SUMMARY: Currently, the treatment for patients with deltoid ligament injuries who require surgical treatment are anatomical repair and reconstruction. The clinicians should understand the exact knowledge of attachment areas of individual bands of deltoid ligament for a successful treatment. We studied 46 ankles of fresh frozen cadavers. The individual bands of deltoid ligament were divided to small fibers. Afterwards, each small fiber of each band was cut and marked with acrylic color on the origin and insertion followed by photo taking. Lastly, the photos of individual origin and insertion were used to calculate the attachment areas. We found six bands of deltoid ligament in all ankles except tibionavicular ligament. Moreover, we discovered deep to tibiocalcaneal and posterior to sustentaculum tali ligaments in 3 cases. Regarding the attachment area, the deep posterior tibiotalar ligament had the largest proximal and distal attachment areas which were 87.36±23.15 mm2 and 88.88±24.24 mm2, respectively. The anterior tibiotalar ligament had the least proximal and distal attachment areas which were 23.12±8.25 mm2 and 33.16±14.63 mm2, respectively. Hence, the accuracy and exact areas of attachment of deltoid ligament are important as it can help clinicians to select the suitable treatments including injury prevention.

RESUMEN: Actualmente, el tratamiento para pacientes con lesiones del ligamento colateral medial de la articulación talocrural (ligamento deltoideo), que requieren tratamiento quirúrgico es la reparación y reconstrucción anatómica. Los médicos, para un tratamiento exitoso, deben conocer exactactamente las áreas de inserción de las partes de ligamento deltoideo. Estudiamos 46 tobillos de cadáveres congelados frescos. Las bandas individuales del ligamento deltoideo se dividieron en fibras pequeñas. Posteriormente, cada pequeña fibra de cada banda se cortó y marcó con color acrílico en el origen y la inserción, seguido de la toma de fotografías. Por último, las fotos de origen e inserción individuales se utilizaron para calcular las áreas. Encontramos seis bandas de ligamento deltoides en todos los tobillos, excepto el ligamento tibionavicular. Además, descubrimos en profundidad hasta los ligamentos tibiocalcaneaos y posteriores al sustentaculum tali en 3 casos. Con respecto al área de inserciónn, la parte tibiotalar posterior profundamente tenía las áreas de inserción proximal y distal más largas, que eran 87.36 ± 23.15 mm2 y 88.88 ± 24.24 mm2, respectivamente. La parte tibiotalar anterior del ligamento deltoideo tpresentaba áreas de unión menos proximales y distales 23.12 ± 8.25 mm2 y 33.16 ± 14.63 mm2, respectivamente. Por lo tanto, la precisión y las áreas exactas de inserción del ligamento deltoideo de la articulación talocrural son importantes, ya que pueden ayudar a los médicos a seleccionar los tratamientos adecuados, incluida la prevención de lesiones.

The strong candidate stability theorem by Dutta et al. [ 4], one of the major theoremsof social choice theory, states that, with a finite number of voters, there exists a dictator for any voting procedure which satisfies strong candidate stability, strong unanimity and independence of irrelevant alternatives (IIA). This paper investigates a decidability problem of voting procedures in a society with an infinite number of individuals (infinite society) using Cantor's diagonal argument presented by Yanofsky [ 19] which is based on Lawvere [ 10]. We will show the following result. The problem whether a strongly candidate stable voting procedure has a dictator or has no dictator in an infinite society is undecidable. It is proved using the arguments similar to those used to prove an extended version of Cantor's theorem that there cannot be an onto function from <img src="/img/revistas/cam/v27n3/n_bastao.gif" align=absmiddle>(the set of natural numbers) to its power set <img src="/img/revistas/cam/v27n3/p1_curs.gif" align=absmiddle>(<img src="/img/revistas/cam/v27n3/n_bastao.gif" align=absmiddle>). This undecidability means that for any strongly candidate stable voting procedure we can not decide whether or not it has a dictator in finite steps by some program. A dictator of a voting procedure is a voter such that if he strictly prefers a candidate (denoted by x) to another candidate (denoted by y), then the voting procedure does not choose y. Strong candidate stability requires that there be no change in the outcome of an election if a candidate withdraws who would lose ifevery candidate stood for office.