On a deterministic mathematical model which efficiently predicts the protective effect of a plant extract mixture in cirrhotic rats

Luis E. Ayala-Hernández; Gabriela Rosales-Muñoz; Armando Gallegos; María L. Miranda-Beltrán; Jorge E. Macías-Díaz; Luis E. Ayala-Hernández; Gabriela Rosales-Muñoz; Armando Gallegos; María L. Miranda-Beltrán; Jorge E. Macías-Díaz

doi:10.3934/mbe.2024011

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 237-252. doi: 10.3934/mbe.2024011

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On a deterministic mathematical model which efficiently predicts the protective effect of a plant extract mixture in cirrhotic rats

1.
Departamento de Ciencias Exactas y Tecnología, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseos de La Montaña, Lagos de Moreno, 47463 Jalisco, Mexico
2.
Departamento de Ciencias de la Tierra y de la Vida, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseos de La Montaña, Lagos de Moreno, 47463 Jalisco, Mexico
3.
Department of Mathematics and Didactics of Mathematics, Tallinn University, Narva Rd. 25, Tallinn, 10120 Harjumaa, Estonia
4.
Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes, 20100 Aguascalientes, Mexico

Received: 06 October 2023 Revised: 04 November 2023 Accepted: 07 November 2023 Published: 12 December 2023

In this work, we propose a mathematical model that describes liver evolution and concentrations of alanine aminotransferase and aspartate aminotransferase in a group of rats damaged with carbon tetrachloride. Carbon tetrachloride was employed to induce cirrhosis. A second groups damaged with carbon tetrachloride was exposed simultaneously a plant extract as hepatoprotective agent. The model reproduces the data obtained in the experiment reported in [Rev. Cub. Plant. Med. 22(1), 2017], and predicts that using the plants extract helps to get a better natural recovery after the treatment. Computer simulations show that the extract reduces the damage velocity but does not avoid it entirely. The present paper is the first report in the literature in which a mathematical model reliably predicts the protective effect of a plant extract mixture in rats with cirrhosis disease. The results reported in this manuscript could be used in the future to help in fighting cirrhotic conditions in humans, though more experimental and mathematical work is required in that case.
Citation: Luis E. Ayala-Hernández, Gabriela Rosales-Muñoz, Armando Gallegos, María L. Miranda-Beltrán, Jorge E. Macías-Díaz. On a deterministic mathematical model which efficiently predicts the protective effect of a plant extract mixture in cirrhotic rats[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 237-252. doi: 10.3934/mbe.2024011

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Abstract

In this work, we propose a mathematical model that describes liver evolution and concentrations of alanine aminotransferase and aspartate aminotransferase in a group of rats damaged with carbon tetrachloride. Carbon tetrachloride was employed to induce cirrhosis. A second groups damaged with carbon tetrachloride was exposed simultaneously a plant extract as hepatoprotective agent. The model reproduces the data obtained in the experiment reported in [Rev. Cub. Plant. Med. 22(1), 2017], and predicts that using the plants extract helps to get a better natural recovery after the treatment. Computer simulations show that the extract reduces the damage velocity but does not avoid it entirely. The present paper is the first report in the literature in which a mathematical model reliably predicts the protective effect of a plant extract mixture in rats with cirrhosis disease. The results reported in this manuscript could be used in the future to help in fighting cirrhotic conditions in humans, though more experimental and mathematical work is required in that case.

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