Extensive hyperdense zone in the mandible: a case report

Hyperdense zones are considered a generic term to define an area of increased density regardless of its cause. Idiopathic hyperdense zones are referred in literature as enostosis, focal osteosclerosis, periapical osteopetrosis or bone scar and are found as imaging finding during a rutine radiograph. They have greater predilection for long bones, but can also appear in the maxillary bones in certain occasions, often located in the jaw, especially in the molar region, with an informed incidence rate that varies from 2,3 to 9,7% depending on the population in which the study is being applied. In 40% of the cases, in spite of being of idiopathic origin, they seem to be associated with patients with occlusal trauma or can be a result of a predominant development of isolated bone during bone growth. The case of a 36-year-old female patient is described, who presents hyperdensity that differs in form, location and imaging features from the commonly documented in this type of anatomical variations. It was diagnosed as idiopathic osteosclerosis, periodic imaging controls were established. The purpose of this case report is to emphasize the importance of performing an appropriate differential diagnosis among hyperdense lesions at maxillofacial level.

Ley matemática para evaluación de la dinámica cardiaca: aplicación en el diagnóstico de arritmias / Mathematical Law for Evaluating Arrhythmic Cardiac Dynamics: Application for the Arrhythmia Diagnosis / Lei matemática para avaliação da dinâmica cardíaca: aplicação no diagnóstico de arritmias

La formulación de una ley matemática para los sistemas dinámicos caóticos ha permitido desarrollar una metodología para la evaluación matemática de la dinámica cardiaca que cuantifica las diferencias entre normalidad y enfermedad, así como su evolución. Materiales y métodos: Se tomaron 70 registros Holter, 60 con presencia de arritmias y 10 normales. Para cada Holter se construyó un atractor a partir de la simulación de los valores de frecuencias cardiacas consecutivas, se midió el espacio de ocupación de cada atractor y su dimensión fractal. Se le aplicó la evaluación matemática a cada Holter y luego se calculó la sensibilidad, especificidad y coeficiente Kappa y se comparó respecto del Gold Standard. Resultados: Los casos diagnosticados convencionalmente como arritmias presentaron espacios de ocupación entre 29 y 198 para la rejilla Kp, y los casos normales presentaron valores mayores a 200. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1. Conclusión: La ley exponencial permite cuantificar diferencias entre dinámicas con arritmias y normales, así como su evolución, lo que se evidencia en un aumento o disminución de los espacios de ocupación del atractor.

The development of a mathematical law for chaotic dynamical systems has allowed to develop a methodology for the mathematical evaluation of cardiac dynamics which quantifies the differences between normality and disease, as well as their evolution. Material and methods: 70 Holter records, 60 with cardiac arrhythmias and 10 normal were taken. From the simulation values of consecutive heart rates, an attractor was built for each Holter. The space occupancy of each attractor and its fractal dimension were measured. Mathematical evaluation was applied to each Holter and then the sensitivity, specificity and Kappa coefficient of this evaluation with respect to the Gold Standard was calculated. Results: The cases conventionally diagnosed as arrhythmias presented space occupancy between 29 and 198 for Kp grid, and normal cases had higher values at 200. The sensitivity and specificity were 100% and Kappa coefficient was 1. Conclusion: The power law quantifies differences between arrhythmias and normal dynamics, assessing the evolution dynamics towards normality or to disease, this was evidenced by an increase or decrease of the space occupied by the attractor.

Introdução: A formulação de uma lei matemática para os sistemas dinâmicos caóticos tem permitido desenvolver uma metodologia para a avaliação matemática da dinâmica cardíaca que quantifica as diferenças entre normalidade e doença, assim como sua evolução. Materiais e métodos: Se tomaram 70 registros Hotler, 60 com presença de arritmias e 10 normais. Para cada Hotler construiu-se um atractor e sua dimensão fractal. Aplicou-se a avaliação matemática a cada Hotler e depois se calculou a sensibilidade, especificidade e coeficiente Kappa e comparou-se respeito do Gold Standard. Resultados: Os casos diagnosticados convencionalmente como arritmias apresentaram espaços de ocupação entre 29 e 198 para a grade KP, e os casos normais apresentaram valores maiores a 200. Os valores de sensibilidade e especificidade foram de 100% e o coeficiente Kappa foi de 1. Conclusão: A lei exponencial permite quantificar diferenças entre dinâmicas com arritmias e normais, assim como sua evolução, o que se evidencia em um aumento ou diminuição dos espaços de ocupação do atractor.

Application of the chaotic power law to the study of cardiac dynamics in patients with arrhythmias / Aplicación de la ley exponencial caótica al estudio de la dinámica cardíaca de pacientes con arritmias

Background. An exponential law for chaotic cardiac dynamics, found previously, allows the quantification of the differences between normal cardiac dynamics and those with acute diseases, as well as the cardiac dynamics of the evolution between these states. Objective. To confirm the clinical applicability of the developed methodology through the mathematical law for cardiac dynamics in dynamics with arrhythmias. Materials and methods. 60 Holter electrocardiograms were 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. 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. Conclusions. The clinical applicability of the methodology for cases with arrhythmia was shown. It is also applicable for the detection of changes in dynamics that are not classified clinically as pathological.

Antecedentes. Se ha encontrado una ley exponencial para los sistemas dinámicos caóticos cardíacos que logra cuantificar las diferencias entre dinámicas cardíacas normales y aquellas con enfermedad aguda, así como la evolución entre estos estados. Objetivo. Confirmar la aplicabilidad clínica de la metodología desarrollada a partir de la ley matemática para la dinámica cardiaca en dinámicas con arritmia. Materiales y métodos. Se analizaron 60 holter, 10 correspondían a sujetos normales y 50 con diferentes tipos de arritmias. Para cada holter se construyó un atractor, se midió su dimensión fractal y ocupación espacial. Se aplicó la evaluación matemática para diferenciar dinámicas cardíacas normales de enfermas y en proceso de evolución. Se calculó la sensibilidad, especificidad y coeficiente Kappa. Resultados. La evaluación matemática diferenció los espacios de ocupación, normalidad, enfermedad aguda y evolución entre estos estados. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1. Conclusiones. Se evidenció la aplicabilidad clínica de la metodología para casos con arritmias, siendo capaz de detectar cambios en la dinámica que no son clasificados como patológicos clínicamente.