Optimal control problems for differential equations applied to tumor growth: state of the art

Rojas, Clara; Belmonte-Beitia, Juan

doi:10.21042/amns.2018.2.00029

Cited by 19 publications

(6 citation statements)

References 45 publications

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“…In this context, the main objective of the present study was to evaluate the protective effects of pomegranate and cocoa extracts during UVAinduced skin cancer in SKH-1 hairless mice. See for other approaches [14,15] or [16].…”

Section: Introductionmentioning

confidence: 99%

Chemopreventive effect of pomegranate and cocoa extracts on ultraviolet radiation-induced photocarcinogenesis in SKH-1 mice

Gómez-García¹,

López²,

Sánchez³

et al. 2020

PLoS ONE

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Non-melanoma skin cancer (NMSC) has a high and increasing incidence all over the world. Solar radiation is the main aetiology for humans. Although most research into photocarcinogenesis uses UVB as a source of radiation, UVA is also carcinogenic in long term. Pomegranate (PGE) and cocoa (CE) extracts have been used for medicinal purposes for time immemorial. Recently, it has been claimed that some of their properties may be an effective preventative measure against photocarcinogenesis and photoaging, but to date in vivo models have not been tested using RUVA, the objective of the present work. A lower incidence of lesions was observed in SKH-1 mice treated with PGE (p<0.001), and lower incidence of invasive squamous carcinoma in both treatment groups (p<0.001 for PGE and p<0.05 for CE); the PGE group also showed a lower level of cell proliferation than the control group (p<0.001). Significantly greater p53 alteration was observed in the control group than the treatment groups (p<0.001 for PGE and p = 0.05 for CE). No significant differences were found in relation to TIMP-1 and MMP-9. Taken together, the results suggest that oral feeding of PGE and CE to SKH-1 mice affords substantial protection against the adverse effects of RUVA, especially PGE.

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Section: Introductionmentioning

confidence: 99%

Chemopreventive effect of pomegranate and cocoa extracts on ultraviolet radiation-induced photocarcinogenesis in SKH-1 mice

Gómez-García¹,

López²,

Sánchez³

et al. 2020

PLoS ONE

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“…New product sales revenue/ total product sales revenue % Table 4. Optimal solution and relaxation variables According to the results in Table 4: 1) Enterprise 1 obtained the optimal solution of θ = 1 during the years of 2015, 2017 and 2018; and enterprise 4 got the optimal solution of θ = 1 during the years of 2016, 2017 and 2018 [10,12]. These results show that enterprise 1 and enterprise 4 have relatively efficient DEA, meaning that both enterprises are efficient in technological innovation.…”

Section: Analysis On the Effectiveness Of Technological Innovation Ofmentioning

confidence: 87%

CCR model-based evaluation on the effectiveness and maturity of technological innovation

Lin¹,

Zhao²

2022

JIMO

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As there are many indexes for evaluating technological innovation in enterprises, it is hard to quantify all those indexes. Therefore, common evaluation methods cannot be applied to solve the absolute value of the evaluation indexes. Therefore, this study used the nonparametric CCR model based on input-output to estimate the relative value of evaluation index, and took dual programming tool to obtain the judgment basis for the most effective and optimal solution. Based on the software evaluation criteria, this paper proposed the concept of "maturity in technological innovation," its four levels, and an evaluation standard for maturity. Based on the homogeneity, the paper selected four Beijing enterprises as evaluation samples. After comparing and analyzing the efficiency, scale return, production surface projection and maturity, we found that the evaluation results conform to the reality of sampling enterprises. CCR model was used to evaluate decision-making units with multiple inputs and outputs. The results show that this method can help accurately obtain the relative order and the enterprises' ability to make technological innovation. Thus, CCR model is able to help enterprises formulate policies on technological innovation.

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“…Mathematics provides the natural environment for modelling and analyzing problems from different areas in particular from health sciences, see for instance some applications to the war against cancer like [12,13]. In the next Appendix A we shall present all mathematical machinery used in this work.…”

Section: Discussionmentioning

confidence: 99%

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

et al. 2019

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The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann–Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53 . 67 years with a standard deviation of 8 . 20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

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Optimal control problems for differential equations applied to tumor growth: state of the art

Cited by 19 publications

References 45 publications

Chemopreventive effect of pomegranate and cocoa extracts on ultraviolet radiation-induced photocarcinogenesis in SKH-1 mice

Chemopreventive effect of pomegranate and cocoa extracts on ultraviolet radiation-induced photocarcinogenesis in SKH-1 mice

CCR model-based evaluation on the effectiveness and maturity of technological innovation

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

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