A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

<p>Abstract</p> <p>Background</p> <p>The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology.</p> <p>Methods</p> <p>The equation [<it>p </it>= 1 - (1 - (1 - (1 - <it>u</it>)^<it>d</it>)^<it>k</it>)^{<it>Nm </it>}] calculates the probability of cancer (<it>p</it>) and contains five parameters: the number of divisions (<it>d</it>), the number of stem cells (<it>N </it>× <it>m</it>), the number of critical rate-limiting pathway driver mutations (<it>k</it>), and the mutation rate (<it>u</it>). In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell.</p> <p>Results</p> <p>When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk.</p> <p>Conclusions</p> <p>The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.</p

Facteurs influençant l’intensité de l’utilisation des semences améliorées de maïs au Bénin

Au Bénin, des nouvelles semences améliorées de maïs ont été introduites dans diverses localités du pays pour contribuer à l’amélioration de la productivité du maïs. Le présent article a pour objectif d’évaluer les déterminants de l’intensité de l’utilisation des semences améliorées de maïs dans les zones favorables à cette culture au Bénin. L’étude contribue à l’amélioration de l'efficacité des services de recherche et de vulgarisation et de politique agricole, pour accroître la productivité des agriculteurs. Cette étude a été réalisée dans les zones agro-écologiques de production du maïs au Bénin. Les données ont été collectées sur un échantillon de 490 producteurs. Il ressort des résultats que les variables "quantité de semence utilisée", "formation particulière reçue sur l’utilisation des semences améliorées", "nombre d’années d’expérience dans la production" et "part sur 10 du revenu agricole annuel qui provient de la production de maïs" sont celles qui influencent l’intensité de l’utilisation des semences améliorées de maïs.Mots clés: Semence améliorée de maïs, adoption, intensité d’utilisation, modèle Tobit, BéninEnglish Title: Factors affecting the intensity of the use of improved maize seeds in BeninEnglish AbstractIn Benin, new improved maize seeds were introduced to improve maize productivity in various places. This paper aims to evaluate the determinants of the intensity of the use of the improved maize seeds in areas favorable maize crop in the country. The research contributes to the improvement of the effectiveness of the agricultural policy and agricultures services of research centers to increase the productivity of the farmers. The study was conducted in the agro-ecological zones of maize production in Benin, where data were collected on a sample of 490 producers. The results reveal that the variables “quantity of seed used”, “training received on the use of the improved seeds”, the “number of year of experiment in the production” and “the part on 10 of annual farm income comes from production of maize”influence significantly the intensity of the use of improved maize seeds.Keywords: Improved maize seeds varieties, adoption, utilization intensity, Tobit model, Beni

Hernia diafragmática congénita de presentación tardía: a propósito de trece casos

Congenital diaphragma..c hernia of late presenta ..on. Report of 13 cases Congenital diaphragma..c hernia (CDH) of late presenta..on is a rare malforma..on in developed countries, being more prevalent in under-development countries. We report 13 pa..ents (from 4 months to 8 years) operated (2006-­-2009) in Afghanistan, Mauritania, Benin and Las Palmas. 11 children had HDC of Bochdalek and 2 Morgagni type. 10 cases debuted with moderate symptoms and the other 3, severe. The predominant symptoms were vomi..ng, dyspnea and growth retarda- ..on. In 10 CDH of Bochdalek diaphragma..c closures proceeded through a laparotomy and one by thoracoscopy. The two Morgagni CDH were operated by laparoscopy. All cases had ini..ally successful outcomes, without significant impact. There was one late death. The incidence of late-onset CDH is higher in developing countries due to lack of symptomatology that accompanies and inadequate implementa ..on of serial check-­-ups to detect problems before they get to important clinical deteriora ..on. Therefore, it is o..en accompanied by malnutri..on and stun..ng. A good predictor is the adapta..on and hypoplas..c lung development.La hernia diafragmá..ca congénita (HDC) de aparición tardía es una malformación poco frecuente en los países desarrollados que, sin embargo, ..ene una mayor incidencia en los países en vía de desarrollo. Presentamos trece pacientes (edad: 4 meses -­- 8 años) tratados quirúrgicamente (período 2006-­-2009) en Afganistán, Mauritania, Benin y Las Palmas. Once niños presentaban HDC de Bochdalek y dos HDC de Morgagni. Diez casos debutaron con sintomatología moderada y los otros tres, grave. La sintomatología predominante fue vómitos, disnea y retraso del crecimiento. En diez HDC de Bochdalek se procedió al cierre diafragmá..co a través de laparotomía y, en una, por toracoscopia. Las dos de Morgagni se intervinieron mediante laparoscopia. Todos los casos evolucionaron, inicialmente, sa..sfactoriamente, sin incidencias significa..- vas. Se registró un fallecimiento tardío. La incidencia de HDC de aparición tardía es superior en paises en via de desarrollo debido a la escasa sintomatología que las acompaña y a la insuficiente implantación de controles pediátricos seriados que permitan detectar los problemas antes que den una sintomatología importante. Por ello, se suelen acompañar de malnutrición y retraso en el crecimiento. Un buen factor pronós..co es la adaptación y e