A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors
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Cites background from "A Review of Mathematical Models for..."
...ing our understanding of these pathologies and providing a means to monitor and forecast tumor growth via patient-specic computer simulations, which can assist physicians in clinical decision-making [1, 5, 10, 18, 72, 79, 100, 101]. Several studies have focused on the eects of chemotherapeutic strategies for various types of tumors [8, 24, 34, 39, 46, 50, 77, 101]. In this context, optimal control theory provides a robust fram...
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...e that these quantitative approaches can play a signicant role in the design of optimal drug regimens, providing the best dosing, timing, and even drug pharmacodynamics to treat each patient’s tumor [39, 45, 63, 101]. Hence, optimal drug protocols can help us reduce the total amount of drug needed to achieve a target tumor size reduction, which is very important considering the harsh side eects of cytotoxic and ...
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... The design of therapeutic solutions could be further rened in multiple directions, e.g., by exploring alternative paradigms to model the dynamic eects of specic cytotoxic and antiangiogenic drugs [28, 34, 39, 53, 73, 101], by explicitly including drug toxicity (e.g., throughout the time integral of drug concentration [6, 53]), by accounting for the synergistic action of drug combinations [39, 66], or by considering ot...
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13 citations
Cites background from "A Review of Mathematical Models for..."
...Unfortunately, the publication and application of individual tumor lesion models in clinical development is very limited.(8,51)...
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References
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5,633 citations
"A Review of Mathematical Models for..." refers methods in this paper
...19).(45) This model structure was recently adopted to obtain an optimal dosing regimen for cancer patients based on simulation....
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1,630 citations
"A Review of Mathematical Models for..." refers result in this paper
...By applying longitudinal monitoring of ctDNA, an adaptive treatment for individual patients may be achieved by selecting drugs that target emerging actionable mutations.(98) Therefore, it is feasible to obtain the information of evolving cancer resistance and, to increase the chance to overcome treatment resistance, it would be helpful if such information could be incorporated in future model-based studies....
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...For example, in a clinical setting, a feasible genetic biomarker that is also correlated with tumor burden has been identified as ctDNA.(98) Three of the included studies have already utilized the available ctDNA data to support the estimation of parameters in the tumor evolution model or to evaluate the model simulation results....
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1,555 citations
"A Review of Mathematical Models for..." refers methods in this paper
...The derived equations were later adopted to estimate the resistance probability of colorectal cancer prior to endothelial growth factor receptor (EGFR) antibody treatment, where the parameters were estimated based on longitudinal KRAS mutation amount measurements.(77) The results indicated that the resistant mutation was highly likely to be present prior to the initiation of treatment....
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...Three of the included studies have already utilized the available ctDNA data to support the estimation of parameters in the tumor evolution model or to evaluate the model simulation results.(77,79,90) It has also been demonstrated that the mutation in ctDNA, which represents treatment resistance, is detectable before disease progression,(99) suggesting the predictive value of ctDNA to the development of drug resistance....
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684 citations
"A Review of Mathematical Models for..." refers background in this paper
...Currently, an increasing number of studies concerning the gene sequencing of tumor biopsies in different cancer types have demonstrated the dynamics of cancer evolution.(2,12) Intratumor heterogeneity that results from cancer evolution and an evolving adaption of heterogeneous tumor to treatment are also increasingly acknowledged as key factors related to the development of resistance....
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...Intratumor heterogeneity that results from cancer evolution and an evolving adaption of heterogeneous tumor to treatment are also increasingly acknowledged as key factors related to the development of resistance.(2,12) To better characterize this process and to account for tumor heterogeneity, mathematical models that consider the evolution of tumors have been proposed....
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565 citations
"A Review of Mathematical Models for..." refers background or methods in this paper
...17 and 18).(43,44) For example, the model structure proposed to describe PSA change in prostate cancer patients treated with a vaccine assumed that the presence of the vaccine upregulated the zero-order production rate of mature dendritic cells and therefore increased the number of cytotoxic T lymphocytes, which increased the decay of tumor tissue....
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...Apart from angiogenesis, the effect of the immune system has also been incorporated in the tumor growth model when patients were undergoing immunotherapy.(43,44) The proposed model structure is presented in Eqs....
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...to simulate the growth of bladder cancer undergoing immunotherapy.(43) The growth of tumor cells was described with a logistic model, and the cell decline rate was set to be linearly or nonlinearly related to the amount of immune components (Eq....
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