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Análisis cinético de indicadores difusos en tobillo y rodilla para clasificar la marcha hemipléjica espástica utilizando diagrama de flujo(Kinetic analysis of fuzzy indicators at ankle and knee to classify spastic hemiplegic up using flowchart)Ubaldo Rafael Padilla-Liendo 1 1 Departamento de Tecnología Industrial, Universidad Simón Bolívar, Estado Vargas, Venezuela.Recibido: 02 de Marzo de 2016. Aceptado: 04 de Julio de 2016. Publicado online: 3 de Septiembre de 2016. [TRABAJO ORIGINAL]Resumen (español)Esta investigación pretende modelar características difusas de indicadores cinéticos en tobillo y rodilla de pacientes hemipléjicos espásticos por parálisis cerebral. Estos indicadores son consistentes con los utilizados por los especialistas, en la interpretación clásica para clasificar la hemiplejia, propuesta por el Dr. Gage. Cumpliendo los protocolos del Hospital Ortopédico Infantil en Caracas, Venezuela, se procesan los registros de 178 pacientes hemipléjicos. A través de análisis de varianza (ANOVA) se determina cuales indicadores son apropiados para clasificar patrones. Se calcula la media, desviación estándar y umbral de separación en aquellos indicadores determinados. La función de membresía describe los rangos de pertenencia a grupos específicos. Basado en los parámetros calculados y la información obtenida, se construye un modelo difuso sobre un diagrama de flujo para discriminar entre los tipos hemipléjicos, comparable a la interpretación clásica. Se procesa el 75% de los registros y el 25% restante validan los resultados, según el grado de pertenencia y sensibilidad. Se obtiene una sensibilidad de 83,33% para el tipo 1; 75% para el tipo 2; 62,5% para el tipo 3 y 85,7% para el tipo 4. Los indicadores son descritos para todos los especialistas a través de un lenguaje médico apropiado.Palabras clave (español)Hemiplejía, espástica, clasificación, tobillos, rodilla, indicadores, cinéticos, difusos, membresía, patrones. Abstract (english)The goal of this research is to model diffuse kinetic characteristics of ankle and knee indicators of spastic hemiplegic patients by cerebral palsy. For those indicators consistent with those used by specialists, in the classical interpretation to classify hemiplegia, proposed by Dr. Gage. Complying with the Children's Orthopedic Hospital protocols in Caracas, Venezuela, records of 178 hemiplegic patients are processed. Through analysis of variance (ANOVA) which indicators are appropriate to classify patterns is determined. The mean, standard deviation and separation threshold in those specific indicators are calculated. The membership function describes the ranges belonging to specific groups. According to the calculated parameters and the information obtained, a diffuse pattern on a flowchart used to discriminate between types hemiplegic is constructed, as done in the classical interpretation. 75% of records are processed and remaining 25% validates the results, depending on the degree of membership and sensitivity. A sensitivity of 83.33% for type 1 is obtained; 75% for type 2; 62.5% for type 3 and 85.7% for type 4. The indicators are described for all specialists through an appropriate medical language.Keywords (english)Hemiplegic, spastic, classification, ankles, knee, indicators, kinematic, fuzzy, membership, patterns. Clasificación difusa de la marcha hemipléjica espática. Padilla-Liendo UR.Padilla-Liendo UR. Clasificación difusa de la marcha hemipléjica espática. Avan Biomed. 2016; 5(2): 66-75.Avan Biomed. 2016; 5(2): 66-75.iVBORw0KGgoAAAANSUhEUgAAAtAAAAPACAYAAAAc9k6zAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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Avances en BiomedicinaPublicación Oficial del Instituto de Inmunología ClínicaMérida-VenezuelaVolumen 5(2), Agosto 2016, p 66-75Copyright: © ULA 2016Depósito Legal: PPI201102ME3935ISSN: 2477-9369 Autor de correspondencia: Ubaldo Padilla-Liendo, Departamento de Tecnología Industrial, Universidad Simón Bolívar, Sede Litoral, Camurí Grande, Parroquia Naiguatá, Estado Vargas, Naiguatá-Vargas 1160, Venezuela. Teléfono: 04127605689. E-mail: ubaldorpl@usb.ve, ubaldorpl@gmail.com Introducción La Hemiplejia Espástica (HE) es una patología compleja en pediatría ortopédica, caracterizada por una alteración neuronal músculo esquelética en un lado del cuerpo. Gage (1991), describe la HE basada en el miembro inferior afectado (Ipsilateral), examinando las alteraciones de los registros normales cinemáticos en el plano sagital (1).Tradicionalmente los registros cinéticos, como momentos y potencia, no son utilizados para clasificar la HE, pero son necesarios en el estudio de rehabilitación clínica (2).Las desviaciones de las marchas observadas en niños con HE, requiere un sistema de clasificación que permita establecer patrones de marcha en grupos ampliamente diferenciados, para el diagnóstico, tratamiento y comunicación clínica. Se insiste en una adecuada validación clínica cuya muestra significativa depende de la profundidad de la investigación y el seguimiento de los pacientes en su rehabilitación (3).En casos clínicos donde el diagnóstico médico es complejo, se debe coordinar un modelo basado en la colaboración de un grupo de médicos, considerando el impacto dinámico del flujo de trabajo de los especialistas en la ejecución de un protocolo de diagnóstico. Se concluye que los rasgos más característicos en la toma de decisión de un grupo, es el apoyo cognitivo, estilo individual en la toma de decisión, soporte integral en la labor médica, toma de decisiones con criterio múltiple e interacción de la base de conocimiento (4).Toro et al 2003, evalúa cómo los médicos y fisioterapeutas emplean el uso de herramientas e instrumentos clínicos para valorar la marcha y si existe condiciones para proponer un método de estandarización. Concluye que la valoración de la marcha mediante técnicas observacionales es limitada y compromete su validez por su naturaleza subjetiva. Los médicos y fisioterapeutas manifestaron necesidad de capacitarse en avanzadas técnicas de evaluación de la marcha y requerir herramientas que puedan manejar cómodamente (5).El objetivo de esta investigación es extraer indicadores cinéticos en tobillo y rodilla apropiados para clasificar pacientes HE y modelarlos en forma difusa, en función de ese modelo proponer un algoritmo para clasificar pacientes HE con un lenguaje cómodo para los médicos traumatólogos y fisioterapeutas. Es necesario cumplir con los siguiente pasos: Generar patrones cinéticos en tobillos y rodilla para cada tipo de HE, proporcionar la media y desviación estándar separada por fases del ciclo de marcha en los patrones cinéticos hemipléjicos, evaluar la capacidad que tiene los rangos de momento y potencia articular en tobillo y rodilla para separar tipos HE, calcular el umbral de separación de los tipos HE, determinar los rangos difusos de los datos y obtener las funciones de membresía vinculada al tipo HE, validar la clasificación utilizando el 25% de los registros cinéticos y crear un modelo apropiado para clasificar utilizando diagrama de flujo.Un diagnóstico efectivo significa clasificar correctamente un paciente HE en uno de los cuatro patrones homogéneos propuesto por Gage (1991). Una clasificación correcta garantiza la adecuada evolución al tratamiento. El método de clasificación clásica compara las curvas cinemáticas del paciente con el patrón de marcha normal y los patrones HE. Este procedimiento introduce elevados niveles de error para clasificar correctamente, dado que depende de la experiencia y factores emocionales del especialista, la subjetividad y condiciones ambientales. Sin embargo, aún en condiciones ideales la característica difusa de los datos, apreciada por el solapamiento de los patrones, genera una incertidumbre adicional. 67Winters et al, 1987, obtuvo patrones homogéneos de la marcha de pacientes HE, analizando los registros cinemáticos del miembro afectado en el plano sagital y los datos electromiográficos. En tal sentido, el estudio se realizó con pacientes entre 3 y 30 años de edad, además se incluyó pacientes HE secuela de parálisis cerebral, accidente cerebro vascular y traumatismo cráneo encefálico. Esto diverge con las investigaciones en niños y adolescentes HE, secuela únicamente de parálisis cerebral (6).Se ha creado modelos difusos empleando registro cinemáticos para los mejores indicadores en rodilla y pelvis. Aun cuando el lenguaje especializado es apropiado, no plantea un algoritmo de clasificación (7, 8).La clasificación hemipléjica empleando el método tradicional, requiere evaluar la posibilidad de mover los pacientes de un grupo a otro, luego de ser sometido a una intervención quirúrgica. Un trabajo futuro abriría la posibilidad de clasificar pacientes HE, con un complemento robusto al incorporar la interpretación del experto en el análisis clínico de la marcha e integrando los patrones cinemáticos y cinéticos (9).El desarrollo de un prototipo de una única base de datos, implementada en Postgres, con todos los reportes integrados del laboratorio de marcha del Hospital Ortopédico Infantil, para evaluar las consultas difusas con datos reales. Aunque permite almacenar archivos con diversos formatos, su uso y lenguaje es difícil de entender por los especialistas (10, 11, 12). Empleando técnicas de construcción para un modelo de clasificación como: árboles de decisión de regresión logística, metaclasificadores y datos de estudios. Se ha obtenido un algoritmo de clasificación de HE basado en registros cinéticos que logra discriminar exitosamente entre los cuatro tipos de la patología. Sin embargo, el lenguaje empleado no es de fácil comprensión y manipulación para los especialistas (13).Las dificultades y restricciones que enfrentan los usuarios y especialistas en la toma de decisiones, para la interpretación y análisis de los registros del movimiento, son del tipo de razonamiento: inductivo, deductivo, creencias o conjeturas. La limitación que afrontan los usuarios es la dificultad para utilizar métodos de aproximación objetivas: modelos matemáticos, estadísticos, sistema experto y redes neurales (14).68Armand et al, 2007, propone un método que vincula el análisis de movimiento con los elementos de interpretación, mediante la técnica de inteligencia artificial para disminuir la subjetividad y proporcionar una herramienta útil para la interpretación. De manera que, la gran cantidad de datos que proporciona los dispositivos de captura de movimiento, hacen que la interpretación sea una tarea difícil para el razonamiento humano (15).La hipótesis planteada en esta investigación es: Existirá indicadores cinéticos en tobillo y rodilla capaces de clasificar pacientes HE, utilizando un lenguaje conocido y coherente con la naturaleza difusa de los datos cinéticos.La marcha normal aprovecha un mínimo gasto energético para desplazar hacia adelante el centro de masa, a través de movimientos alternantes y equilibrados de las extremidades, donde una de las características que la identifica es la conservación de la energía (16, 17). La articulación en tobillo y rodilla tiene porcentajes de tiempo que permite segmentar el ciclo de marcha. La cinética integra las fuerzas internas y externas como la fuerza de gravedad, la fuerza de reacción del suelo, la contracción muscular e inercia durante la fase de apoyo, específicamente entre contacto inicial y apoyo terminal (16, 17).El presente estudio además de validar los aportes existentes en la clasificación hemipléjica utilizando los registros cinéticos, pretende aportar el análisis de las ineludibles características difusas de los indicadores cinéticos obtenidos.Materiales y métodos Población. Los registros procesados en esta investigación son un conjunto de datos recopilados del laboratorio de marcha del Hospital Ortopédico Infantil, Caracas, Venezuela. En la investigación realizada la muestra estuvo conformada por 178 pacientes en edades entre 4 y 16 años, con diagnóstico de hemiplejia espástica secuela de parálisis cerebral infantil con evidente trastorno patológico de la marcha.Pruebas funcionales. Las pruebas fueron realizadas para la adquisición de los registros cinemáticos, cinético, electromiografía dinámica y consumo energético. Dichas pruebas consistieron en el recorrido del paciente a lo largo de una pista de marcha, con placas de fuerza para registrar los momentos y potencias; las cámaras infrarrojas detectan los marcadores lumínicos adheridos en los puntos óseos anatómicos más prominentes del paciente; la electromiografía dinámica registra la sumatoria de los potenciales de acción que viaja a lo largo de la membrana celular de los músculos esqueléticos, durante la marcha son capturados en la superficie de los principales grupos musculares de los miembros inferiores. Cada paciente proporciona 3 registros cinemáticos en formato GCD (Gait Cycle Data) iVBORw0KGgoAAAANSUhEUgAABSEAAAOpCAIAAABq2nVSAAAAAXNSR0IArs4c6QAA/8pJREFUeF7s
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Figura 1. Patrones e indicadores cinéticos de los momentos articulares en tobillo y rodilla.utilizando el sistema VICOM 370(Web Site Vicon, 2015) (18), obtenidos en el laboratorio de marcha del Hospital Ortopédico Infantil, Caracas, Venezuela. El protocolo Davis es utilizado como parámetro fundamental en la colocación de los marcadores ópticos en los puntos óseos anatómicos más prominentes de ambos miembros inferiores del paciente, para obtener el modelo biomecánico que describe la cinemática de la marcha (19, 20).Análisis estadísticos. Los registros en formato original GCD son convertido y procesados en Microsoft Office Excel 2010 y software MATLAB® 2010. Se aplica herramientas estadísticas a los registros agrupados por tipo de HE, para hallar la media y desviación estándar, para graficar los patrones de momentos y potencia articular en tobillo y rodilla. La figura 1 describe los patrones e indicadores de momentos articulares en tobillo y rodilla, obtenidos al procesar los registros. Esta investigación se enfocó específicamente en los registros de los momentos y potencias articulares en tobillo y rodilla, desglosados en cada una de las fases del ciclo de marcha. Sobre estos registros se aplicó la prueba Análisis de Varianza (ANOVA) para evaluar la capacidad de los momentos y potencias en determinadas fases del ciclo marcha, que permita clasificar grupos hemipléjicos. La prueba de ANOVA es una herramienta estadística utilizada para evaluar, bajo ciertas premisas, la capacidad de los indicadores para discriminar entre grupos hemipléjicos. Las pruebas de ANOVA sobre el ciclo completo de marcha, demostraron que las potencias articulares en tobillo y rodilla no son adecuados para clasificar, mientras que los momentos en contacto inicial y apoyo medio en tobillo, al igual que apoyo terminal en rodilla, son excelentes indicadores apropiados para clasificar grupos hemipléjicos. La figura 1 muestra encerrada en círculo los indicadores cinéticos de los momentos articulares de tobillo de izquierda a derecha, contacto inicial y apoyo medio; en momentos articulares de rodilla muestra encerrada en círculo el apoyo terminal. 69A cada uno de los indicadores cinéticos obtenidos empleando ANOVA, se le determina la media y la desviación estándar, luego se calcula el umbral de separación entre grupos HE mediante la técnica de Análisis Lineal Discriminante (ALD). Se aplica (ALD) para determinar el umbral de separación entre tipos HE (21). Esto contribuirá para determinar las funciones de membresías necesarias para describir la naturaleza difusa de los datos en la clasificación. Se establece un algoritmo de clasificación siguiendo el proceso de interpretación desde distal a proximal utilizado en la clasificación tradicional, pero basada en la característica difusa de las funciones de membresía de los indicadores cinéticos de tobillo y rodilla (22). iVBORw0KGgoAAAANSUhEUgAAAwkAAAGkCAIAAAD15P7CAAAAAXNSR0IArs4c6QAATulJREFUeF7t
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bVSjwjKpEpCABCQgAQnkTkBtlDtiI5CABCQgAQlIoEYEhp47d65GyTWpEpCABCQggVgEhg4dOtj9
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z9xSEr0/zO89FSXjg1XFNM9WtnqrjRJqo7i1Icr9jWxy/at+9I6g82x+PUJlW6YJk0BrCUTpLSPC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Figura 2. Umbral entre dos grupos.Se procesa el 75% de los registros para diseñar y construir el modelo de algoritmo y se realizan pruebas para validación del modelo difuso con el 25% de los datos.Aspectos éticos. Esta investigación procesó únicamente los datos numéricos de los registros cinéticos etiquetado con un nombre alfanumérico, razón por la cual se desconoce la identidad de los pacientes. Aunque el autor requiere familiarizarse con los protocolos clínicos para la obtención de los registros, la valoración clínica es una actividad exclusiva, inherente e intransferible del fisioterapeuta y médico traumatólogo. Esto incluye: contacto directo con el paciente para la evaluación clínica en estático y dinámico, colocación de los sensores, y persuasión del paciente para que realice las actividades necesarias durante la adquisición de los registros, según su característica personal y emocional. En función de estas aseveraciones, esta investigación está dentro del marco filosófico de la disciplina del bien, relacionada con la moral, ética y valores humanos del bien común. ResultadosEl ALD requiere de la media y la desviación estándar de cada grupo. La Figura 2 ilustra dos grupos con media y desviación estándar, el grupo a la izquierda del umbral (c) tiene una media (H4sIAAAAAAAEC7t+9tgsBjBwYFJgYuQEMQviGBmADOaTQDYTgwxYlhVIcjKBmCAWEyMjlMXI9P//
f7CYHqMEVIwbro4HaKYDkxBQXI2Nn0GKAaj2PwODAJB/AMhaBuIB1R4DGsYNVcPD4JtYkhFSWZDK
wBAAtvs3kwJQDwhMANvKwsQgEJKZm1qs4JdarhCUn5uYx/Bi48fyj0Cs4PC5fJlgWhwLULUu0FQO
IG3E9YAxC6zTsRLkl99MDf+AFBCQah4jA8jcD3BzGxitGEDhkFvJBSRBPuQC+xAkxgB1uwADO5i3
BxwmjExMSsGVxSWpuQxxIHcyAHUoMnRBNADVbfksDLYD5HaIXYwMzGD9AICuHFaoAQAA
) y el de la derecha (H4sIAAAAAAAEC7t+9tgsBjBwYFJgYuQEMQviGBmADOaTQDYTgwxYlhVIcjKBmCAWEyMjlMXI9P//
f7CYHqMEVIwbro4HaKYDkxBQXI2Nn0GKAaj2PwODAJB/AMhaBuIB1R4DGsYNVcPD4JtYkhFSWZDK
wBAAtvs3kwJQDwhMANvKwsQgEJKZm1qs4JdarhCUn5uYx/Bi48fyj0Cs4PC5/JFgWh8LULUu0FQO
IG3E9YAxHqzTqRLkl99MDf+AFBCQah4jA8jcD3BzGxitGEDhkFvJBSRBPuQC+xAkxgB1uwADO5i3
BxwmjExMSsGVxSWpuQx9IHcyAHUoMnRBNADVbfksDLYD5HaIXYwMzGD9AMvnb+CoAQAA
).El umbral (H4sIAAAAAAAECyVPP0vDcBB9d622TQqGQqF0Cg7ZKip+DR1s55JQAnWIFlIo2Tq5Cc5+Cj+Ag5Ob
s2s/QveA6bvLD+7u3Xv37/f3+/MBf7GkogOD86WAoPNGrBi7ekY/UINdmorAGNGmaZy5kokzNyrk
TQu92tBQU4llRJScX2AK9jRAxPybKGE80F7ZGDJazRD32Xa9qDY5cO0X1Lr/p8j3zt28QhEtnoq8
jB/yXfz4UmTPwKfdNqPcZ7wNIHew2hUCepsb+G7j2v21Ruh59uXXiurlvCq3edH+c8ZdNvPIlo7X
nQAxTNVWMAEAAA==
) se calcula usando las siguientes expresiones:H4sIAAAAAAAEC5VRMUjDUBC9uyRq06rBLiIZvg5udXB0qu6K2C6CIFUiCsYKLYRsf3Zyrm6CswVH
B6duzq6OjoaOBePdNe0gOPjDv//u/t17ufvvb4Me6LKeISwJfDpEYOB4CEAQ6q3HtkQCBRHylSKk
PM8VbeByEStP8ypkyHpLHF+fWYQV4NwcIGD/ldEj7zrTDZisXORUYLfVPW+m1xHAvmqPyHCNrFtV
dQmC5kUcdcxelJiDdty6gs9+lmS8TX2YzC+chS5n15h1js9N/wP7rvzvTjrxj5RpO5XeRmS/+eD1
X34E0fma6ljsOaITFzoWt2Ds/9bhJOIvaKTxSfsS4M73j++z6p99jHWw6MfiKQnvQ+qzlcn6OlmJ
QTGzAGbVe9G3QKK1RtrpRjGEMh/gilW40QIxz8Oq9lLjuUx6crT+Bygyqh8gAgAA
((1)H4sIAAAAAAAEC5VSv0vDQBh9d/2dpDVYBBGHqCCIVFBcCyqKkyJt/4EqEQVjhRZKFumsi7M4OHUv
OIlCpzo5uzo6NnQsNH7fNY1EcPDC3b33/Xp39+XjvXeP8chZEhmG6yXBILYnAIl55U3QmpEMGUlB
LoWE9H1foTUxG9j0MM6QVDM3Tfbl5BTmQLE+YBLvEmrT7GaBHhXTgxgDB9XGWcW9soEjpT2UFuXw
uFOqcQmzcu7YdevQblqlmlO9xFfHa3o0ra1Bcyl7ijhFF6hqmvYN7VOsZPm8O+6Ez2hR/pxkvh36
H2NjzncfytaINhr/1RfqHH0qNdZtiVGa6zqBTktcyyjfBPMT97cuGSV9Ztl1jmsXQCenvT54+T/v
zffv02tNdC2D6+6GurrOvBDytxTzYsjbiWj8bZz5aujfV50ouhpZubOa6izHIOiZiZRiL+pfEFIu
lt16w3YA7g8oYwE3KoGXp0E+6NnPm8VU/jdAsaZ6oAIAAA==
((2)H4sIAAAAAAAEC5VTOUgDURCdP7uaZFcxh4iIxXogikTEQlAQolgJCh6VnUJEwfUgQtguCGms0gmC
kt7KxkrQSghobZtGsbCIWIgHxpnZ7+JZOGF/3pud+fNmMrm6PN8DsbKdMyHCcHNaMTAOFR3QKm9r
6IwgQ0ao6JUghdVqVVCfatY+O4irw5xZtuPk76ptgBag2CpAlPgZoWN6ijbAoAlAXxJTB5MLW8tz
3kYaoAJh8j7TbZzBRoGQpNKsoREn4NRglMAm9BH7rsMfPh81Ygp3dVwKt23u5wUd0sFWkE5MhOjc
ipvOOFPprDOz7i6swe3RffaeHif1kH2qX8r7tZVoGrB6zJEIz2DMY43Mh2qZj2peUefWV94R/sof
zc/5YEyKklHP15d7o8vI/qsPZUYVusvXRfkhruNqXQVVNnz+Sx3kOcx67uL6KsB+3OqPPif+nAPP
o6JQ1ykZjvSX0XVKRqyG63zwgjqQeWV+9EdBSJ+g7k3Muvi77vf+Skan9Ncb9Ncrda4Cfic6kpoX
cR5Z10jAh4H5uGfRyVtqyZayD2T3XzAKIWEnstcKsX3Wy2ylXcjzXgBltMGOJPDR/ZrQe6r0b4H0
L2J7B2i3vfJsAwAA
((3)H4sIAAAAAAAEC5WUTWgTQRSA37zZtM1ma9JkKSIeogelSAV78CAKadVLwR5sEEQQK6QodK2QQliE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=
((4)H4sIAAAAAAAEC5VTMUgjURCdP7u5JJtdLl6CHGIRLQQRBYNecXgQbQThUpwBa5WIgntREghbGNJq
FdsrjrRXWFxjo4WVkELB4rBNeWWih4UhxpnZn5DcaXGz7Oe9+fP/vJmdvb26/AZidadsQpjh/ppi
YJwpWmBUdgO0hpEhI1S0JUhhp9MRNKPea1+kF2dj2aw778g/8eYtjADFdgCixC8IndJbdQA+mAAR
HWPD5/XCdsbbywI0IETeR7qNT7BRIExTatYQxxW4CTCK4TD6iH1/rK7PR3FM4Q8dl8Jjh+tpYYJ0
sFWkEhMhmtlxs/lEOltMfMm561/h989msUlvInVffLC3Sn5uJZqS1qSZjnAPljzWyHwlxHxR84b6
ZQ/ypDXIQ8H+82B8N/x9X1/5iS4j+199KD1qUFW+rooaCvO9rtZVUXeBfl7FAxzkc8B803tBB3Kf
Vj13I7cLUHKs64Vm7NU+cb8aCrWOmjEr9ee1jpoxLvV3eUWdSD/z/+Sla5CeXt62bSVfz/t3/TVj
Xuqf6tX/UfLc9nhbdExrXsVDk+vvxldxWSbkk2eRl6fYkinmGJB/o4VRCAo7l7lXiOOrXr6QdaHE
cwN0YgyO5AAvmfuYnmOlvxXSX8b2DOMRNl2MAwAA
((5)H4sIAAAAAAAEC5VTPUhbURQ+97wXk7wk+mqkFOmQdiiUEgcRt5bYRQjYoYqDm5WUFny1ECG8QXk4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((6)Dónde:H4sIAAAAAAAEC41QPUsDQRCdmcSPXA48tBGxWC3sYiHYpNIfEBFNYSWkONHiVEjguO5qq9T+AHvB
0uKqdNa2VsEyIWgT8HwzrGebgZ19O/vmzcf72+iRzApxwg2Fk0smgNoXsNC2/S7BN0ShImH2iKUs
S4vt86aPNSteCM1C1hHfW16jLQK3JIrwLoCecHJwRxBrek5Ind7gupvdx0SnVnsu+Q8+YUMtSnWh
qHuTxH13Eqfu7C7p3dLn8zSd4rijWfodXo3r4LXAXsV9EOR8KJraznSWuTj0oDa0KRbXY1LdSaX7
wRemcOx1//vUaovrgmu6XPXbJlVIsgBeNxfY5jRGficRrdjr1XbNIrvnWX8QJzTW+QkZO/RgCepe
ZhtWo4V+/2aoWf4vlmwlYAACAAA=
Media del grupo tipo AH4sIAAAAAAAEC7t+9tgsBjBYwKTAxMwJYk6KY2QAMpi/AtlMDDJgWVYgyckEYoJYTIyMUBYj0///
/8FieowSUDFuuDoeoJkLmISA4mps/AxSDEC1/xkYBID8A0DWMiBOAKo9BjSMG6qGh8E3sSQjpLIg
lYEhAGz3b6aGf0BJIJgAspSBhYlBICQzN7VYwS+1XCEoPzcxj+HFxo/lH4FYweFzeRJP2mYWoDpd
oGoOIG3E1cAowwTSalUJ8stvJgWgG0BgAtgXxJvHyAAy9wPc3AeM9mATHKHmItwJVMIEMje4Mjcp
P4eBoZKb686cj8I43QkxlxHhXgaQe4sruYAkKOS4wCEHEmOAhokAAzuYtwcc1oxMTErBlcUlqbkM
m0H+ZwDqUGToAmsAEVs+C4Pdrgt0L8wPzGD9ADZJuCoAAgAA
Desviación Estándar del tipo AH4sIAAAAAAAEC41QK0wDQRCdmZZPr5dwAUMIYkHgikBWEYItIfQ0ScUREAckbXI5V42qRqHqSS0C
VYdCYE8iaRpUE443k+WwnWRn386+efP5eJs+klkhTqSh8P2SCaD2DSy0a78r8A1RqEiYPWIpy9Ji
h7ztY82KF0KzkE3ED1Y3aIfALYkivF+BxjhP4E4h1vSckDq9wXWc3ydE51Z7IcMffMJGWpTqQlF8
kyZ9d5Zk7uIu7d3S5/Msm+G443k2Dq8mdfBaYK/jPgqGfCqa2s51loU49KA2simW12NS3a9Kt+Cu
KZx43f8+tdryuuCaLlf9tkkV0jyA180FtjmNkd9JRGv2erFds8h+N+8PkpQmOj8hY48eLEFdPN+y
Gi30+zdDzfJ/AR6/yAkAAgAA
Media del grupo tipo BH4sIAAAAAAAEC41QPUsDQRB9O4kfuQQ9TCOSYlVIFwvBRlKIvSLmaiHCGYWcES5wXHe1VWp/gL29
xVXprG0tLXMEq4DnzHieleDA7r6dffP2zby+TB+gkZIlUxM4uzBgUPlgTGjp6xLvNRIoiIwpkKE8
zzW3ZzaLXL3kNVgzpQ3Ot5fXsQXm5oDL95TRI6+EuVMWqxecBk7642svvvOBM/17QcknP3JM5FNU
Ca53E/ihPfUjez4K+rd4f8qijJc9mke77tWgyrwOs1f53HcSc0BSehhLLwuy7EFiol38X89AdGel
7pvpqsJxofvrkykkur04uBwNgeGa0+5mzT99fuua0m8L4jeMHd5lco5OTnIoZuJiRW/POmtDtNOL
w7EfYCD9gyu2ca8FsnnzpnrvsN+fHipa/wVcX5hKAAIAAA==
Desviación Estándar del tipo BPara calcular el umbral de separación entre tipos hemipléjicos adyacentes, se requiere extraer la desviación estándar y la media de los indicador Contacto Inicial (CI) y Apoyo Medio (AM) en tobillo, y Apoyo Terminal (AT) en rodilla. Función de membresía. La función de membresía cuantifica una entrada en un grado de verdad. La forma básica de una función de pertenencia trapezoidal tiene unidad a la izquierda (23). La función de membresía se ejecuta en el rango lineal de valores de entrada utilizando, para el caso de la trapezoidal, las siguientes expresiones:H4sIAAAAAAAEC41QIU/DUBD+7joY65bQMEMI4oEgIEDwC3CbgRCopxNdQBSWbEl5jiBRSMK/wCNQ
dWiCRyBZJkkod7eyTHLJe/3u3nff17u31+IRFkkApobCwRlBQPAumLFurwtyN1ihIiaqEHFZllbb
o9Wq1pzxWgxOghWpby0uYw3CLYFI8hdBhRwXAIWINStOC4e90XnsBylwbN7ffPMjjxL3aooaI4ov
snTojtLcnVxlvUt8Po3zsRx3MMld1O/UhLcr7CX57ocJPbC27vi/vGv/v+11tnl9Zf1fn6A+X3M+
H6Z7PfO5hSr2fSi3biC0DWgN1WwR6pY9286IefPUD0dpho7OAenYwN20QXjxpG2eOtvUmyALlPgF
AQ1AL8gBAAA=
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(9)70Otra función de pertenencia es la forma básica es triangular. Las funciones de membresía triangular requieren un conjunto más amplio de valores de entradas, las expresiones para construirlas son:H4sIAAAAAAAEC7t+9tgsBjBIYGZgYuQEMQviGRmADOabQDYTgwxYlhVIcjKBmCAWEyMjlMXI9P//
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(13)Se procura modelar a cada indicador cinético como una combinación de funciones de membresías trapezoidales y triangulares, donde cada tipo hemipléjicos es una función con un rango de dominio compartido con otros tipos de hemiplejias adyacente. La figura 3 muestra este modelo difuso que cuantifica el grado de pertenencia para una entrada dada (12, 17).La característica más apreciable de las funciones de membresía mostradas en la figura 4 es el solapamiento existente entre ellas (8). En el caso del indicador contacto inicial en tobillo, la función de membresía tipo 3 es muy selectiva dado que la base de su triángulo es más reducida, se observa también que la función del tipo 4 solapa todos los demás tipos de hemiplejia. Los indicadores apoyo medio en tobillo y apoyo terminal en rodilla, tienen funciones con base más amplia que permite mayor rango de selección de momentos de fuerza articular.iVBORw0KGgoAAAANSUhEUgAAA0gAAAEzCAIAAACE/7SnAAAAAXNSR0IArs4c6QAASJtJREFUeF7t
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Figura 3. Funciones de membresías.Al evaluar el momento de fuerza articular de un paciente en cualquiera de las funciones de membresía de los indicadores obtenidos, se tendrá un grado de ponderación entre 0 y 1. Mientras más cercano a 1 sea el valor ponderado, mayor es su pertenencia a un determinado tipo de hemiplejia. Al incrementarse esta pertenencia a un específico tipo hemipléjico, la membresía a los demás tipo adyacentes disminuye.Algoritmo de Clasificación. Siguiendo la metodología de clasificación utilizada por los especialistas al analizar los registros cinemáticos desde distal a proximal, se construye el algoritmo de la figura 5. En este caso los indicadores corresponden a los rangos de los momentos cinéticos en tobillo y rodilla.La figura 6 muestra la validación de los resultados con el 25% de los registros, se evalúa los momentos de fuerza articular promediado de los registros de los pacientes sobre las funciones de membresía de los indicadores. Los grados de pertenencias son pesos representados en porcentajes que expresa en forma difusa la pertenencia a determinado tipo hemipléjico.Validación. El 25% de los registros es utilizado para validar el modelo. Cada uno de los pacientes es un registro individual al que se evalúa su valor promediado del momento cinético sobre las funciones de membresía de los indicadores en tobillo y rodilla. Como se muestra en la figura 6, el criterio en la toma de decisión para decidir que un registro de un paciente pertenece a un tipo hemipléjico es si al menos dos de los tres indicadores tienen el mismo tipo hemipléjico. Es ideal cuando el modelo coincide con el mismo tipo hemipléjico en los tres indicadores. El modelo es imposible para clasificar cuando los tres indicadores difieren en el tipo de hemiplejia. El término conocido como verdaderos positivos es el número de instancias o casos clasificados dentro de una clase a la que realmente pertenece. La expresión falso negativo se refiere a aquellas instancias o casos clasificados dentro de una clase a la que no pertenece. La sensibilidad es la probabilidad de clasificar correctamente una instancia y se le conoce como la tasa de verdaderos positivos (12, 17).El modelo muestra un 83,33% de sensibilidad para detectar y clasificar correctamente los pacientes tipo 1, 75% para el tipo 2, 62,5% para el tipo 3 y para el tipo 4 se obtiene una sensibilidad de 85,7 %.Discusión 71Los grupos hemipléjicos tipos 1 y tipo 2 requieren ser clasificados considerando sólo los patrones cinemáticos en el plano sagital. La hemiplejia tipo 3 y 4 deben ser clasificados complementando las características cinemáticas y cinéticas. Aquellos casos que resultaron imposibles de clasificar requieren ser complementados con el método tradicional de clasificación cinemática. Si aun así se obtienen iVBORw0KGgoAAAANSUhEUgAAAuQAAAJDCAIAAADM35ZkAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAO
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