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Mathematical methods for cancer evolution [electronic resource]

Mathematical methods for cancer evolution [electronic resource]

자료유형
E-Book(소장)
개인저자
Suzuki, Takashi.
서명 / 저자사항
Mathematical methods for cancer evolution [electronic resource] / Takashi Suzuki.
발행사항
Singapore :   Springer,   2017.  
형태사항
1 online resource (vii, 144 p.) : ill.
총서사항
Lecture notes on mathematical modelling in the life sciences,2193-4789
ISBN
9789811036705 9789811036712 (eBook)
요약
The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
일반주기
Title from e-Book title page.  
내용주기
1 Molecular Dynamics -- 2 Amounting the Balance -- 3 Averaging Particle Movements -- 4 Mathematical Analysis.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Tumors --Growth --Mathematical models. Carcinogenesis --Mathematical models.
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020 ▼a 9789811036712 (eBook)
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100 1 ▼a Suzuki, Takashi.
245 1 0 ▼a Mathematical methods for cancer evolution ▼h [electronic resource] / ▼c Takashi Suzuki.
260 ▼a Singapore : ▼b Springer, ▼c 2017.
300 ▼a 1 online resource (vii, 144 p.) : ▼b ill.
490 1 ▼a Lecture notes on mathematical modelling in the life sciences, ▼x 2193-4789
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 1 Molecular Dynamics -- 2 Amounting the Balance -- 3 Averaging Particle Movements -- 4 Mathematical Analysis.
520 ▼a The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Tumors ▼x Growth ▼x Mathematical models.
650 0 ▼a Carcinogenesis ▼x Mathematical models.
830 0 ▼a Lecture notes on mathematical modelling in the life sciences.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-981-10-3671-2
945 ▼a KLPA
991 ▼a E-Book(소장)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 616.99400151 등록번호 E14016406 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

1 Molecular Dynamics.- 2 Amounting the Balance.- 3 Averaging Particle Movements.- 4 Mathematical Analysis.


정보제공 : Aladin

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