Calibrations and validations of biological models with an application on the renal fibrosis

Akbarinejad

Hao

et al. 2020

JCM

Self Cite

Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.

Section: Non-dimensionalization and Sensitivity Analysismentioning

confidence: 99%

Data Driven Mathematical Model of Colon Cancer Progression

Akbarinejad

Hao

et al. 2020

JCM

Self Cite

“…To analyze the effect of parameter values on the dynamics of the system, we perform sensitivity analysis [ 117 , 118 , 119 ]. For the system

consider (first order) sensitivity S of non-dimensional solution X with respect to the model parameters

to be defined as a vector

…”

Section: Methodsmentioning

confidence: 99%

Data Driven Mathematical Model of FOLFIRI Treatment for Colon Cancer

Budithi

et al. 2021

Cancers

Many colon cancer patients show resistance to their treatments. Therefore, it is important to consider unique characteristic of each tumor to find the best treatment options for each patient. In this study, we develop a data driven mathematical model for interaction between the tumor microenvironment and FOLFIRI drug agents in colon cancer. Patients are divided into five distinct clusters based on their estimated immune cell fractions obtained from their primary tumors’ gene expression data. We then analyze the effects of drugs on cancer cells and immune cells in each group, and we observe different responses to the FOLFIRI drugs between patients in different immune groups. For instance, patients in cluster 3 with the highest T-reg/T-helper ratio respond better to the FOLFIRI treatment, while patients in cluster 2 with the lowest T-reg/T-helper ratio resist the treatment. Moreover, we use ROC curve to validate the model using the tumor status of the patients at their follow up, and the model predicts well for the earlier follow up days.

“…For additional numerical stability and to eliminate scale dependence, we perform non-dimensionalization of the system. For variable X converging to a steady state X ∞ , we consider non-dimensional variable Then, satisfies the equation The (first order) solution sensitivity S with respect to the model parameter is defined as a vector In general, the sensitivity vector is time dependent and varies for different solutions and parameter sets [74–76]. However, here we consider sensitivity at the steady state of the equation.…”

Section: Methodsmentioning

confidence: 99%

“…In general, the sensitivity vector is time dependent and varies for different solutions and parameter sets [74][75][76]. However, here we consider sensitivity at the steady state of the equation.…”

Section: Necrotic Cellsmentioning

confidence: 99%

Data driven mathematical model of colon cancer progression

Akbarinejad

Hao

et al. 2020

Preprint

Self Cite

Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients, the size of the tumor is sensitive to the parameters related to macrophages such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.