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Fractal geometry applied to the analysis of cervix biopsy

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Abstract

Background: the measurement of the spaces of occupation of irregular objects in the context of fractal geometry has had some applications at a cellular morphometric level, where characterizations of normality and disease have been established. The objective of the present study is to apply a fractal methodology to characterize images from cervical colposcopy. Materials and methods: a mathematical and geometrical characterization of 67 cell samples was performed by measuring cellular fractal characteristics through the Box-Counting method, being nine normal, eight low-intraepithelial lesions, 16 high-intraepithelial lesions, eight carcinomas in situ, 20 squamous cell carcinomas and six endocervical carcinomas. Results: the values of fractal dimension of the nuclear and cytoplasmic borders with respect to the totality varied between 0.719 to 1128 and 0.81 to 1024 while the occupation spaces in the 2 pixels grid were between 293 to 1606 and 64 to 693 respectively and in the 4 pixels grid oscillated between 153 to 894 and 36 to 361, respectively. Exocervical cells values had sensitivities between 78.3% to 100% in order to differentiate them from different types of cervical lesions. Conclusions: according to the results obtained, the mathematical values found are suggestive of being able to differentiate between normality and some colposcopy-guided cervical biopsy lesions.

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Background: Mathematical models can be useful tools in exploring disease trends and health consequences of interventions in a population over time. Most cancers, in particular cervical cancer, have long incubation periods. The time from acquisition of HPV infection to development of invasive cancer can be up to two decades or more. Mathematical models can be used to translate short-term findings from prevention and mitigations trials into predictions of long-term health outcomes. The main objective of this paper is to develop a mathematical model of HPV for African American women (AAW) in the United States and give quantitative insight into current U.S. prevention and mitigations against cervical cancer. Methods: A compartmental mathematical model of the cycle of HPV that includes the choices individuals make once they become infected; treatment versus no treatment, was developed. Using this mathematical model we evaluated the impact of human papillomavirus (HPV) on a given population and determined what could decrease the rate at which AAW become infected. All state equations in the model were approximated using the Runge-Kutta 4th order numerical approximation method using MatLab software. Results: In this paper we found that the basic reproductive number ROU is directly proportional to the rate of infectivity of HPV and the contact rate in which a human infects another human with HPV. The ROU was indirectly proportional to the recovery rate plus the mortality by natural causes and the disease. The second ROT is also directly proportional to the rate of infectivity of HPV and contact rate in which humans infect another human with HPV and indirectly proportional to the recovery rate plus the mortality from HPV related cause and natural causes. Based on the data of AAW for the parameters; we found that ROU and ROTwere 0.519798 and 0.070249 respectively. As both of these basic reproductive numbers are less than one, infection cannot therefore get started in a fully susceptible population, however, if mitigation is to be implemented effectively it should focus on the HPV untreated population as ROTis greater than 0.5. Conclusion: Mathematical models, from individual and population perspectives, will help decision makers to evaluate different prevention and mitigation measures of HPV and deploy synergistically to improve cancer outcomes. Integrating the best-available epidemiologic data, computer-based mathematical models used in a decision-analytic framework can identify those factors most likely to influence outcomes and can help in formulating decisions that need to be made amidst considerable lack of data and uncertainty. Specifically, the model provides a tool that can accommodate new information, and can be modified as needed, to iteratively assess the expected benefits, costs, and cost-effectiveness of different policies in the United States. This model can help show the direct relationship between HPV and cervical cancer. If any of the rates change it will greatly impact the graphs. These graphs can be used to discover new methods of treatment that will decrease the rate of infectivity of HPV and Cervical cancer with time.
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Historically, the incidence and mortality of cervical cancer has declined in countries that have instituted and sustained mass-organised cytology-based screening programmes. These programmes, however, required frequent repeats of the screening tests. They also require a functioning healthcare infrastructure, with laboratories for smear processing and interpretation, mechanisms for quality control, referral for colposcopy, treatment of precursors, and follow-up to detect failures of treatment. Although this approach has been successful in preventing cervical cancer where implemented correctly, it has proved inordinately complex and expensive for developing countries. Consequently, no successful screening programmes have been established in poor countries, and cervical cancer remains the most common cancer among women in developing countries, despite the existence of cytology and the knowledge of cervical cancer prevention. New technologies, specifically the development of liquid-based cytology, have improved the performance of cytology as a screening test, but do not obviate the infrastructural challenges posed to health systems by cytology-based screening programmes. In this chapter, the history of cytological screening and the challenges posed by secondary prevention strategies are reviewed.
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The term pap-smear refers to samples of human cells stained by the so-called Papanicolaou method. The purpose of the Papanicolaou method is to diagnose pre-cancerous cell changes before they progress to invasive carcinoma. In this paper a metaheuristic algorithm is proposed in order to classify the cells. Two databases are used, constructed in different times by expert MDs, consisting of 917 and 500 images of pap smear cells, respectively. Each cell is described by 20 numerical features, and the cells fall into 7 classes but a minimal requirement is to separate normal from abnormal cells, which is a 2 class problem. For finding the best possible performing feature subset selection problem, an effective genetic algorithm scheme is proposed. This algorithmic scheme is combined with a number of nearest neighbor based classifiers. Results show that classification accuracy generally outperforms other previously applied intelligent approaches.
An alisis de situaci on del c ancer en Colombia
  • Instituto Nacional De Cancerología
Instituto Nacional de Cancerología. An alisis de situaci on del c ancer en Colombia 2020 http://www.cancer.gov.co/Situacio/n_del_Cancer_ en_Colombia_2015.pdf/
Cervical cell classification by means of the KNN algorithm using nucleus' features
  • S Rodríguez
  • A Martinez
  • J Lorenzo
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