Back to Search
Start Over
A numerical approach for a discrete Markov model for progressing drug resistance of cancer
- Source :
- PLoS Computational Biology, PLoS Computational Biology, Vol 15, Iss 2, p e1006770 (2019)
- Publication Year :
- 2019
- Publisher :
- Public Library of Science, 2019.
-
Abstract
- The presence of treatment-resistant cells is an important factor that limits the efficacy of cancer therapy, and the prospect of resistance is considered the major cause of the treatment strategy. Several recent studies have employed mathematical models to elucidate the dynamics of generating resistant cancer cells and attempted to predict the probability of emerging resistant cells. The purpose of this paper is to present numerical approach to compute the number of resistant cells and the emerging probability of resistance. Stochastic model was designed and developed a method to approximately but efficiently compute the number of resistant cells and the probability of resistance. To model the progression of cancer, a discrete-state, two-dimensional Markov process whose states are the total number of cells and the number of resistant cells was employed. Then exact analysis and approximate aggregation approaches were proposed to calculate the number of resistant cells and the probability of resistance when the cell population reaches detection size. To confirm the accuracy of computed results of approximation, relative errors between exact analysis and approximation were computed. The numerical values of our approximation method were very close to those of exact analysis calculated in the range of small detection size M = 500, 100, and 1500. Then computer simulation was performed to confirm the accuracy of computed results of approximation when the detection size was M = 10000,30000,50000,100000 and 1000000. All the numerical results of approximation fell between the upper level and the lower level of 95% confidential intervals and our method took less time to compute over a broad range of cell size. The effects of parameter change on emerging probabilities of resistance were also investigated by computed values using approximation method. The results showed that the number of divisions until the cell population reached the detection size is important for emerging the probability of resistance. The next step of numerical approach is to compute the emerging probabilities of resistance under drug administration and with multiple mutation. Another effective approximation would be necessary for the analysis of the latter case.<br />Author summary Drug therapies for cancer have dramatically succeeded since molecular-targeted drugs have been introduced in medical practice; however, drug treatment often fails owing to the emergence of drug-resistant cells. A variety of approaches, including mathematical modeling, has been undertaken to clarify the mechanism of resistance and subsequently avoid resistance to therapy. This paper proposes one of the mathematical approaches that uses a stochastic model and provides the emerging probabilities of resistance at detection size.
- Subjects :
- 0301 basic medicine
Stochastic modelling
Cancer Treatment
0302 clinical medicine
Neoplasms
Range (statistics)
Medicine and Health Sciences
Cell Cycle and Cell Division
lcsh:QH301-705.5
Mathematics
education.field_of_study
Ecology
Mathematical model
Approximation Methods
Pharmaceutics
Markov Chains
Computational Theory and Mathematics
Oncology
Cell Processes
Modeling and Simulation
Physical Sciences
symbols
Probability distribution
Research Article
Computer Modeling
Computer and Information Sciences
Markov Models
Biochemical Phenomena
Population
Markov process
Markov model
03 medical and health sciences
Cellular and Molecular Neuroscience
symbols.namesake
Drug Therapy
Genetics
Applied mathematics
Point Mutation
Humans
Computer Simulation
education
Molecular Biology
Ecology, Evolution, Behavior and Systematics
Probability
Models, Statistical
Markov chain
Models, Genetic
Biology and Life Sciences
Cell Biology
Models, Theoretical
Probability Theory
Probability Distribution
030104 developmental biology
lcsh:Biology (General)
Drug Resistance, Neoplasm
Mutation
030217 neurology & neurosurgery
Subjects
Details
- Language :
- English
- ISSN :
- 15537358 and 1553734X
- Volume :
- 15
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- PLoS Computational Biology
- Accession number :
- edsair.doi.dedup.....d95df434c206830258d61649ae309e63