Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

The influence of differente speeds on backpacker's gait kinectics

This study analyzed the influence of different speeds on ground reaction force’s (GRF), impulses and mean vertical force during gait of people submitted to occasional overload (backpack). A force plate was used to record the GRF data of 60 young adult subjects walking in two different cadences: 69 steps/min (slow gait) and 120 steps/min (fast gait). During the slow gait, the impact and propulsive impulses of vertical GRF, propulsive impulse of anterior-posterior GRF, impulse of medial-lateral GRF and duration of stance phase were larger than during the fast gait; the mean vertical force was the only variable that showed larger values during fast gait. Therefore, slow gait may present a larger possibility of blister development and gait unbalance, while the fast gait, even presenting a small impulse, seems to be more harmful to the musculoskeletal system.

Comparative analysis of the ground reaction forces, during the support phase, in a group of pregnant women on their 3rd trimester of pregnancy and in a group of not pregnant women

PURPOSE: To analyze and compare the Ground Reaction Forces (GRF), during the stance phase of walking in pregnant women in the 3rd trimester of pregnancy, and non pregnant women. METHODS: 20 women, 10 pregnant and 10 non pregnant, voluntarily took part in this study. GRF were measured (1000 Hz) using a force platform (BERTEC 4060-15), an amplifier (BERTEC AM 6300) and an analogical-digital converter of 16 Bits (Biopac). RESULTS: The study showed that there were significant differences among the two groups concerning absolute values of time of the stance phase. In what concerns to the normalized values the most significant differences were verified in the maximums values of vertical force (Fz3, Fz1) and in the impulse of the antero-posterior force (Fy2), taxes of growth of the vertical force, and in the period of time for the antero-posterior force (Fy) be null. CONCLUSIONS: It is easier for the pregnant to continue forward movement (push-off phase). O smaller growth rates in what concerns to the maximum of the vertical force (Fz1) for the pregnant, can be associated with a slower speed of gait, as an adaptation strategy to maintain the balance, to compensate the alterations in the position of her center of gravity due to the load increase. The data related to the antero-posterior component of the force (Fy), shows that there is a significant difference between the pregnant woman’s left foot and right foot, which accuses a different functional behavior in each one of the feet, during the propulsion phase (TS).

Modelação do transporte e dispersão de um marcador corado no Rio Febros

O rio Febros é um pequeno curso de água, situado no concelho de Vila Nova de Gaia, com cerca de 15 km de extensão, cuja bacia hidrográfica ocupa uma área de aproximadamente 35,4 km2. Nasce em Seixezelo e desagua na margem esquerda do Rio Douro no Cais do Esteiro, em Avintes. Em Maio de 2008, um acidente de viação teve como consequência o derrame de cerca de quatro toneladas de ácido clorídrico que rapidamente convergiu às águas do rio. Apenas um dia depois, o pH desceu para três e muitos foram os peixes que morreram. A solução adoptada para evitar o desaire foi introduzir milhares de litros de água de modo a diluir o ácido presente, ao longo de todo o curso de água. Tal facto não evitou a destruição de parte de um ecossistema, que ainda nos dias de hoje se encontra em recuperação. De forma a avaliar-se o impacto destas possíveis perturbações sejam estas de origem antropogénica ou natural é necessário possuir conhecimentos dos processos químicos tais como a advecção, a mistura devida à dispersão e a transferência de massa ar/água. Estes processos irão determinar o movimento e destino das substâncias que poderão ser descarregadas no rio. Para tal, recorrer-se-á ao estudo hidrogeométrico do curso de água assim como ao estudo do comportamento de um marcador, simulando uma possível descarga. A rodamina WT será o marcador a ser utilizado devido à panóplia de características ambientalmente favoráveis. Os estudos de campo com este corante, realizados em sequência de descarga previamente estudada, fornecem uma das melhores fontes de informação para verificação e validação de modelos hidráulicos utilizados em estudos de qualidade de águas e protecção ambiental. Escolheram-se dois pontos de descarga no Febros, um em Casal Drijo e outro no Parque Biológico de Gaia, possuindo cada um deles, a jusante, duas estações de monitorização. Pelo modelo ADE os valores obtidos para o coeficiente de dispersão longitudinal para as estações Pontão d’ Alheira, Pinheiral, Menesas e Giestas foram, respectivamente, 0,3622; 0,5468; 1,6832 e 1,7504 m2/s. Para a mesma sequência de estações, os valores da velocidade de escoamento obtidos neste trabalho experimental foram de 0,0633; 0,0684; 0,1548 e 0,1645 m/s. Quanto ao modelo TS, os valores obtidos para o coeficiente de dispersão longitudinal para as estações Pontão d’ Alheira, Pinheiral, Menesas e Giestas foram, respectivamente, 0,2339; 0,1618; 0,5057e 1,1320 m2/s. Para a mesma sequência de estações, os valores da velocidade de escoamento obtidos neste trabalho experimental foram de 0,0652; 0,0775; 0,1891 e 0,1676 m/s. Os resultados foram ajustados por um método directo, o método dos momentos, e por dois métodos indirectos, os modelos ADE e TS. O melhor ajuste corresponde ao modelo TS onde os valores do coeficiente de dispersão longitudinal e da velocidade de escoamento são aqueles que melhor se aproximam da realidade. Quanto ao método dos momentos, o valor estimado para a velocidade é de 0,162 m/s e para o coeficiente de dispersão longitudinal de 9,769 m2/s. Não obstante, a compreensão da hidrodinâmica do rio e das suas características, bem como a adequação de modelos matemáticos no tratamento de resultados formam uma estratégia de protecção ambiental inerente a futuros impactos que possam suceder.

O terrível nascimento da beleza: a criação literária em diversos autores

De onde brota a inspiração para baladas de amor e canções de guerra, lendas e narrativas, tragédias e comédias? Ao longo de séculos, escritores e leitores interrogaram-se acerca do nascimento da beleza. Neste artigo, abordo essa questão intrigante, em quatro etapas: a) Examino algumas personificações criadas por Hesíodo, Homero, Luís de Camões e Federico García Lorca para descreverem a inspiração; b) Exploro as estratégias utilizadas por Samuel Coleridge, Salvador Dalí e William Burroughs, para penetrar no reino da fantasia, o inconsciente; c) Apresento as explicações científicas propostas por Sigmund Freud, Carl Jung e Robert Sperry para o impulso criativo; d) Para concluir, menciono as razões que levaram Fernando Pessoa, Eugénio de Andrade e Emily Dickinson a desconfiarem da musa inspiradora, preferindo o esforço que corrige a emoção e gera a obra de arte. Seguindo uma perspectiva comparada, o meu objectivo é mostrar diferentes formas de perceber a criatividade literária. Para tanto, recorro ao trabalho dos escritores e cientistas atrás mencionados e, naturalmente, à minha opinião.

Interlimb coordination during the stance phase of gait in subjects with stroke

Objective: To analyze the relation between contralesional and ipsilesional limbs in subjects with stroke during step-to-step transition of walking. Design: Observational, transversal, analytical study with a convenience sample. Setting: Physical medicine and rehabilitation clinic. Participants: Subjects (nZ16) with poststroke hemiparesis with the ability to walk independently and healthy controls (nZ22). Interventions: Not applicable. Main Outcome Measures: Bilateral lower limbs electromyographic activity of the soleus (SOL), gastrocnemius medialis, tibialis anterior, biceps femoris, rectus femoris, and vastus medialis (VM) muscles and the ground reaction force were analyzed during double-support and terminal stance phases of gait. Results: The propulsive impulse of the contralesional trailing limb was negatively correlated with the braking impulse of the leading limb during double support (rZ .639, PZ.01). A moderate functional relation was observed between thigh muscles (rZ .529, PZ.035), and a strong and moderate dysfunctional relation was found between the plantar flexors of the ipsilesional limb and the vastus medialis of the contralesional limb, respectively (SOL-VM, rZ .80, P<.001; gastrocnemius medialis-VM, rZ .655, PZ.002). Also, a functional moderate negative correlation was found between the SOL and rectus femoris muscles of the ipsilesional limb during terminal stance and between the SOL (rZ .506, PZ.046) and VM (rZ .518, PZ.04) muscles of the contralesional limb during loading response, respectively. The trailing limb relative impulse contribution of the contralesional limb was lower than the ipsilesional limb of subjects with stroke (PZ.02) and lower than the relative impulse contribution of the healthy limb (PZ.008) during double support. Conclusions: The findings obtained suggest that the lower performance of the contralesional limb in forward propulsion during gait is related not only to contralateral supraspinal damage but also to a dysfunctional influence of the ipsilesional limb.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.

Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04