Clasificación difusa de la marcha hemipléjica utilizando indicadores cinemáticos en pelvis(Fuzzy Classification of hemiplegic gait using kinematic indicators in pelvis)Ubaldo Padilla-Liendo 11 Departamento de Tecnología Industrial, Universidad Simón Bolívar, Estado Vargas, Venezuela.Recibido: 07 de Enero de 2015. Aceptado: 17 de Mayo de 2015. Publicado online: 29 de Mayo de 2015[TRABAJO ORIGINAL]Resumen (español)Esta investigación tiene como objetivo modelar características difusas de indicadores hemipléjicos en la pelvis. Estos indicadores son consistentes con los utilizados por los especialistas para clasificar la hemiplejía espástica, considerando la clasificación propuesta por el Dr. Gage. La muestra consistió en 83 pacientes con disfunción motora subtipo de hemiplejía espástica. Estos pacientes han sido tratados con los protocolos del Hospital Ortopédico Infantil (HOI) en Caracas, Venezuela, entre 1999 y 2009. Utilizando herramientas estadísticas sobre los indicadores en la pelvis, se calcula la media, la desviación estándar y el análisis de la varianza (ANOVA). Estas estadísticas son adecuadas para la construcción de un modelo difuso con funciones de pertenencia para discriminar los tipos de hemiplejía comparables al mundo real. Si ANOVA tiene un valor de p << 0,05; los indicadores hemipléjicos en la pelvis son apropiados para la clasificación. Se procesó el 75% de los registros y con el 25% restante se validaron los resultados de acuerdo al grado de pertenencia y sensibilidad. La sensibilidad obtenida fue 89% para el tipo 1, 100% para el tipo 2, 67% para el tipo 3 y 90% para el tipo 4. Los especialistas afirmaron que los términos que describen a los indicadores en pelvis, tienen un lenguaje natural, lo que permite clasificar a los pacientes hemipléjicos de una manera difusa por grados de pertenencia.Palabras clave (español)Hemiplejía espástica, Indicadores pélvicos, Características difusas, Interpretación clínica, Biomecánica, Patrones de Marcha.Abstract (english)This research aims to model fuzzy characteristics of hemiplegic indicators in the pelvis. These indicators are consistent with those used by specialists to classify spastic hemiplegia following the classification proposed by Dr. Gage. The sample consisted of 83 patients with motor dysfunction subtype of spastic hemiplegia. These patients have been treated with protocols of Children's Orthopedic Hospital (HOI) in Caracas, Venezuela, between 1999 and 2008. Using statistical tools to indicators in pelvis, the average, the standard deviation and analysis of variance (ANOVA) are calculated. These statistics are suitable for building a fuzzy model with membership functions to discriminate types of hemiplegia comparable to the real world. If ANOVA has a value of p << 0.05; hemiplegic indicators in the pelvis are appropriate for the classification. 75% of records were processed and the remaining 25% were used to validate the results according to membership degree and sensitivity. The sensitivity obtained was 89% for type 1, 100% for type 2, 67% for type 3 and 90% for type 4. Experts said that the terms that describe the indicators pelvis, have a natural language, which allows classifying hemiplegic patients in a fuzzy way by degrees of membership.Keywords (english)Spastic hemiplegia, Pelvic indicators, Fuzzy characterization, Clinical interpretation, Biomechanics, Patterns gait.Introducción La Hemipléjica Espástica (HE) secuela de parálisis cerebral es una patología compleja para la cirugía ortopédica pediátrica. Se caracteriza por una alteración neuronal músculo esquelética predominantemente en un lado del cuerpo, originando disfuncionalidad de la marcha. El Dr. Gage (1991), describe y clasifica la HE en términos del miembro inferior afectado (Ipsilateral), analizando los registros cinemáticos en el plano sagital (1).Los especialistas analizan los registros cinemáticos de la pelvis, comparando cualitativamente los rangos articulares con el patrón normal y los patrones hemipléjicos propuesto por Gage, en determinados segmentos del ciclo de marcha (2-4). La marcha normal está dividida en dos fases, apoyo y balanceo; subdividida en porcentajes con respecto al ciclo de marcha (5).El único movimiento articular que describe la pelvis es la inclinación. Este movimiento es la variación del ángulo entre dos líneas imaginarias, una línea horizontal paralela a la línea de progresión y la otra, es la línea que conecta la Espina Ilíaca Anterosuperior (EIAS) con la Espina Ilíaca Posterosuperior (EIPS) (6).La biomecánica de la pelvis en la marcha normal describe una constante inclinación, con un promedio de 12 grados y un rango de excursión articular alrededor de los 4 grados. El incremento excesivo del ángulo de inclinación pélvica origina lordosis lumbar, según Salazar et al (2011) (7).La HE secuela parálisis cerebral, es una lesión no progresiva del cerebro inmaduro, resultando en un trastorno patológico neuromuscular de la marcha. Alterando la estabilidad, dificultando el paso libre del pie en balanceo y desequilibrando el consumo energético (8).En todos los tipos de hemiplejía se aprecia un incremento de la inclinación pélvica con respecto al patrón normal. La HE tipo 1 muestra un leve incremento de inclinación alrededor de 6 grados aparentemente constante en todo el ciclo de la marcha, por la dificultad del pie equino al paso libre en balanceo. En el tipo 2 se evidencia lordosis lumbar, con rango de excursión variable a lo largo del ciclo de marcha. El tipo 3 describe un aumento estimable de la inclinación pélvica, con variabilidad del rango de excursión. Por último, la HE tipo 4 muestra elevada inclinación pélvica, exagerada al final de la fase de apoyo y al comienzo de la fase de balanceo (4). La articulación de la pelvis describe diferentes patrones de movimiento pélvico durante la marcha con respecto al tipo de hemiplejía del paciente (9, 10).Entre los patrones hemipléjicos y el normal existe solapamiento de las señales cinemáticas, esto infiere inexactitud para clasificar un paciente, porque los datos de los registros se difuminan en la incertidumbre con característica difusa. Otras investigaciones reportan métodos de clasificación, emplean técnicas de minería de datos sobre los registros, manejando indicadores difíciles de entender debido al lenguaje desconocido por los especialistas (11- 13). Utilizando indicadores conocidos por los usuarios de los datos, reportados y validados en rigurosas investigaciones (4), se establece la siguiente incógnita: ¿Será posible clasificar la HE en pelvis en un ambiente natural difuso, empleando técnicas de validación a través de su sensibilidad? Clasificar a través de grados de membresía, implica modelar los datos en su natural característica difusa, donde no se circunscribe la subjetividad y los errores humanos durante la interpretación y análisis.Esta investigación pretende crear un modelado difuso a partir de los indicadores cinemáticos en pelvis, validado para clasificar en previas investigaciones. Esto se logrará cumpliendo las siguientes actividades: Generar los patrones cinemáticos en pelvis a partir de los registros. Determinar la media y desviación estándar en los rangos articulares de los indicadores cinemáticos en pelvis. Construir funciones trapezoidal y triangular para describir los grados de pertenencias a los tipos de hemiplejía. Calcular el nivel umbral de separación de los tipos de hemiplejía. Evaluar los rangos articulares de los pacientes en las funciones de pertenencias que cuantifique los grados de membresía a los grupos hemipléjicos. Clasificar la HE con un lenguaje natural y consistente, utilizando indicadores cinemáticos de la pelvis. Validar con herramientas estadísticas la clasificación.Materiales y métodos 20Selección de pacientes. La muestra está conformada por 83 pacientes en edades comprendidas entre 4 a 16 años, con marcha patológica subtipo hemiplejía espástica, estudiados en el Hospital Ortopédico Infantil, Caracas, Venezuela, entre 1999 y 2009. Cada paciente proporciona 3 registros cinemáticos GCD (Gait Data Cycle) utilizando el sistema VICON 370 (Revisado el sitio web de VICON en Junio de 2014) (14). Recoleccion de datos. La adquisición de los registros cinemático, cinético, electromiografía dinámica y consumo energético, implica pruebas experimentales que consiste en el recorrido del paciente a través de una pista de marcha, con placas de fuerza y cámaras infrarrojas que visualiza los marcadores lumínicos adheridos a los puntos óseos anatómicos más prominentes del paciente.Está investigación se fundamenta en tres elementos: los indicadores en pelvis, los registros cinemáticos de los 83 pacientes previamente clasificados por especialistas y un método de clasificación difusa.Existen aportes que clasifican satisfactoriamente la hemiplejía empleando los registros cinéticos mediante lógica difusa (11), evaluando la electromiografía de la clasificación cinemática (12), utilizando metaclasificadores (13), por diagnóstico de la marcha patológica mediante análisis cinético (15). El presente estudio es un avance que busca integrar en el futuro, los registros cinemáticos y cinéticos basado en un método difuso de clasificación, para validar los aportes existente en este campo.El protocolo Davis es utilizado para colocar los marcadores ópticos sobre los puntos óseos anatómicos, más prominentes, de ambos miembros inferiores y obtener el modelo biomecánico que describe la cinemática de la marcha. La figura 1 presenta según el tipo de hemiplejía, 34 registros de pacientes pertenecientes al tipo 1, 15 al tipo 2, 11 para el tipo 3 y 23 pertenecen al tipo 4.Figura 1. Organización de los registros cinemáticos por tipo de hemiplejía.Con el 75% de los registros se procesan los datos para diseñar y construir el modelo. Se extrae la media y desviación estándar de los registros agrupados por tipo de HE, para graficar los patrones cinemáticos de la pelvis. En la figura 2a se aprecia los patrones cinemáticos en pelvis utilizados por los especialistas para análisis y clasificación de las curvas cinemáticas de la pelvis, a partir de los datos procesados. La figura 2b ilustra dentro de un círculo los indicadores evaluados, fase de apoyo, apoyo terminal y fase de balanceo (4).Analisis estadísticos. El Análisis de Varianza (ANOVA, Analysis Of Variance) aplicado en los indicadores con la finalidad de evaluar la capacidad de estos para diferenciar entre los grupos hemipléjicos. Se contrasta entre los tipos de hemiplejía y el patrón normal. ANOVA estudia las varianzas para desarrollar una hipótesis estadística basada en el contraste entre las medias aritméticas de dos grupos de población con distribución normal. ResultadosLos resultados del Análisis Lineal discriminante (ALD) es el umbral de separación entre dos grupos (12). El ALD requiere de la media y la desviación estándar de cada grupo. La Figura 3a ilustra dos grupos con media y desviación estándar. El grupo a la izquierda del umbral () tiene una media () y el de la derecha (), se concluye que:El umbral () se calcula usando las siguientes expresiones:Dónde: Media del grupo tipo A Desviación Estándar del tipo A Media del grupo tipo B21 Desviación Estándar del tipo BFigura 2. Indicadores sobre los patrones cinemáticos evaluados con ANOVA. Fig.2a: indicadores sobre los patrones cinemáticos pélvicos hemipléjicos. Fig.2b: indicadores evaluados con ANOVA. AT: Apoyo Terminal, FA: Fase de Apoyo, FB: Fase de Balanceo.La media y desviación estándar se extrae de los indicadores para cada grupo hemipléjicos y normal. Los valores mostrados en la Tabla 1 son indispensables para determinar el umbral de separación entre los grupos hemipléjicos. Los indicadores fase de apoyo, apoyo terminal y fase de balanceo observadas en la tabla 1 describen los promedios y desviaciones estándar utilizados para determinar los puntos nulos y el umbral de separación entre los grupos HE.Función de membresía: La función de membresía cuantifica una entrada en un grado de verdad. La figura 3b muestra la forma básica de una función de pertenencia trapezoidal con unidad a la izquierda (16-18).La función de membresía se ejecuta en el rango lineal de valores de entrada utilizando, para el caso de la trapezoidal, las siguientes expresiones:22Otra función de pertenencia es la figura 3c, en este caso, la forma básica es triangular. Las funciones de membresía triangular requieren un conjunto más amplio de valores de entradas, las expresiones para construirlas son:La figura 3d, muestra varias funciones de membresía: trapezoidales y triangulares, cada una representa un conjunto difuso que cuantifica el grado de pertenencia para una entrada dada (17,18). Los indicadores especifican los valores medios de cada grupo, éstos son: x(1), x(2), x(3), x(4), x(5), visto en la figura 3d.La figura 4a muestra las funciones de membresía trapezoidales y triangulares de la fase de apoyo. El tipo 2 solapa tres grupos hemipléjico, la pendiente determina el grado de pertenencia. Las funciones tipo 1 y 2, se solapan en un amplio rango, a medida que la inclinación pélvica incrementa también aumenta la pertenencia al tipo 2 y disminuye la membresía al tipo 1.La figura 4b muestra los conjuntos difusos a través de funciones que permiten medir el nivel de membresía a los grupos HE en el indicador apoyo terminal. Las funciones de pertenencia representan Tabla 1. Desviación estándar, media aritmética y umbral para cada indicador.Normalm, (sd)UmbralTipo 4m, (sd)UmbralTipo 3m, (sd)UmbralTipo 1m, (sd)UmbralTipo 2m, (sd)Fase de Apoyo12,22(2,56)13,36914,6(2,73)15,66816,82(2,95)15,88719,16(2,44)17,05821,6(4,53)Apoyo Terminal12,79(5,76)14,75718,89(2,98)17,44215,77(2,58)19,84520,68(2,26)21,65622,94(2,99)Fase de Balanceo12,37(1,69)5,04915,48(1,89)15,02414,46(2,34)15,51916,22(1,55)17,05818,02(1,79)m: Media, sd:Deviación Estándar.adecuado espaciamiento y solapamiento para describir un comportamiento difuso de inclinación pélvica.Figura 4. Funciones de membresías obtenida de los datos de los indicadores en Pelvis. Fig.4a: fase de apoyo. Fig.4b: fase de apoyo terminal. Fig.4c: fase de balanceo.Observe que a medida que la función de membresía normal solapa la tipo 3, la primera reduce su grado de pertenencia mientras que la última se incrementa.Las funciones de membresía de la figura 4c, definen los conjuntos difusos del indicador fase de balanceo, a través de la cual mide el grado de pertenencia. Se observa un rango articular muy selectivo para las hemiplejías tipo 1 y 4.23Figura 3a. Se refiere al umbral entre dos grupos.3b-d. Se refiere a funciones de Membresía. 3b. trapezoidal. 3c. triangular. 3d agrupacion de las funciones de membresia trapezoidal y triangular.Es posible que el amplio rango de inclinación descrito por la función de pertenencia de la hemiplejía tipo 3, obedezca a la circunducción de cadera en el plano transverso.Validación. Los indicadores son validados con un 25% de los registros. A los pacientes hemipléjicos se les toman los valores promediados articulares en los indicadores: fase de apoyo, apoyo terminal y fase de balanceo. Esos valores son evaluados en las funciones de membresía, el paciente pertenecerá al tipo HE cuya evaluación tenga el mayor grado de pertenencia. Tabla 2. Resultado de la clasificación y toma de decisión.TrialFase de ApoyoApoyo TerminalFase de BalanceoToma de decisiónVPFNS%EvaluaciónGrado de pertenenciaEvaluaciónGrado de pertenenciaEvaluaciónGrado de pertenenciaID620_08Tipo 415,12Tipo 4: 82%17,98Tipo 4: 63%15,53Tipo 4: 98%Tipo 49190ID620_0913,81Tipo 4: 73%18,58Tipo 4: 86%14,59Tipo 3: 82%Tipo 4ID620_1013,62Tipo 4: 64%17,65Tipo 4: 56%14,46Tipo 3: 87%Tipo 4ID620_1513,85Tipo 4: 67%18,15Tipo 4: 76%16,23Tipo 1: 91%Tipo 4ID541_0312,61Normal: 76%18,91Tipo 4: 98%15,34Tipo 4: 86%Tipo 4ID541_0415,34Tipo 4: 71%17,78Tipo 4: 62%15,67Tipo 4: 95%Tipo 4ID541_0815,98Tipo 3: 69%19,59Tipo 4: 72%15,63Tipo 4: 91%Tipo 4ID450_1014,67Tipo 4: 95%19,02Tipo 4: 96%13,62Tipo 3: 63%Tipo 4ID450_1613,97Tipo 4: 83%19,33Tipo 4: 79%16,67Tipo 1: 68%Tipo 4ID450_2016,38Tipo 3: 89%19,13Tipo 4: 94%14,10Tipo 3: 81%Tipo 3ID534_07Tipo 316,32Tipo 3: 86%16,32Tipo 3: 78%14,35Tipo 3: 97%Tipo 34267ID534_0814,11Tipo 4: 83%15,48Tipo 3: 86%12,18Normal: 92%Imp.ID534_0916,56Tipo 3: 98%14,65Tipo 3: 69%13,81Tipo 3: 71%Tipo 3ID649_0515,38Tipo 4: 69%15,81Tipo 3: 98%14,61Tipo 3: 89%Tipo 3ID649_0618,53Tipo 1: 79%16,76Tipo 3: 73%12,72Tipo 4: 68%Imp.ID649_0717,02Tipo 3: 93%13,23Normal: 93%14,81Tipo 3: 81%Tipo 3ID486_17Tipo 221,36Tipo 2: 97%20,78Tipo 1: 96%17,86Tipo 2: 98%Tipo 260100ID486_2019,41Tipo 1: 87%21,91Tipo 2: 68%17,82Tipo 2: 97%Tipo 2ID486_2117,71Tipo 3: 73%22,34Tipo 2: 81%17,54Tipo 2: 61%Tipo 2ID584_0417,46Tipo 3: 79%22,56Tipo 2: 88%17,78Tipo 2: 78%Tipo 2ID584_1421,25Tipo 2: 91%21,29Tipo 1: 73%17,32Tipo 2: 52%Tipo 2ID584_1917,87Tipo 3: 63%22,79Tipo 2: 98%17,61Tipo 2: 72%Tipo 2ID462_13Tipo 118,81Tipo 1: 85%22,13Tipo 2: 71%16,01Tipo 1: 81%Tipo 18189ID462_1719,31Tipo 1: 96%20,013Tipo 1: 65%16,31Tipo 1: 94%Tipo 1ID481_0619,23Tipo 1: 98%19,29Tipo 4: 81%16,18Tipo 1: 86%Tipo 1ID481_0819,65Tipo 1: 83%20,81Tipo 1: 98%15,56Tipo 4: 97%Tipo 1ID481_0919,75Tipo 1: 73%19,32Tipo 4: 73%16,41Tipo 1: 98%Tipo 1ID365_1718,32Tipo 1: 64%22,56Tipo 2: 87%16,23Tipo 1: 98%Tipo 1ID365_1919,79Tipo 1: 78%21,31Tipo 1: 67%17,85Tipo 2: 91%Tipo 1ID365_2019,68Tipo 1: 81%18,95Tipo 4: 96%17,61Tipo 2: 81%Imp.ID365_2319,98Tipo 1: 69%20,56Tipo 1: 97%16,81Tipo 1: 61%Tipo 1VP: verdadero positivo, FN: falso negativo, Imp: imposibleLa tabla 2 contiene las anotaciones de los ensayos realizados, en ella se muestran los valores promediados del paciente en cada indicador, se elige el tipo HE que tenga el mayor grado de pertenencia. La toma de decisiones será posible si al menos dos indicadores coinciden con el mismo tipo de HE, si los tres son distintos la decisión final será imposible de clasificar. Verdaderos Positivos (VP): Cantidad de instancias clasificadas dentro de una clase a la que pertenece (15). Estas fueron 8 de 9 casos para el tipo 1. El tipo 3 muestra 4 de un universo de 6 casos y el tipo 4 tiene 9 de un total de 10. Solo el tipo 2 presenta un 100% de verdadero positivo. La sensibilidad es la probabilidad de clasificar correctamente una instancia y se le conoce como la tasa de verdaderos positivos (15, 19). La Tabla 2 indica que el modelo tiene 89% de sensibilidad para detectar y clasificar correctamente los pacientes Tipo 1, 100% para el tipo 2, 67% para el tipo 3 y 90% para el tipo 4.24Discusión Este trabajo ofrece una nueva aplicación de la lógica difusa en el análisis de los indicadores cinemáticos pélvicos de pacientes hemipléjicos para su clasificación, a través de un lenguaje conocido por los especialistas y sin ignorar la naturaleza realmente difusa de los datos.Esta metodología permite abordar los problemas asociados a la variabilidad de los datos, la exactitud e incertidumbre en la clasificación cinemática. Si bien es necesario abordar detalles como el tamaño muestral y fortalecer la validación de los resultados, la sensibilidad indica que los grados de membresía de los rangos de inclinación pélvica, ofrece muy buenos resultados para la clasificación hemipléjica.En condiciones normales la inclinación pélvica está entre un rango de 10 a 12 grados, a medida que la inclinación aumenta entra en las funciones de pertenencia de los tipos hemipléjicos. A través de las funciones de pertenencia de los indicadores, se evidencia elevada inclinación pélvica en la hemiplejía espástica tipo 2, que es aún mayor en apoyo terminal, momento en que se aprecia más su inherente lordosis lumbar.Se recomienda para estudios futuros, aplicar técnicas estadísticas que reduzcan el sesgo y permitan mejorar la validación de los resultados obtenidos en esta investigación. Se sugiere incrementar el número de pacientes, pero es necesario definir el tamaño de la muestra y determinar un estimador asintóticamente insesgado que indique que la muestra es representativa. Luego, tomar de cada uno de los pacientes los registros cinemáticos y aplicar la metodología de esta investigación. Los resultados obtenidos de la clasificación mejorarían si se incluyese características difusas de los registros cinéticos, electromiografía dinámica y consumo energético de los pacientes. Una variante significativa es verificar la migración de un paciente de un grupo hemipléjico a otro, luego de recibir tratamiento ortopédico o quirúrgico. También extender el modelo propuesto en este trabajo al miembro no afectado por la hemiplejía, con la finalidad de evaluar los movimientos compensatorios.Se sugiere optimizar proceso de validación con más del 25% de la muestra. 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