations of Cancer Chemotherapy

2021 ◽  
pp. 717-730
Author(s):  
Frank Nani ◽  
Mingxian Jin
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulations ◽  
Cancer Chemotherapy

Using mathematical modeling to estimate time-independent cancer chemotherapy efficacy parameters

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Christine Pho ◽  
Madison Frieler ◽  
Giri R. Akkaraju ◽  
Anton V. Naumov ◽  
Hana M. Dobrovolny
Keyword(s):  
Mathematical Modeling ◽  
Cancer Chemotherapy ◽  
Efficacy Parameters ◽  
Chemotherapy Efficacy

Kinetic Analysis of Peritoneal Fluid and Solute Transport with Combination of Glucose and Icodextrin as Osmotic Agents

2009 ◽  
Vol 29 (1) ◽  
pp. 72-80 ◽  
Author(s):  
Magda Galach ◽  
Andrzej Werynski ◽  
Jacek Waniewski ◽  
Philippe Freida ◽  
Bengt Lindholm
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulations ◽  
Clinical Data ◽  
Extracellular Volume ◽  
Sodium Concentration ◽  
Pore Model ◽  
Fluid Removal ◽  
Sodium Removal ◽  
Osmotic Agents ◽  
Dialysis Fluids

Background Controlling extracellular volume and plasma sodium concentration are two crucial objectives of dialysis therapy, as inadequate sodium and fluid removal by dialysis may result in extracellular volume overload, hypertension, and increased cardiovascular morbidity and mortality in end-stage renal disease patients. A new concept to enhance sodium and fluid removal during peritoneal dialysis (PD) is the use of dialysis solutions with two different osmotic agents. Aim To investigate and compare, with the help of mathematical modeling and computer simulations, fluid and solute transport during PD with conventional dialysis fluids (3.86% glucose and 7.5% icodextrin; both with standard sodium concentration) and a new combination fluid with both icodextrin and glucose (CIG; 2.6% glucose/6.8% icodextrin; low sodium concentration). In particular, this paper is devoted to improving mathematical modeling based on critical appraisal of the ability of the original three-pore model to reproduce clinical data and check its validity across different types of osmotic agents. Methods Theoretical investigations of possible causes of the improved fluid and sodium removal during PD with the combination solution (CIG) were carried out using the three-pore model. The results of computer simulations were compared with clinical data from dwell studies in 7 PD patients. To fit the model to the low net ultrafiltration (366 ± 234 mL) obtained after a 4-hour dwell with 3.86% glucose, some of the original parameters proposed in the three-pore model (Rippe & Levin. Kidney Int 2000; 57:2546-56) had to be modified. In particular, the aquaporin-mediated fractional contribution to hydraulic permeability was decreased by 25% and small pore radius increased by 18%. Results The simulations described well clinical data that showed a dramatic increase in ultrafiltration and sodium removal with the CIG fluid in comparison with the two other dialysis fluids. However, to adapt the three-pore model to the selected group of PD patients (fast transporters with small ultrafiltration capacity on average), the peritoneal pore structure had to be modified. As the mathematical model was capable of reproducing the clinical data, this shows that the enhanced ultrafiltration with the combination fluid is caused by the additive effect of the two different osmotic agents and not by a specific impact of the new dialysis fluid on the transport characteristics of the peritoneum.

Introduction to Mathematical Modeling and Computer Simulations

2018 ◽  
Author(s):  
Vladimir Mityushev ◽  
Wojciech Nawalaniec ◽  
Natalia Rylko
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulations

scholarly journals Mathematical Modeling to Perform an Analysis of Social Isolation Periods in the Dissemination of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 595-608
Author(s):  
A. Molter ◽  
R. S. Quadros ◽  
M. Rafikov ◽  
D. Buske ◽  
G. A. Gonçalves
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Social Isolation ◽  
Computer Simulations ◽  
The Other ◽  
Stable Level ◽  
The Social ◽  
The World ◽  
Second Peak

The outbreak of COVID-19 has made scientists from all over the world do not measureefforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

Computer Turn in the Philosophy of the XXI Century (Reflection on the Book “Calculated Surprises.A Philosophy of Computer Simulation” by Johannes Lenhard)

2021 ◽  
pp. 36-46
Author(s):  
Timur V. Khamdamov ◽  
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulations ◽  
New World ◽  
Verification And Validation ◽  
Research Practice ◽  
The Third ◽  
New Methods ◽  
Research Material ◽  
Verification Methods ◽  
Scientific Experiments

In 2019, a new book by Lenhard was published. Lenhard attempts to separate computer simulations from classical mathematical modeling. Structuring in three parts the accumulated over the years research material, Lenhard correctly, with­out undertaking the construction of revolutionary metaphysical concepts, ac­quaints the reader with the new world of the philosophy of computer simula­tions. In the first part, the author reveals the thesis that computer simulations are a completely new, previously unknown, type of mathematical modeling. The second part focuses on the conceptual epistemic transformations of mathe­matical modeling from the perspective of the phenomenon of computer simula­tions. This part also deals with the verification methods that are used in scientific experiments: verification and validation. In the third part, Lenhard, questioning the purely scientific rational way of knowing, tries to grope for the contours of new methods, the specificity of which is due to the use of computer simulations in scientific research practice. In this review, I will analyze the main problems that Lenhard identifies in his book as the most important for understanding the philosophical essence of computer simulations.

Computer Simulation

2015 ◽  
Author(s):  
Johannes Lenhard
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulation ◽  
Philosophy Of Science ◽  
Computer Simulations ◽  
Simulation Modeling ◽  
New Type

This article interprets computer simulation modeling as a new type of mathematical modeling that comprises a number of interdependent components, among them experimentation, visualization, and adaptability. Furthermore, it is argued, simulation modeling can be characterized as a particular style of reasoning, namely a combinatorial style, that assembles and balances elements from different other styles. Two examples are discussed that exemplify the transformative force of this style: what counts as “understanding phenomena” and what counts as a “solution.” Both are seminal pieces of traditional mathematical modeling and both are transformed, if not inverted, in simulation modeling. Finally, some challenges are considered that computer simulations pose for philosophy of science.

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