BackgroundFractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications. Starting from a previous work, here we made a theoretical research based on a geometric generalization of the experimental results, to develop a theoretical generalization of the stenotic and restenotic process, based on fractal geometry and Intrinsic Mathematical Harmony.MethodsStarting from all the possibilities of space occupation in box-counting space, all arterial prototypes differentiating normality and disease were obtained with a computational simulation. Measures from 2 normal and 3 re-stenosed arteries were used as spatial limits of the generalization.ResultsA new methodology in animal experimentation was developed, based on fractal geometric generalization. With this methodology, it was founded that the occupation space possibilities in the stenotic process are finite and that 69,249 arterial prototypes are obtained as a total.ConclusionsThe Intrinsic Mathematical Harmony reveals a supra-molecular geometric self-organization, where the finite and discrete fractal dimensions of arterial layers evaluate objectively the arterial stenosis and restenosis process.

Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. MethodsWe did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung's disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. FindingsWe included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung's disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58•0%) were male. Median gestational age at birth was 38 weeks (IQR 36-39) and median bodyweight at presentation was 2•8 kg (2•3-3•3). Mortality among all patients was 37 (39•8%) of 93 in low-income countries, 583 (20•4%) of 2860 in middle-income countries, and 50 (5•6%) of 896 in high-income countries (p<0•0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90•0%] of ten in lowincome countries, 97 [31•9%] of 304 in middle-income countries, and two [1•4%] of 139 in high-income countries; p≤0•0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2•78 [95% CI 1•88-4•11], p<0•0001; middle-income vs high-income countries, 2•11 [1•59-2•79], p<0•0001), sepsis at presentation (1•20 [1•04-1•40], p=0•016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4-5 vs ASA 1-2, 1•82 [1•40-2•35], p<0•0001; ASA 3 vs ASA 1-2, 1•58, [1•30-1•92], p<0•0001]), surgical safety checklist not used (1•39 [1•02-1•90], p=0•035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1•96, [1•4...

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A partir de la evaluación de las dimensiones fractales y aplicando el concepto de variabilidad y armonía matemática intrínseca celular (AMI), se desarrolló un método matemático de aplicación clínica para el diagnóstico de células preneoplásicas y neoplásicas del epitelio escamoso cervical, el cual supera el diagnóstico de ASCUS (células escamosas atípicas de significado no determinado). A partir de un método desarrollado previamente para el diagnóstico de células normales, ASCUS y L-SIL, se realizaron permutaciones estructurales fractales con los valores generales de la AMI y de variabilidad fractal para normalidad y enfermedad, buscando los prototipos generales de células normales, preneoplásicas y neoplásicas. Se midieron cinco células ASCUS y cinco cancerígenas del epitelio escamoso del cuello uterino y se encontró que para la normalidad hay 18 prototipos, mientras que para la anormalidad 44, incluyendo todos los estados de evolución hasta carcinoma.Estos resultados fueron confirmados al comparar los resultados obtenidos por las técnicas convencionales con los obtenidos por esta metodología; lo que hace pensar que se desarrolló una nueva metodología que permite diferenciar los distintos tipos de células del epitelio escamoso del cuello uterino (normales o cancerígenas).

<p>Background. An exponential law for chaotic cardiac dynamics,<br />found previously, allows the quantification of the differences<br />between normal cardiac dynamics and those with acute<br />diseases, as well as the cardiac dynamics of the evolution<br />between these states.</p><p><br />Objective. To confirm the clinical applicability of the developed<br />methodology through the mathematical law for cardiac<br />dynamics in dynamics with arrhythmias.</p><p><br />Materials and methods. 60 Holter electrocardiograms were<br />analyzed, 10 corresponded to normal subjects, and 50 to subjects with different arrhythmias. For each Holter, an attractor was performed, and its fractal dimension and spatial occupancy were measured. A mathematical evaluation was applied in order to differentiate normal dynamics from pathological ones. Sensitivity, specificity and the Kappa coefficient were calculated.</p><p><br />Results. The mathematical evaluation differentiated occupation spaces, normal dynamics, acute illness dynamics, and evolution between these states. The sensitivity and specificity values were 100%, and the Kappa coefficient was 1.</p><p>Conclusions. The clinical applicability of the methodology<br />for cases with arrhythmia was shown. It is also applicable for<br />the detection of changes in dynamics that are not classified<br />clinically as pathological.</p>