Periodic Model in General Toxin Elimination by the Liver and the Kidneys

Annia Valiente Monte de Oca; Sandy Sanchez Dominguez; Adolfo Arcenio Fernández García; Antonio Iván Ruiz Chaveco

doi:doi:10.11648/j.sr.20231105.13

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Periodic Model in General Toxin Elimination by the Liver and the Kidneys

Annia Valiente Monte de Oca, Sandy Sanchez Dominguez, Adolfo Arcenio Fernández García, Antonio Iván Ruiz Chaveco

Published in Science Research (Volume 11, Issue 5)

Received: 11 July 2023 Accepted: 18 August 2023 Published: 9 October 2023

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Abstract

The problem of mathematical modeling has multiple applications, both in other sciences and in Mathematics itself; modeling in Physics and engineering is much more widespread, it is not the same in Medicine and Biology, where there are still few modeled processes; this is the fundamental purpose of this work. This article provides a general study of the kidneys, liver and circulatory system, their characteristics, their main functions, detailing some aspects of the toxin elimination process; the main diseases of these organs are indicated and how to predict these diseases. A compartmental model is created using a system of differential equations with periodic coefficients in general that simulates the toxin elimination process. The system is transformed into a system where the matrix of the linear part has constant coefficients, applying Floket theory; If a qualitative study is carried out, conditions are created that guarantee the stability of the organism's functioning while there is still toxin in our body, an example is given to show in practice what was demonstrated theoretically

Published in	Science Research (Volume 11, Issue 5)
DOI	10.11648/j.sr.20231105.13
Page(s)	111-116
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Liver, Kidneys, Circulatory System, Compartmental Model

References

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[2]	Aguilar B, L. Leão, S. Sánchez, K. Oliveira, M. Lacort, R. Ferreira, E. Rodrigues, A. I Ruiz.” Combined normal form in the model of an injectable drug”. Journal of I multidisciplinary engineering science and technology (JMEST). ISSN: 2458-9403 Vol. 7 Issue 2, February - 2020 www.jmest.org JMESTN42353284 PP 11535-11540.
[3]	Aguilar B, N. Fernandes, K. Oliveira, E. Rodrigues F, L. Leão, A. Libório, S. Sánchez, A. I. Ruiz. “Two critical cases of the model of an inhalable drug”. Iosr journal of mathematics (IOSR-JM). e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 16, Issue 1 Ser. II (Jan – Feb 2020), PP 58-64.
[4]	Batistab E, L. Leãoc, S. Sáncheza, E. Rodrigues Pb, R. Ferreirab, N. Fernandes. E. Rodrigues Fd, A. I. Ruizb. “Mathematical Modeling with General Periodic Coefficients in elimination of Pollution”. IOSR JOURNAL OF MATHEMATICS (IOSR-JM). e-ISSN: 22785728, p-ISSN: 2319-765X. Volume 15, Issue 6 Ser. II (Nov – Dec 2019), PP 01-06.
[5]	Chaveco, A. I. R. And others. Modelagem de Processos Diversos. Curitiba: Appris, 2018, v. 1. p. 320. Áreas do conhecimento: Matemática Aplicada. Referências adicionais: Brasil/Português. Meio de divulgação: Impresso, ISBN: 9788547305116 de divulgação: Impresso, ISBN: 9788544412534.
[6]	Koeppen, Bruce M.; Stanton, Bruce A. (2009). Berne & Levy - Fisiologia 6a ed. Rio de Janeiro: Elsevier. ISBN 978-85-352-3057-4. OCLC 889254065.
[7]	Lacortt, M., Cukla, A. R., Chaveco, A. I. R., de Oliveira Marinho, K. K., Lopes, L. M. L., Dominguez, S. S., & Gonçalves, N. F. (2021). O FÍGADO E OS RINS NA ELIMINAÇÃO DE TOXINAS. MODELAGEM MATEMÁTICA. Revista CIATEC–UPF, 13 (3), 1-10. 2021.
[8]	Leão L M d, Oliveira K Kd, Lima Pc, Araújo M Ed, Sousa Vb, Costa Td, Libório Ac, Caetano Wd, Santos Fd, RodríguesAd, Fernandes Ne, Ribeiro Zd, IglesiaN d, Libório A Mc, Sánchez Sf, Ruiz A Id. “Periodic shaping the ozone layer and the ultraviolet rays”. INTERNATIONAL JOURNAL OF EMERGING TRENDS & TECHNOLOGY IN COMPUTER SCIENCE (IJETTCS). Volume 9, Issue 6, November - December 2020 ISSN 2278-6856 Page 5-10.
[9]	Ruiz Aa, Leão L Mc, Oliveira Kb, Fernandes Nd, Sánchez Sa, Fernández Aa, Ruiz A Ib. “Periodic model of the interaction between a predator with a double mutualist”. BRITISH JOURNAL OF BIO-MEDICAL RESEARCH. Vol. 05, Issue 02, Pg. 1507-1515, March-April 2021.
[10]	Sánchez S; A. Fernández; Z. Ribeiro; M. Lacortt; Nascimento R; A. I. Ruiz. ”Model of Siklemia with Periodic Coefficients for a Combined Critical Case”. International Journal of Innovative Science, Engineering & Technology, Vol. 5 Issue 3, March 2018. ISSN (Online) 2348–7968.
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APA Style

Annia Valiente Monte de Oca, Sandy Sanchez Dominguez, Adolfo Arcenio Fernández García, Antonio Iván Ruiz Chaveco. (2023). Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Science Research, 11(5), 111-116. https://doi.org/10.11648/j.sr.20231105.13

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ACS Style

Annia Valiente Monte de Oca; Sandy Sanchez Dominguez; Adolfo Arcenio Fernández García; Antonio Iván Ruiz Chaveco. Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Sci. Res. 2023, 11(5), 111-116. doi: 10.11648/j.sr.20231105.13

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AMA Style

Annia Valiente Monte de Oca, Sandy Sanchez Dominguez, Adolfo Arcenio Fernández García, Antonio Iván Ruiz Chaveco. Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Sci Res. 2023;11(5):111-116. doi: 10.11648/j.sr.20231105.13

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@article{10.11648/j.sr.20231105.13,
  author = {Annia Valiente Monte de Oca and Sandy Sanchez Dominguez and Adolfo Arcenio Fernández García and Antonio Iván Ruiz Chaveco},
  title = {Periodic Model in General Toxin Elimination by the Liver and the Kidneys},
  journal = {Science Research},
  volume = {11},
  number = {5},
  pages = {111-116},
  doi = {10.11648/j.sr.20231105.13},
  url = {https://doi.org/10.11648/j.sr.20231105.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20231105.13},
  abstract = {The problem of mathematical modeling has multiple applications, both in other sciences and in Mathematics itself; modeling in Physics and engineering is much more widespread, it is not the same in Medicine and Biology, where there are still few modeled processes; this is the fundamental purpose of this work. This article provides a general study of the kidneys, liver and circulatory system, their characteristics, their main functions, detailing some aspects of the toxin elimination process; the main diseases of these organs are indicated and how to predict these diseases. A compartmental model is created using a system of differential equations with periodic coefficients in general that simulates the toxin elimination process. The system is transformed into a system where the matrix of the linear part has constant coefficients, applying Floket theory; If a qualitative study is carried out, conditions are created that guarantee the stability of the organism's functioning while there is still toxin in our body, an example is given to show in practice what was demonstrated theoretically},
 year = {2023}
}

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TY  - JOUR
T1  - Periodic Model in General Toxin Elimination by the Liver and the Kidneys
AU  - Annia Valiente Monte de Oca
AU  - Sandy Sanchez Dominguez
AU  - Adolfo Arcenio Fernández García
AU  - Antonio Iván Ruiz Chaveco
Y1  - 2023/10/09
PY  - 2023
N1  - https://doi.org/10.11648/j.sr.20231105.13
DO  - 10.11648/j.sr.20231105.13
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 111
EP  - 116
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20231105.13
AB  - The problem of mathematical modeling has multiple applications, both in other sciences and in Mathematics itself; modeling in Physics and engineering is much more widespread, it is not the same in Medicine and Biology, where there are still few modeled processes; this is the fundamental purpose of this work. This article provides a general study of the kidneys, liver and circulatory system, their characteristics, their main functions, detailing some aspects of the toxin elimination process; the main diseases of these organs are indicated and how to predict these diseases. A compartmental model is created using a system of differential equations with periodic coefficients in general that simulates the toxin elimination process. The system is transformed into a system where the matrix of the linear part has constant coefficients, applying Floket theory; If a qualitative study is carried out, conditions are created that guarantee the stability of the organism's functioning while there is still toxin in our body, an example is given to show in practice what was demonstrated theoretically
VL  - 11
IS  - 5
ER  -

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Author Information

Annia Valiente Monte de Oca

Department of Mathematics, Faculty of Sciences, Guantánamo University Center, Guantánamo, Cuba
Sandy Sanchez Dominguez

Department of Mathematics, Faculty of Mathematics and Computing, Universidad de Oriente, Santiago de Cuba, Cuba
Adolfo Arcenio Fernández García

Department of Mathematics, Faculty of Mathematics and Computing, Universidad de Oriente, Santiago de Cuba, Cuba
Antonio Iván Ruiz Chaveco

Department of Mathematics, Centro de Estudos Superiores de Tefé, State University of Amazonas, Amazonas, Brazil

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Plain Text BibTeX RIS

APA Style

Annia Valiente Monte de Oca, Sandy Sanchez Dominguez, Adolfo Arcenio Fernández García, Antonio Iván Ruiz Chaveco. (2023). Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Science Research, 11(5), 111-116. https://doi.org/10.11648/j.sr.20231105.13

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ACS Style

Annia Valiente Monte de Oca; Sandy Sanchez Dominguez; Adolfo Arcenio Fernández García; Antonio Iván Ruiz Chaveco. Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Sci. Res. 2023, 11(5), 111-116. doi: 10.11648/j.sr.20231105.13

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AMA Style

Annia Valiente Monte de Oca, Sandy Sanchez Dominguez, Adolfo Arcenio Fernández García, Antonio Iván Ruiz Chaveco. Periodic Model in General Toxin Elimination by the Liver and the Kidneys. Sci Res. 2023;11(5):111-116. doi: 10.11648/j.sr.20231105.13

Copy | Download

@article{10.11648/j.sr.20231105.13,
  author = {Annia Valiente Monte de Oca and Sandy Sanchez Dominguez and Adolfo Arcenio Fernández García and Antonio Iván Ruiz Chaveco},
  title = {Periodic Model in General Toxin Elimination by the Liver and the Kidneys},
  journal = {Science Research},
  volume = {11},
  number = {5},
  pages = {111-116},
  doi = {10.11648/j.sr.20231105.13},
  url = {https://doi.org/10.11648/j.sr.20231105.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20231105.13},
  abstract = {The problem of mathematical modeling has multiple applications, both in other sciences and in Mathematics itself; modeling in Physics and engineering is much more widespread, it is not the same in Medicine and Biology, where there are still few modeled processes; this is the fundamental purpose of this work. This article provides a general study of the kidneys, liver and circulatory system, their characteristics, their main functions, detailing some aspects of the toxin elimination process; the main diseases of these organs are indicated and how to predict these diseases. A compartmental model is created using a system of differential equations with periodic coefficients in general that simulates the toxin elimination process. The system is transformed into a system where the matrix of the linear part has constant coefficients, applying Floket theory; If a qualitative study is carried out, conditions are created that guarantee the stability of the organism's functioning while there is still toxin in our body, an example is given to show in practice what was demonstrated theoretically},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Periodic Model in General Toxin Elimination by the Liver and the Kidneys
AU  - Annia Valiente Monte de Oca
AU  - Sandy Sanchez Dominguez
AU  - Adolfo Arcenio Fernández García
AU  - Antonio Iván Ruiz Chaveco
Y1  - 2023/10/09
PY  - 2023
N1  - https://doi.org/10.11648/j.sr.20231105.13
DO  - 10.11648/j.sr.20231105.13
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 111
EP  - 116
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20231105.13
AB  - The problem of mathematical modeling has multiple applications, both in other sciences and in Mathematics itself; modeling in Physics and engineering is much more widespread, it is not the same in Medicine and Biology, where there are still few modeled processes; this is the fundamental purpose of this work. This article provides a general study of the kidneys, liver and circulatory system, their characteristics, their main functions, detailing some aspects of the toxin elimination process; the main diseases of these organs are indicated and how to predict these diseases. A compartmental model is created using a system of differential equations with periodic coefficients in general that simulates the toxin elimination process. The system is transformed into a system where the matrix of the linear part has constant coefficients, applying Floket theory; If a qualitative study is carried out, conditions are created that guarantee the stability of the organism's functioning while there is still toxin in our body, an example is given to show in practice what was demonstrated theoretically
VL  - 11
IS  - 5
ER  -

Copy | Download