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Abstract: This paper presents the power analysis to the mechanical model of the basilar membrane in the cochlea as a system of forced damped harmonic oscillators without lateral coupling proposed by Lesser and Berkeley. The Lagrange's equation for dissipative mechanical systems and the energy method are used to obtain the general equation of the system. Next a solution by complex exponential is proposed using the resonance analysis considering only excitations of pure tones to obtain the equation of displacement, and with its derived the equation of velocity. The power in the system is the multiplication between the equations of the velocity and the excitation force. Finally the equation of the average power in the system is obtained. This new solution has the advantage of determining the relationship between the excitation frequency of the system and the position along the basilar membrane where the average power is maximum. This implies that the distance where there is maximum transfer of energy between the wave propagating in the perilymph and the mechanical displacement of the basilar membrane on the hair cells in the organ of Corti is known. The power analysis is successfully compared with the two-dimensional model of the cochlea developed by Neely using finite differences and with the experimental results of Békésy. In both experiments are used the same mechanical parameters of the basilar membrane and the same set of frequencies of evaluation proposed in the original papers in order to compare the different methodologies.
Resumen: En este artículo se presenta el análisis de potencia del modelo mecánico de la membrana basilar en la cóclea como un sistema de osciladores armónicos forzados amortiguados sin acoplamiento lateral propuesto por Lesser y Berkeley. Se usa la ecuación de Lagrange para sistemas mecánicos disipativos y el método de energías para obtener la ecuación general del sistema. A continuación se propone su solución en forma exponencial compleja usando el análisis por resonancia considerando únicamente excitaciones de tonos puros obteniendo la ecuación del desplaza miento, y a partir de su derivada la ecuación de la velocidad. Posteriormente se determina la ecuación de potencia mediante el producto entre las ecuaciones de la velocidad y la fuerza de excitación. Por último se obtiene la ecua ción de la potencia promedio en el sistema. Esta nueva solución tiene la ventaja de determinar la relación entre la frecuencia de excitación del sistema y la posición a lo largo de la membrana basilar donde la potencia promedio es máxima, con lo cual se conoce la distancia donde se genera la máxima transferencia de energía entre la onda que se propaga en la perilinfa y el desplazamiento mecánico de la membrana basilar sobre los cilios en el órgano de Corti. El análisis de potencia se compara satisfactoriamente con el modelo en dos dimensiones por diferencias finitas de la cóclea desarrollado por Neely y con los resultados experimentales obtenidos por Békésy. En ambos experimentos se usan los mismos parámetros mecánicos de la membrana basilar y el mismo conjunto de frecuencias de evaluación propuestos en los trabajos originales con el objetivo de comparar las diferentes metodologías.
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Abstract In this paper a new solution to micromechanical model of the cochlea developed by Neely and Kim is presented using Lagrange's equation. This solution has the advantage over previous methodologies to provide a mathematical model for the displacement exercised on the outer hair cells in the organ of Corti that only depends of the mechanical characteristics in the system and the value of the excitation frequency in the inner ear. For the evaluation of this new model the parameters developed by Ku are used and is considers that the amplitude of the excitation frequency is normalized. The model developed is satisfactorily compared with the impedance method and its numerical solution proposed by Neely and Kim, the state space analysis developed by Elliot, Ku and Lineton and the physiological measurements taken from Békésy.
Resumen En este trabajo se presenta una nueva solución utilizando la ecuación de Lagrange al modelo micromecánico de la cóclea desarrollado por Neely y Kim. Esta solución tiene la ventaja respecto a las ya existentes de proporcionar un modelo matemático del desplazamiento ejercido a los cilios en el órgano de Corti que sólo depende de las características mecánicas del sistema y del valor de la frecuencia de excitación en el oído interno. Para su evaluación se utilizan los parámetros desarrollados por Ku y se considera que la amplitud de la frecuencia de excitación está normalizada. El modelo desarrollado se compara satisfactoriamente con el método de impedancias y su solución numérica propuesta por Neely y Kim, el método de análisis de espacio estado desarrollado por Elliot, Ku y Lineton y con las mediciones fisiológicas realizadas por Békésy.
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BACKGROUND: Low bone mineral density (BMD) and vertebral fractures (VF) have been associated with atherosclerosis in the general population. We sought to investigate the relationship between BMD and VF and carotid atherosclerosis in women with systemic lupus erythematosus (SLE). METHODS: We studied 122 women with SLE. All patients had BMD, carotid intima-media thickness (IMT), and carotid artery atherosclerotic plaque assessment by ultrasound. RESULTS: Mean age at study entry was 44 years and mean disease duration was 11 years. Carotid plaque was found in 13 (11%) patients (9 postmenopausal and 4 premenopausal). Patients in the highest IMT quartile were more likely to be older (p = 0.001), have a higher body mass index (p = 0.008), and exhibit dyslipidemia at study entry (p = 0.041), compared with the lower three quartiles. BMD at the lumbar spine was lower in patients in the highest IMT quartile compared with the lower quartiles in the multivariate logistic analysis, however, there was no association between lumbar or total hip BMD and IMT (p = 0.91 and p = 0.6, respectively). IMT measurements did not differ according to the presence or absence of VF (0.08 ± 0.12 vs. 0.06 ± 0.03 mm, p = 0.11). A trend towards higher incidence of VF was found in patients with carotid plaque compared with those without (33% vs. 21%; p = 0.2). CONCLUSIONS: In patients with SLE, the presence of carotid atherosclerosis is not associated with low BMD or VF.
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Densidad Ósea , Enfermedades de las Arterias Carótidas/epidemiología , Vértebras Lumbares/lesiones , Lupus Eritematoso Sistémico/epidemiología , Osteoporosis/epidemiología , Fracturas de la Columna Vertebral/epidemiología , Vértebras Torácicas/lesiones , Acetábulo/fisiopatología , Adulto , Índice de Masa Corporal , Enfermedades de las Arterias Carótidas/diagnóstico por imagen , Grosor Intima-Media Carotídeo , Estudios Transversales , Dislipidemias/epidemiología , Femenino , Cabeza Femoral/fisiopatología , Humanos , Vértebras Lumbares/fisiopatología , Persona de Mediana Edad , Posmenopausia , Premenopausia , Radiografía , Factores de Riesgo , Fracturas de la Columna Vertebral/diagnóstico por imagenRESUMEN
The objective of this study was to investigate the efficacy and safety of anti-CD20 treatment in Hispanic patients with refractory systemic lupus erythematosus and to determine whether baseline parameters predict disease flare. Fifty-two patients with systemic lupus erythematosus, 13 with active lupus nephritis, eight with thrombocytopenia, three with leukocytopenia, 25 with severe musculoskeletal involvement and three with skin involvement) refractory to conventional therapy were treated with anti-CD20 treatment (rituximab; MabThera, Roche) plus ongoing immunosuppressive treatment. Disease activity was assessed monthly using the SLEDAI validated for the Mexican population with a follow-up period of 6 months. At 6 months of follow-up, significant clinical improvements were detected, with a reduction in the global SLEDAI validated for the Mexican population score. Five of the 13 patients with lupus nephritis (38.4%) had a complete renal response and five (38.4%) had a partial response. Rituximab was also effective in patients with autoimmune thrombocytopenia, inducing a significant increase in platelet counts (p = 0.012). Nineteen of 25 patients with severe musculoskeletal involvement had remission of arthritis. Only one of the three patients with skin involvement had no lesions at 6 months. Rituximab treatment also allowed a reduction of the oral prednisone dose in the majority of patients. No baseline predictors of flare were found. Treatment was discontinued after the first infusion in two patients due to serum sickness and in another due to pulmonary infection. In conclusion, the addition of rituximab to conventional immunosuppressive therapy may be an effective strategy for lupus nephritis, autoimmune thrombocytopenia and inflammatory polyarthritis in patients with refractory systemic lupus erythematosus.