Investigating new positive, bounded, and convergent numerical solution for the nonlinear time‐dependent breast cancer dynamic competition model

2021 ◽  
Author(s):  
Manish Goyal ◽  
Vinod Kumar Bhardwaj ◽  
Amit Prakash
Keyword(s):  
Breast Cancer ◽  
Numerical Solution ◽  
Competition Model ◽  
Time Dependent ◽  
Dynamic Competition

scholarly journals Improved risk estimation of locoregional recurrence, secondary contralateral tumors and distant metastases in early breast cancer: the INFLUENCE 2.0 model

2021 ◽  
Author(s):  
Vinzenz Völkel ◽  
Tom A. Hueting ◽  
Teresa Draeger ◽  
Marissa C. van Maaren ◽  
Linda de Munck ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Locoregional Recurrence ◽  
Clinical Decision Making ◽  
Metastatic Breast ◽  
Distant Metastases ◽  
Time Dependent ◽  
Individual Risk ◽  
Primary Tumors ◽  
Statistical Approaches

Abstract Purpose To extend the functionality of the existing INFLUENCE nomogram for locoregional recurrence (LRR) of breast cancer toward the prediction of secondary primary tumors (SP) and distant metastases (DM) using updated follow-up data and the best suitable statistical approaches. Methods Data on women diagnosed with non-metastatic invasive breast cancer were derived from the Netherlands Cancer Registry (n = 13,494). To provide flexible time-dependent individual risk predictions for LRR, SP, and DM, three statistical approaches were assessed; a Cox proportional hazard approach (COX), a parametric spline approach (PAR), and a random survival forest (RSF). These approaches were evaluated on their discrimination using the Area Under the Curve (AUC) statistic and on calibration using the Integrated Calibration Index (ICI). To correct for optimism, the performance measures were assessed by drawing 200 bootstrap samples. Results Age, tumor grade, pT, pN, multifocality, type of surgery, hormonal receptor status, HER2-status, and adjuvant therapy were included as predictors. While all three approaches showed adequate calibration, the RSF approach offers the best optimism-corrected 5-year AUC for LRR (0.75, 95%CI: 0.74–0.76) and SP (0.67, 95%CI: 0.65–0.68). For the prediction of DM, all three approaches showed equivalent discrimination (5-year AUC: 0.77–0.78), while COX seems to have an advantage concerning calibration (ICI < 0.01). Finally, an online calculator of INFLUENCE 2.0 was created. Conclusions INFLUENCE 2.0 is a flexible model to predict time-dependent individual risks of LRR, SP and DM at a 5-year scale; it can support clinical decision-making regarding personalized follow-up strategies for curatively treated non-metastatic breast cancer patients.

scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

Time-dependent resource use and costs associated with different states of disease in patients diagnosed with HER-2-positive metastatic breast cancer

2013 ◽  
Vol 139 (2) ◽  
pp. 489-495
Author(s):  
G. W. J. Frederix ◽  
J. L. Severens ◽  
A. M. Hövels ◽  
J. G. C. van Hasselt ◽  
J. A. M. Raaijmakers ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Metastatic Breast Cancer ◽  
Resource Use ◽  
Metastatic Breast ◽  
Time Dependent ◽  
Her 2

Numerical Solution of the Time-Dependent Schrödinger Equation and Application toH+-H

1979 ◽  
Vol 43 (7) ◽  
pp. 512-515 ◽  
Author(s):  
Vida Maruhn-Rezwani ◽  
Norbert Grün ◽  
Werner Scheid
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Time Dependent

scholarly journals Energy Dependence of Total Cross Sections for Reactions with 4, 6he, 6, 7, 9li Nuclei

KnE Energy ◽  
2018 ◽  
Vol 3 (1) ◽  
pp. 21
Author(s):  
Yu Penionzhkevich ◽  
Yu Sobolev ◽  
V Samarin ◽  
M Naumenko
Keyword(s):  
Experimental Data ◽  
Energy Range ◽  
Numerical Solution ◽  
Energy Dependence ◽  
Cross Sections ◽  
Beam Energy ◽  
Microscopic Analysis ◽  
Time Dependent ◽  
Total Cross Sections ◽  
Good Agreement

The paper presents the results of measurement of the total cross sections for reactions 4,6He + Si and 6,7,9Li + Si in the beam energy range 5−50 A⋅MeV. The enhancements of the total cross sections for reaction 6He + Si compared with reaction 4He + Si, and 9Li + Si compared with reactions 6,7Li + Si have been observed. The performed microscopic analysis of total cross sections for reactions 6He + Si and 9Li + Si based on numerical solution of the time-dependent Schrödinger equation for external neutrons of projectile nuclei 6He and 9Li yielded good agreement with experimental data.

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