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Optimizing Chemotherapy Scheduling By Iteratively Solving a Recurrence Equation
2008
Algorithmic Operations Research
unpublished
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We illustrate how an iterative method and the idea of recurrence can be employed to optimize chemotherapy scheduling. ...
The optimal treatment schedule can be derived directly from the optimal objective function values at different states. We use an iterative method to solve the equation numerically. ...
In section 4, we introduce the iterative method to solve this equation numerically. ...
fatcat:6nqyh6njdvfetall4h7blnapua
A survey of optimization models on cancer chemotherapy treatment planning
2011
Annals of Operations Research
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As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit ...
While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction ...
Acknowledgements This paper is supported by National Science Foundation grant CMMI-0844423, NSFC projects (70672077, 71072026, 70832005) and NSFC major program (71090404/71090400). ...
doi:10.1007/s10479-011-0869-4
fatcat:eedq446nhzb4hic52ks2azyxdy
Optimal control of acute myeloid leukaemia
[article]
2018
bioRxiv
pre-print
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AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. ...
Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. ...
Computational resources were provided by the eResearch Office at QUT. ...
doi:10.1101/429811
fatcat:gp6eitzgavcr5aolf3ac6wcjce
Treating Glioblastoma Multiforme (GBM) with super hyperfractionated radiation therapy: Implication of temporal dose fractionation optimization including cancer stem cell dynamics
2021
PLoS ONE
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Results show that optimal outcome was achieved by first delivering infrequent fractions followed by dense once per day fractions in the middle and end of the treatment course, with sparse and low dose ...
In this study, optimization of temporal dose modulation based on the ODE equation is performed to explore the feasibility of improving GBM treatment outcome. ...
The optimization problem was solved using a paired simulated annealing algorithm [38] , in which a pair of elements within decided variable for change (T, D U , or D V ) were changed in each iteration ...
doi:10.1371/journal.pone.0245676
pmid:33524046
fatcat:7vsvjhpdnbgpjak5f44ogd7cim
Hybrid modeling frameworks of tumor development and treatment
2019
Wiley Interdisciplinary Reviews: Systems Biology and Medicine
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Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization ...
The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. ...
The optimization models integrated with the physics-based models can provide a way to systematically search for optimal treatment protocols using a minimal number of iterations. ...
doi:10.1002/wsbm.1461
pmid:31313504
pmcid:PMC6898741
fatcat:qomxxeo67fejtmftespb2mt5o4
Scheduling the adjuvant endocrine therapy for early stage breast cancer
2010
Annals of Operations Research
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Based on the data available through published trial results, we build a mixed integer nonlinear programming (MINLP) model in order to find an optimal treatment plan for a given Hr+ early stage breast cancer ...
The results of numerical experiments suggest the effectiveness of some of the schedules currently used in practice, as well as indicate some effective alternative treatment plans. ...
Hicks was partially supported by NSF grant DMI-0521209. ...
doi:10.1007/s10479-010-0741-y
fatcat:noe3ostxtndcvhasnofjm5wuue
PI-D CONTROLLER BASED ON AN IMPROVED CROW SEARCH ALGORITHM FOR CANCER GROWTH TREATMENT
2021
Journal of Engineering and Sustainable Development
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An optimal Proportion Integral-Derivative (PI-D) controller is introduced in this paper based on a suggested Improved Crow Search Algorithm (ICSA) to enhance the outcome of oncolytic virotherapy. ...
The ICSA used the inertia factor and boundary handle mechanism in the position update equation to balance exploration and exploitation. ...
It has been widely used to solve many optimization problems and has proven itself compared to many modern optimization algorithms available in the litterateurs [17] . where 𝑃 i 𝑡 Position matrix representing ...
doi:10.31272/jeasd.25.6.9
fatcat:rkpey426bfcafb7r6htpgprvpq
Optimal Treatment Strategies for HIV with Antibody Response
2014
Journal of Applied Mathematics
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Numerical analysis and optimization tools are used to suggest improved therapies to try and cure HIV infection. ...
An HIV model of ordinary differential equation, which includes immune response, neutralizing antibodies, and multidrug effects, is improved. ...
Acknowledgments This research was supported by the Natural Science Foundation of China (11271371) (71272209), and the Humanity and Social Science Foundation of Ministry of Education of China (12YJA630170 ...
doi:10.1155/2014/685289
fatcat:2biaj6qn5bdyzdhkldtlfpw2ei
Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data
[article]
2019
arXiv
pre-print
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A feature of the approach is that we iterate between full order solves with new parameters to compute a POD basis function and sensitivity based parameter estimation for the ROM problems. ...
Neuroimaging data are used to define the highly inhomogeneous diffusion tensors as well as to define a target functional in a patient specific manner. ...
A. Bizzi (Istituto Neurologico Besta, Milan) for providing the neuroimaging data and their guidance on key aspects of the clinical practice. ...
arXiv:1912.08036v1
fatcat:63yibapccjau5ad6ixlddbcqja
Prospect for application of mathematical models in combination cancer treatments
[article]
2021
arXiv
pre-print
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CCTs often utilize multiple combinatorial modes of action and thus potentially constitute a promising approach to overcome drug resistance. ...
The long-term efficacy of targeted therapeutics for cancer treatment can be significantly limited by the type of therapy and development of drug resistance, inter alia. ...
Contains equation-solving packages which can be used to plot functions, solve blocks of equations, perform curve-fitting operations as well as solving differential equations using iterative methods. ...
arXiv:2012.00683v2
fatcat:lih2f75ccjdstaaap4ak45f5ue
Tumor Development Under Combination Treatments with Anti-angiogenic Therapies
[chapter]
2012
Lecture Notes on Mathematical Modelling in the Life Sciences
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, which is partially funded by the European Commission under the 7 th framework program. ...
The research of A. d'Onofrio has been done in the framework of the Integrated Project "p-medicine -from data sharing and integration via VPH models to personalized medicine," project identifier: 270089 ...
schedules for a given amount of inhibitors has been solved in [40] . ...
doi:10.1007/978-1-4614-4178-6_11
fatcat:lk4wtrxzlrgmlflwr5owb7sq3i
Comprehensive Joint Modeling of First-Line Therapeutics in Non-Small Cell Lung Cancer
[article]
2020
medRxiv
pre-print
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To help accelerate the development of novel therapeutics and computer-based tools for optimizing individual therapy, we have collated data from 11 different clinical trials in NSCLC and developed a semi-mechanistic ...
First-line antiproliferatives for non-small cell lung cancer (NSCLC) have a relatively high failure rate due to high intrinsic resistance rates and acquired resistance rates to therapy. 57% patients are ...
Mathematical modeling is a key strategy for addressing these needs, as its use in cancer is a proven method for solving problems in optimization and precision medicine (4) (5) (6) (7) . ...
doi:10.1101/2020.11.24.20238212
fatcat:qs2lyy7egbfjtkszxqcyqbjijy
Combination Chemotherapy Optimization with Discrete Dosing
[article]
2021
arXiv
pre-print
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Previous chemotherapy optimization models have mainly relied on optimal control, which does not lend itself to capturing complex and vital operational constraints in chemotherapy planning involving discrete ...
In this paper, we develop a mixed-integer program for combination chemotherapy (utilization of multiple drugs) optimization that incorporates various important operational constraints and, besides dose ...
Ajayi, Hosseinian, Schaefer, Fuller: Combination Chemotherapy Optimization with Discrete Dosing ...
arXiv:2111.02000v1
fatcat:jj6x6w2zovcfjefsuyup6pemj4
In SilicoModelling of Treatment-Induced Tumour Cell Kill: Developments and Advances
2012
Computational and Mathematical Methods in Medicine
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Fractionated radiotherapy, chemotherapy, and combined therapies are reviewed, providing a comprehensive overview of the modelling literature for current modellers and radiobiologists to ignite the interest ...
This technique is useful for modelling systems with a large number of coupled degrees of freedom, which are difficult to solve using equation-based methods. ...
theory by means of new equation sets. ...
doi:10.1155/2012/960256
pmid:22852024
pmcid:PMC3407630
fatcat:zkcstoml6jdw5poflatfdg2upe
Employing dynamical computational models for personalizing cancer immunotherapy
2016
Expert Opinion on Biological Therapy
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A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of ...
However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. ...
Funding The authors are supported by the Chai Foundation. ...
doi:10.1080/14712598.2016.1223622
pmid:27564141
fatcat:ylgoynyte5hizatvgn6rp5yolu
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