scispace - formally typeset
Search or ask a question
Journal ArticleDOI

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

01 Oct 2019-Vol. 8, Iss: 10, pp 720-737
TL;DR: The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.
Abstract: Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model-based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model-based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model-based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.
Citations
More filters
Book ChapterDOI
Neil Dubin1
01 Jan 1976
TL;DR: The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic.
Abstract: Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

565 citations

Journal ArticleDOI
TL;DR: A non-exhaustive overview of models according to their intrinsic features of in silico cancer models is provided, using the hallmarks of cancer as a guidance.

30 citations

Journal ArticleDOI
TL;DR: The results suggest that only cytotoxic chemotherapy is required to optimize therapeutic performance and it is shown that the optimal control framework can produce superior solutions to combined therapy with docetaxel and bevacizumab.
Abstract: Prostate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cy...

18 citations


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...

    [...]

  • ...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 ...

    [...]

  • ... 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...

    [...]

Journal ArticleDOI
01 Aug 2020
TL;DR: This review is to comprehensively summarize the history of TGD, and present case examples of the recent advance ofTGD modeling (mixture model and joint model), as well as the TGD impact on regulatory decisions, thus illustrating challenges and opportunities.
Abstract: Model-informed drug development (MIDD) approaches have rapidly advanced in drug development in recent years Additionally, the Prescription Drug User Fee Act (PDUFA) VI has specific commitments to further enhance MIDD Tumor growth dynamic (TGD) modeling, as one of the commonly utilized MIDD approaches in oncology, fulfills the purposes to accelerate the drug development, to support new drug and biologics license applications, and to guide the market access Increasing knowledge of TGD modeling methodologies, encouraging applications in clinical setting for patients' survival, and complementing assessment of regulatory review for submissions, together fueled promising potentials for imminent enhancement of TGD in oncology This review is to comprehensively summarize the history of TGD, and present case examples of the recent advance of TGD modeling (mixture model and joint model), as well as the TGD impact on regulatory decisions, thus illustrating challenges and opportunities Additionally, this review presents the future perspectives for TGD approach

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)...

    [...]

Journal ArticleDOI
TL;DR: In this paper , the authors focused on tumour heterogeneity and its relation to resistance to targeted-therapy, based on treatment selective pressure across different tumour types, including lung, colorectal, prostate, breast cancer and melanoma.

11 citations

References
More filters
BookDOI
John Gerring1
07 Jul 2011
TL;DR: On May 25, 1977, IEEE member, Virginia Edgerton, a senior information scientist employed by the City of New York, telephoned the chairman of CSIT's Working Group on Ethics and Employment Practices, having been referred to the committee by IEEE Headquarters.
Abstract: On May 25, 1977, IEEE member, Virginia Edgerton, a senior information scientist employed by the City of New York, telephoned the chairman of CSIT's Working Group on Ethics and Employment Practices, having been referred to the committee by IEEE Headquarters. She said that she had encountered a situation that might lead to the degradation of a data processing system (called SPRINT) used to dispatch police cars in response to emergency calls, and that her immediate superior, who disagreed with this assessment, refused to have the problem studied. Ms. Edgerton sought advice from the committee.

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....

    [...]

Journal ArticleDOI
TL;DR: The field is now in an exciting transitional period in which ctDNA analysis is beginning to be applied clinically, although there is still much to learn about the biology of cell-free DNA.
Abstract: Improvements in genomic and molecular methods are expanding the range of potential applications for circulating tumour DNA (ctDNA), both in a research setting and as a 'liquid biopsy' for cancer management. Proof-of-principle studies have demonstrated the translational potential of ctDNA for prognostication, molecular profiling and monitoring. The field is now in an exciting transitional period in which ctDNA analysis is beginning to be applied clinically, although there is still much to learn about the biology of cell-free DNA. This is an opportune time to appraise potential approaches to ctDNA analysis, and to consider their applications in personalized oncology and in cancer research.

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....

    [...]

  • ...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....

    [...]

Journal ArticleDOI
28 Jun 2012-Nature
TL;DR: Results suggest that the emergence of KRAS mutations is a mediator of acquired resistance to EGFR blockade and that these mutations can be detected in a non-invasive manner, which explains why solid tumours develop resistance to targeted therapies in a highly reproducible fashion.
Abstract: Colorectal tumours that are wild type for KRAS are often sensitive to EGFR blockade, but almost always develop resistance within several months of initiating therapy. The mechanisms underlying this acquired resistance to anti-EGFR antibodies are largely unknown. This situation is in marked contrast to that of small-molecule targeted agents, such as inhibitors of ABL, EGFR, BRAF and MEK, in which mutations in the genes encoding the protein targets render the tumours resistant to the effects of the drugs. The simplest hypothesis to account for the development of resistance to EGFR blockade is that rare cells with KRAS mutations pre-exist at low levels in tumours with ostensibly wild-type KRAS genes. Although this hypothesis would seem readily testable, there is no evidence in pre-clinical models to support it, nor is there data from patients. To test this hypothesis, we determined whether mutant KRAS DNA could be detected in the circulation of 28 patients receiving monotherapy with panitumumab, a therapeutic anti-EGFR antibody. We found that 9 out of 24 (38%) patients whose tumours were initially KRAS wild type developed detectable mutations in KRAS in their sera, three of which developed multiple different KRAS mutations. The appearance of these mutations was very consistent, generally occurring between 5 and 6 months following treatment. Mathematical modelling indicated that the mutations were present in expanded subclones before the initiation of panitumumab treatment. These results suggest that the emergence of KRAS mutations is a mediator of acquired resistance to EGFR blockade and that these mutations can be detected in a non-invasive manner. They explain why solid tumours develop resistance to targeted therapies in a highly reproducible fashion.

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....

    [...]

  • ...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....

    [...]

Journal ArticleDOI
03 May 2018-Cell
TL;DR: The data showed that resistant genotypes were pre-existing and adaptively selected by NAC, while transcriptional profiles were acquired by reprogramming in response to chemotherapy in TNBC patients.

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....

    [...]

  • ...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....

    [...]

Book ChapterDOI
Neil Dubin1
01 Jan 1976
TL;DR: The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic.
Abstract: Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

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....

    [...]

  • ...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....

    [...]

  • ...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....

    [...]