Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development
Understanding the relationship between hepatocellular carcinoma (HCC) and immunity is crucial for HCC immunotherapy. However, the existing research has solely focused on a novel population of primary tumor-induced non-leukocytes called Ter-cells and their circulating components in distant organs, ne...
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MDPI AG
2023-10-01
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4261 |
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| author | Juan Shen Xiao Tu Yuanyuan Li |
| author_facet | Juan Shen Xiao Tu Yuanyuan Li |
| author_sort | Juan Shen |
| collection | DOAJ |
| description | Understanding the relationship between hepatocellular carcinoma (HCC) and immunity is crucial for HCC immunotherapy. However, the existing research has solely focused on a novel population of primary tumor-induced non-leukocytes called Ter-cells and their circulating components in distant organs, neglecting the examination of immunity’s impact on cancer. In order to thoroughly examine the dynamics of Ter cells, HCC, and the known regulatory elements in the immunological milieu, we used a mathematical model in the form of a system of differential equations in this work. According to simulation studies, tumor cells cannot be completely eliminated by either the effective killing of HCC by cytotoxic T lymphocytes (CTL) or the inhibition of tumor cell proliferation. Nonetheless, continuous CTL activation and TGF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-induced differentiation of CTL facilitated a transition from a high steady-state of HCC quantity to an unstable state, followed by a low state of HCC quantity, aligning with the three phases of the cancer immunoediting concept (escape, equilibrium, and elimination). Our survival study revealed that the ratio of CTL proliferation to CTL killing and relative TGF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-induced differentiation of CTL have a significant impact on cancer-free survival. Sensitivity and bifurcation analysis of these parameters demonstrated that the rate of CTL proliferation, as well as the number of HCCs when the production rate reaches half of one, strongly affects the number of HCCs. Our findings highlight the critical role of immune system activation in cancer therapy and its potential impact on HCC treatment. |
| first_indexed | 2024-03-10T21:05:15Z |
| format | Article |
| id | doaj.art-e7969f89e81c4f7abfdc89789a27a8ab |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:05:15Z |
| publishDate | 2023-10-01 |
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| series | Mathematics |
| spelling | doaj.art-e7969f89e81c4f7abfdc89789a27a8ab2023-11-19T17:13:29ZengMDPI AGMathematics2227-73902023-10-011120426110.3390/math11204261Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma DevelopmentJuan Shen0Xiao Tu1Yuanyuan Li2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaSchool of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, ChinaUnderstanding the relationship between hepatocellular carcinoma (HCC) and immunity is crucial for HCC immunotherapy. However, the existing research has solely focused on a novel population of primary tumor-induced non-leukocytes called Ter-cells and their circulating components in distant organs, neglecting the examination of immunity’s impact on cancer. In order to thoroughly examine the dynamics of Ter cells, HCC, and the known regulatory elements in the immunological milieu, we used a mathematical model in the form of a system of differential equations in this work. According to simulation studies, tumor cells cannot be completely eliminated by either the effective killing of HCC by cytotoxic T lymphocytes (CTL) or the inhibition of tumor cell proliferation. Nonetheless, continuous CTL activation and TGF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-induced differentiation of CTL facilitated a transition from a high steady-state of HCC quantity to an unstable state, followed by a low state of HCC quantity, aligning with the three phases of the cancer immunoediting concept (escape, equilibrium, and elimination). Our survival study revealed that the ratio of CTL proliferation to CTL killing and relative TGF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-induced differentiation of CTL have a significant impact on cancer-free survival. Sensitivity and bifurcation analysis of these parameters demonstrated that the rate of CTL proliferation, as well as the number of HCCs when the production rate reaches half of one, strongly affects the number of HCCs. Our findings highlight the critical role of immune system activation in cancer therapy and its potential impact on HCC treatment.https://www.mdpi.com/2227-7390/11/20/4261mathematical modeldynamical analysisbifurcationtumor therapy |
| spellingShingle | Juan Shen Xiao Tu Yuanyuan Li Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development Mathematics mathematical model dynamical analysis bifurcation tumor therapy |
| title | Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development |
| title_full | Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development |
| title_fullStr | Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development |
| title_full_unstemmed | Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development |
| title_short | Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development |
| title_sort | mathematical modeling reveals mechanisms of cancer immune interactions underlying hepatocellular carcinoma development |
| topic | mathematical model dynamical analysis bifurcation tumor therapy |
| url | https://www.mdpi.com/2227-7390/11/20/4261 |
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