(Q38644551)

5 September 2017

The mathematics of cancer: integrating quantitative models (English)

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5 September 2017

3

Franziska Michor

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5 September 2017

Philipp M Altrock

1

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5 September 2017

Lin L Liu

series ordinal

2

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5 September 2017

language of work or name

English

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publication date

1 November 2015

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5 September 2017

Nature Reviews Cancer

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5 September 2017

15

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5 September 2017

12

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5 September 2017

730-745

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maintained by WikiProject

5 September 2017

WikiProject Mathematics

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https://scigraph.springernature.com/pub.10.1038/nrc4029

inferred from title

exact match

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cites work

The Hallmarks of Cancer

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The clonal evolution of tumor cell populations

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Cancer immunoediting: from immunosurveillance to tumor escape

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Effector memory T cells, early metastasis, and survival in colorectal cancer

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Mechanisms of therapy-related carcinogenesis

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Metastasis: from dissemination to organ-specific colonization

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Tumor self-seeding by circulating cancer cells

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Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment.

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Integrative mathematical oncology.

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Dissecting cancer through mathematics: from the cell to the animal model

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Mutation and cancer: statistical study of retinoblastoma

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Expression of recessive alleles by chromosomal mechanisms in retinoblastoma

31 March 2020

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Evolutionary dynamics of cancer in response to targeted combination therapy

31 March 2020

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Tyrosine kinase inhibitor therapy can cure chronic myeloid leukemia without hitting leukemic stem cells

31 March 2020

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The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers

31 March 2020

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Comparative lesion sequencing provides insights into tumor evolution

31 March 2020

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Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules

31 March 2020

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Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model

31 March 2020

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Drug resistance in cancer: principles of emergence and prevention

31 March 2020

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Mathematical modeling of cancer progression and response to chemotherapy

31 March 2020

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Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy

31 March 2020

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A two-stage theory of carcinogenesis in relation to the age distribution of human cancer

31 March 2020

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A new theory on cancer-inducing mechanism

31 March 2020

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A hypothesis for the origin of cancer foci

31 March 2020

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31 March 2020

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A smoking-based carcinogenesis model for lung cancer risk prediction

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Accumulation of driver and passenger mutations during tumor progression

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Cancer initiation with epistatic interactions between driver and passenger mutations

31 March 2020

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Half or more of the somatic mutations in cancers of self-renewing tissues originate prior to tumor initiation

31 March 2020

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Cancer etiology. Variation in cancer risk among tissues can be explained by the number of stem cell divisions

31 March 2020

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Cancer: Risk factors and random chances

31 March 2020

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Cancer risk: role of environment

31 March 2020

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Cancer risk: accuracy of literature

31 March 2020

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Cancer risk: tumors excluded.

31 March 2020

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Cancer risk: role of environment—response.

31 March 2020

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Peto's paradox and human cancers.

31 March 2020

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Impact of deleterious passenger mutations on cancer progression

31 March 2020

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Tug-of-war between driver and passenger mutations in cancer and other adaptive processes

31 March 2020

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Stochastic dynamics of cancer initiation

31 March 2020

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Random processes in genetics

31 March 2020

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An Evolutionary Approach for Identifying Driver Mutations in Colorectal Cancer

31 March 2020

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Genetic progression and the waiting time to cancer

31 March 2020

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A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

31 March 2020

1 reference

Dynamics of mutant cells in hierarchical organized tissues

31 March 2020

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A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics

31 March 2020

1 reference

Stochastic elimination of cancer cells.

31 March 2020

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Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications.

31 March 2020

1 reference

A progenitor cell origin of myeloid malignancies

31 March 2020

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Mathematical model for the cancer stem cell hypothesis

31 March 2020

1 reference

The probable cell of origin of NF1- and PDGF-driven glioblastomas

31 March 2020

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A genetic model for colorectal tumorigenesis

31 March 2020

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Genetic alterations during colorectal-tumor development

31 March 2020

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Comprehensive molecular characterization of human colon and rectal cancer

31 March 2020

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Integrated genomic analyses of ovarian carcinoma

31 March 2020

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Comprehensive genomic characterization of squamous cell lung cancers

31 March 2020

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Genomic and epigenomic landscapes of adult de novo acute myeloid leukemia

31 March 2020

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COSMIC: mining complete cancer genomes in the Catalogue of Somatic Mutations in Cancer

31 March 2020

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International network of cancer genome projects

31 March 2020

1 reference

The consensus coding sequences of human breast and colorectal cancers

31 March 2020

1 reference

The mutational landscape of head and neck squamous cell carcinoma

31 March 2020

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Inferring tree models for oncogenesis from comparative genome hybridization data

31 March 2020

1 reference

Distance-based reconstruction of tree models for oncogenesis.

31 March 2020

1 reference

Statistical behavior of complex cancer karyotypes

31 March 2020

1 reference

Learning multiple evolutionary pathways from cross-sectional data

31 March 2020

1 reference

Construction of tree models for pathogenesis of nasopharyngeal carcinoma.

31 March 2020

1 reference

Construction of oncogenetic tree models reveals multiple pathways of oral cancer progression

31 March 2020

1 reference

New probabilistic network models and algorithms for oncogenesis.

31 March 2020

1 reference

Quantifying cancer progression with conjunctive Bayesian networks

31 March 2020

1 reference

The temporal order of genetic and pathway alterations in tumorigenesis

31 March 2020

1 reference

A mathematical framework to determine the temporal sequence of somatic genetic events in cancer

31 March 2020

1 reference

A mathematical methodology for determining the temporal order of pathway alterations arising during gliomagenesis

31 March 2020

1 reference

Fixation of strategies for an evolutionary game in finite populations.

31 March 2020

1 reference

Temporal and spatial evolution of somatic chromosomal alterations: a case-cohort study of Barrett's esophagus

31 March 2020

1 reference

Accurate reconstruction of the temporal order of mutations in neoplastic progression

31 March 2020

1 reference

Clonal evolution in breast cancer revealed by single nucleus genome sequencing.

31 March 2020

1 reference

Evolutionary pathways in BRCA1-associated breast tumors

31 March 2020

1 reference

Temporal dissection of tumorigenesis in primary cancers

31 March 2020

1 reference

Estimation of rearrangement phylogeny for cancer genomes

31 March 2020

1 reference

Methods and challenges in timing chromosomal abnormalities within cancer samples

31 March 2020

1 reference

A Big Bang model of human colorectal tumor growth

31 March 2020

1 reference

The pathogenesis of cancer metastasis: the 'seed and soil' hypothesis revisited

31 March 2020

1 reference

The microenvironment of the tumour-host interface

31 March 2020

1 reference

Friends or foes - bipolar effects of the tumour stroma in cancer

31 March 2020

1 reference

Growth of necrotic tumors in the presence and absence of inhibitors.

31 March 2020

1 reference

A new mathematical model for avascular tumour growth

31 March 2020

1 reference

Reaction-diffusion model for the growth of avascular tumor

31 March 2020

1 reference

Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis

31 March 2020

1 reference

Multiscale modelling and nonlinear simulation of vascular tumour growth.

31 March 2020

1 reference

Hybrid models of tumor growth.

31 March 2020

1 reference

'Go or grow': the key to the emergence of invasion in tumour progression?

31 March 2020

1 reference

Continuous and discrete mathematical models of tumor-induced angiogenesis.

31 March 2020

1 reference

Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.

31 March 2020

1 reference

A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion

31 March 2020

1 reference

An integrated computational model of the bone microenvironment in bone-metastatic prostate cancer

31 March 2020

1 reference

Three-dimensional multispecies nonlinear tumor growth-II: Tumor invasion and angiogenesis

31 March 2020

1 reference

Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method

31 March 2020

1 reference

Prediction of drug response in breast cancer using integrative experimental/computational modeling

31 March 2020

1 reference

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

31 March 2020

1 reference

THE METABOLISM OF TUMORS IN THE BODY

31 March 2020

1 reference

A cellular automaton model of early tumor growth and invasion

31 March 2020

1 reference

A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype

31 March 2020

1 reference

Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion

31 March 2020

1 reference

The evolution of mathematical modeling of glioma proliferation and invasion.

31 March 2020

1 reference

Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model

31 March 2020

1 reference

Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology

31 March 2020

1 reference

Incorporation of diffusion-weighted magnetic resonance imaging data into a simple mathematical model of tumor growth

31 March 2020

1 reference

Clinically relevant modeling of tumor growth and treatment response.

31 March 2020

1 reference

Toward a science of tumor forecasting for clinical oncology

31 March 2020

1 reference

PIK3CA and APC mutations are synergistic in the development of intestinal cancers

31 March 2020

1 reference

Mechanisms of integrin-vascular endothelial growth factor receptor cross-activation in angiogenesis

31 March 2020

1 reference

Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

31 March 2020

1 reference

Complexity and stability in growing cancer cell populations

31 March 2020

1 reference

Non-cell-autonomous driving of tumour growth supports sub-clonal heterogeneity

31 March 2020

1 reference

Migration rules: tumours are conglomerates of self-metastases.

31 March 2020

1 reference

Angiogenesis in cancer and other diseases

31 March 2020

1 reference

Multiscale modeling of fluid transport in tumors.

31 March 2020

1 reference

Mathematical modeling of tumor-induced angiogenesis

31 March 2020

1 reference

Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach.

31 March 2020

1 reference

The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy.

31 March 2020

1 reference

Cancer immunotherapy: moving beyond current vaccines

31 March 2020

1 reference

T cells with chimeric antigen receptors have potent antitumor effects and can establish memory in patients with advanced leukemia

31 March 2020

1 reference

Cancer immunotherapy: a treatment for the masses

31 March 2020

1 reference

The blockade of immune checkpoints in cancer immunotherapy

31 March 2020

1 reference

A validated mathematical model of cell-mediated immune response to tumor growth.

31 March 2020

1 reference

A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences

31 March 2020

1 reference

Interleukin-21 is a T-helper cytokine that regulates humoral immunity and cell-mediated anti-tumour responses

31 March 2020

1 reference

Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model

31 March 2020

1 reference

SimB16: modeling induced immune system response against B16-melanoma

31 March 2020

1 reference

The cancer diaspora: Metastasis beyond the seed and soil hypothesis

31 March 2020

1 reference

31 March 2020

Self-seeding in cancer

1 reference

System dynamics of metastatic process from an implanted tumor

31 March 2020

1 reference

Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics

31 March 2020

1 reference

Genetic and phenotypic diversity in breast tumor metastases

31 March 2020

1 reference

Unifying metastasis--integrating intravasation, circulation and end-organ colonization

31 March 2020

1 reference

Comments on hematogenous metastatic patterns in humans as revealed by autopsy

31 March 2020

1 reference

A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth.

31 March 2020

1 reference

A filter-flow perspective of haematogenous metastasis offers a non-genetic paradigm for personalised cancer therapy.

31 March 2020

1 reference

Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy

31 March 2020

1 reference

Computational modeling of pancreatic cancer reveals kinetics of metastasis suggesting optimum treatment strategies

31 March 2020

1 reference

The evolution of tumor metastases during clonal expansion

31 March 2020

1 reference

A stochastic Markov chain model to describe lung cancer growth and metastasis

31 March 2020

1 reference

Spreaders and sponges define metastasis in lung cancer: a Markov chain Monte Carlo mathematical model.

31 March 2020

1 reference

Surgical treatment of lung cancer with adrenal metastasis

31 March 2020

1 reference

Adrenal metastases in lung cancer: clinical implications of a mathematical model.

31 March 2020

1 reference

Independent regulation of tumor cell migration by matrix stiffness and confinement.

31 March 2020

1 reference

What does physics have to do with cancer?

31 March 2020

1 reference

Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model

31 March 2020

1 reference

Normalizing tumor microenvironment to treat cancer: bench to bedside to biomarkers

31 March 2020

1 reference

A stochastic model for the origin and treatment of tumors containing drug-resistant cells.

31 March 2020

1 reference

Growth Curve of an Experimental Solid Tumor Following Radiotherapy

31 March 2020

1 reference

Randomized Trial of Dose-Dense Versus Conventionally Scheduled and Sequential Versus Concurrent Combination Chemotherapy as Postoperative Adjuvant Treatment of Node-Positive Primary Breast Cancer: First Report of Intergroup Trial C9741/Cancer and Leu

31 March 2020

1 reference

Clinical relevance of different sequencing of doxorubicin and cyclophosphamide, methotrexate, and Fluorouracil in operable breast cancer

31 March 2020

1 reference

Evolution of acquired resistance to anti-cancer therapy

31 March 2020

1 reference

Evolution of resistance to targeted anti-cancer therapies during continuous and pulsed administration strategies

31 March 2020

1 reference

Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling

31 March 2020

1 reference

Effects of pharmacokinetic processes and varied dosing schedules on the dynamics of acquired resistance to erlotinib in EGFR-mutant lung cancer

31 March 2020

1 reference

Dynamics of chronic myeloid leukaemia.

31 March 2020

1 reference

Response classification based on a minimal model of glioblastoma growth is prognostic for clinical outcomes and distinguishes progression from pseudoprogression

31 March 2020

1 reference

Toward patient-specific, biologically optimized radiation therapy plans for the treatment of glioblastoma.

31 March 2020

1 reference

Mathematical modeling of prostate cancer progression in response to androgen ablation therapy

31 March 2020

1 reference

31 March 2020

1 reference

Inducing catastrophe in malignant growth

31 March 2020

1 reference

Somatic mosaicism and cancer: inference based on a conditional Luria-Delbrück distribution

31 March 2020

1 reference

The evolution of two mutations during clonal expansion

31 March 2020

1 reference

Evolution of resistance and progression to disease during clonal expansion of cancer.

31 March 2020

1 reference

Evolutionary dynamics of escape from biomedical intervention.

31 March 2020

1 reference

Stochastic modeling of cellular colonies with quiescence: an application to drug resistance in cancer

31 March 2020

1 reference

Timing and heterogeneity of mutations associated with drug resistance in metastatic cancers

31 March 2020

1 reference

Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer

31 March 2020

1 reference

Stochastic modeling of drug resistance in cancer.

31 March 2020

1 reference

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

31 March 2020

1 reference

Deterministic evolutionary game dynamics in finite populations.

31 March 2020

1 reference

Dynamics of resistance development to imatinib under increasing selection pressure: a combination of mathematical models and in vitro data

31 March 2020

1 reference

Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance.

31 March 2020

1 reference

Emergence of stable polymorphisms driven by evolutionary games between mutants

31 March 2020

1 reference

Stochastic game dynamics under demographic fluctuations

31 March 2020

1 reference

Reply to Gerlee and Altrock: Diffusion and population size in game theory models of cancer

31 March 2020

1 reference

Tumorigenesis: it takes a village

31 March 2020

1 reference

The ecology of cancer from an evolutionary game theory perspective

31 March 2020

1 reference

Evolution of cooperation among tumor cells

31 March 2020

1 reference

Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies

31 March 2020

1 reference

Investigating prostate cancer tumour-stroma interactions: clinical and biological insights from an evolutionary game

31 March 2020

1 reference

Critical transitions in a game theoretic model of tumour metabolism

31 March 2020

1 reference

Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion

31 March 2020

1 reference

The Impact of Microenvironmental Heterogeneity on the Evolution of Drug Resistance in Cancer Cells

31 March 2020

1 reference

12 December 2020

Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review.

1 reference

12 December 2020

Quantitative model for multiple levels of drug resistance in clinical tumors.

1 reference

12 December 2020

Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies.

1 reference

12 December 2020

Cancer immunology: the search for specificity--G. H. A. Clowes Memorial lecture

1 reference

12 December 2020

A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate

1 reference

12 December 2020

A reaction-diffusion model of cancer invasion.

1 reference

12 December 2020

Patterns of Cell Division and the Risk of Cancer

1 reference

12 December 2020

A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment.

1 reference

12 December 2020

The distribution of secondary growths in cancer of the breast. 1889

1 reference

12 December 2020

Mutations of Bacteria from Virus Sensitivity to Virus Resistance

1 reference

12 December 2020

Chromosome abnormalities in ovarian adenocarcinoma: III. Using breakpoint data to infer and test mathematical models for oncogenesis

1 reference

12 December 2020

The genetic origin of drug resistance in neoplasms: implications for systemic therapy.

1 reference

12 December 2020

Identifiers

DOI

10.1038/NRC4029

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Dimensions Publication ID

5 September 2017

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