Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy

Mamat, Mustafa; Subiyanto, .; Kartono, Agus Priyono

doi:10.12988/ams.2013.13023

Cited by 32 publications

(36 citation statements)

References 14 publications

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“…Similar success was achieved under combinations of T cell boosts, IL-2 and cancer vaccines [112,113]. A selection of other combination immune-and chemotherapy treatments have been modeled computationally [114,115]. The main observation from such models to date has been that the synergistic effects of combination treatments are sufficiently beneficial to justify further investigations and implementation of such methods in the clinic on a more regular basis.…”

Section: Combination Therapiesmentioning

confidence: 97%

From concept to clinic: mathematically informed immunotherapy

Walker

Enderling

2015

Preprint

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IntroductionMathematical modeling has become a valuable tool in the continued effort to understand, predict and ultimately treat a wide range of cancers in recent years [1,2]. By describing biological phenomena in the concise and formal language of mathematics, it is possible to elucidate key components of complex systems and ultimately develop tools capable of quantifying and predicting system behavior under given conditions. When these tools are applied as a complement to the detailed understanding of cancer biology provided by biological scientists and clinicians, new insights can be gained into the mechanisms and first-order principles of cancer development and control [3].To date, although mathematical tools have been applied extensively in understanding tumor growth and dynamic interactions between cancer and host, studies involving the theoretical modeling of patient response to treatment and the contribution of such findings to the development of clinically-actionable therapeutic protocols remain strikingly limited. In particular, despite the rising emergence of immunotherapy as a promising cancer treatment, knowledge gained from mathematical modeling of tumorimmune interactions often still eludes application to the clinic. The currently underutilized potential of such techniques to forecast response to treatment, aid the development of immunotherapeutic regimes and ultimately streamline the transition from innovative concept to clinical practice is hence the focus of this review. Mathematical oncologyDue to the simplifications inherent in the development of a mathematical model of a complex biological system, early attempts at combining mathematics with biology were often met with skepticism from experimentalists and clinicians. The misconception that simplifications render mathematical models meaningless is still found in some more conservative areas of medical research. Thankfully, the great potential for theoretical models to help unravel highly complex and multifaceted processes without the need for . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/027979 doi: bioRxiv preprint first posted online 2 time-consuming experimentation is becoming more widely appreciated [4]. Insights can be gained into mechanisms or relationships that may not be obvious or intuitive, allowing the generation of novel hypotheses on which to base future experimentation.Formalized descriptions of dynamic processes that have achieved a balance of both simplicity and applicability have contributed greatly to biological research to date. For example, in the field of oncology, tumor growth has been modeled extensively using methods ranging from simple one-equation models featuring logistic, Gompertz or exponential growth functions to detailed 3-dimensional spatio-temporal systems [5][6][7][8][9][10][11][12][13][14][15]. Detailed reviews of tumor growth modeling over the last few decades are...

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Section: Combination Therapiesmentioning

confidence: 97%

From concept to clinic: mathematically informed immunotherapy

Walker

Enderling

2015

Preprint

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“…It is well known that regression analysis regularly emerges in economics, finance, trade, meteorology, medicine biology, chemistry physics and etc. [39][40][41][42][43]. The classical regression model is defined by…”

Section: Introductionmentioning

confidence: 99%

A new family of conjugate gradient coefficient with application

Shapiee¹,

Rivaie²,

Mamat³

et al. 2018

IJET

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Conjugate gradient (CG) methods are famous for their utilization in solving unconstrained optimization problems, particularly for large scale problems and have become more intriguing such as in engineering field. In this paper, we propose a new family of CG coefficient and apply in regression analysis. The global convergence is established by using exact and inexact line search. Numerical res ults are presented based on the number of iterations and CPU time. The findings show that our method is more efficient in comparison to some of the previous CG methods for a given standard test problems and successfully solve the real life problem.

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“…[1][2][3][4] World Health Organization (WHO) estimated about six million deaths due to cancer. 4 Cancer is an uncontrolled growth of abnormal cells and it is just like a wound that never heals.…”

Section: Introductionmentioning

confidence: 99%

“…1 In previous decades, efforts have been diverted towards controlling the growth of cancer by studying its dynamical properties with an aim to predict how the tumor will grow in order to divert medicine to the part of tumor where most growth is expected. The model, governing cancer growth, is chaotic where small changes in initial condition may results in huge changes in the final results.…”

Section: Introductionmentioning

confidence: 99%

Improved numerical solutions for chaotic-cancer-model

et al. 2017

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In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR) method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.

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Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy

Cited by 32 publications

References 14 publications

From concept to clinic: mathematically informed immunotherapy

From concept to clinic: mathematically informed immunotherapy

A new family of conjugate gradient coefficient with application

Improved numerical solutions for chaotic-cancer-model

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