Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries.

Viscoelastic models can be used to better understand arterial wall mechanics in physiological and pathological conditions. The arterial wall reveals very slow time-dependent decays in uniaxial stress-relaxation experiments, coherent with weak power-law functions. Quasi-linear viscoelastic (QLV) theory was successfully applied to modeling such responses, but an accurate estimation of the reduced relaxation function parameters can be very difficult. In this work, an alternative relaxation function based on fractional calculus theory is proposed to describe stress relaxation experiments in strips cut from healthy human aortas. Stress relaxation (1 h) was registered at three incremental stress levels. The novel relaxation function with three parameters was integrated into the QLV theory to fit experimental data. It was based in a modified Voigt model, including a fractional element of order α, called spring–pot. The stressrelaxation predictionwas accurate and fast. Sensitivity plots for each parameter presented a minimum near their optimal values. Least-squares errors remained below 2%. Values of order α = 0.1–0.3 confirmed a predominant elastic behavior. The other two parameters of the model can be associated to elastic and viscous constants that explain the time course of the observed relaxation function. The fractional-order model integrated into the QLV theory proved to capture the essential features of the arterial wall mechanical response

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. Darboux-Crum transformations are applied to connect the well-known shape invariant Hamiltonians of the radial oscillator and the Darboux-P\"oschl-Teller potential to the shape invariant potentials of Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of generalised Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure

Simulation of the arterial elasticity influence on the Ambulatory Arterial Stiffness Index AASI

Recientemente se propuso un índice de rigidez arterial denominado AASI (Ambulatory Arterial Stiffness Index) derivado de mediciones ambulatorias de presión arterial durante 24 horas. Su asociación como índice de rigidez y la infl uencia estadística de la dispersión en los valores presivos continúa bajo discusión. Proponemos estudiar estas controversias en el contexto de un modelo estadístico. Se realizó una simulación con valores similares a los de pacientes de arterias normales, rígidas y compliantes, utilizando 3 curvas exponenciales presión-diámetro. Se generaron diámetros pulsátiles aleatorios siguiendo distribuciones normales y se obtuvieron presiones sistólicas y diastólicas en tiempos paramétricos equivalentes a 24 horas. Se calculó el AASI como uno menos la pendiente de la regresión de presión arterial sistólica y diastólica. El AASI del grupo normal resultó 0,42, aumentó a 0,50 en el rígido y disminuyó a 0,34 en el compliante (siempre con r2>0,9). Disminuir la dispersión del rango de presiones provocó una disminución de r2 en la regresión de la nube de puntos de presión sistólica y diastólica, aumentando artifi cialmente el AASI. Por primera vez la elasticidad no-lineal de la pared arterial ayuda a explicar la asociación del AASI como índice de rigidez arterial. La simulación corrobora que la dispersión de los valores presivos condicionan el cálculo del AASI debido a su naturaleza estadística.Recently, an arterial stiffness index called AASI (Ambulatory Arterial Stiffness Index) calculated from ambulatory blood pressure measurements during 24 hours was proposed. The associations with arterial stiffness and the pressure dispersion dependence remain under discussion. We propose to study these controversies in a statistical model framework. A simulation was performed including values similar to the ones in patients with normal, rigid and compliant arteries. Three exponential curves of pressure-diameter were simulated. Based on diameters randomly generated following normal distributions, systolic and diastolic pressures were calculated in a 24h parametric time. AASI was calculated as one minus the slope of the regression of systolic to diastolic pressure. The AASI for the normal group was 0,42, increased to 0,50 in the rigid group and decreased to 0,34 in the compliant case (always r2>0,9). A dispersion decrease in the pressure values was followed by an r2 decrease in the diastolic vs systolic pressure regression, artifi cially increasing AASI. For the fi rst time the non-linearity of the arterial wall helps to explain the association of AASI with a stiffness index. The simulation corroborates that 24 h pressure variability conditions AASI values due to its statistical nature

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractionalorder internal model control and external adaptive control

A fractional-order internal model control technique is applied to a three-dimensional resistive-capacitive network to enforce desired closed loop dynamics of first order. In order to handle model mismatch issues resulting from the random allocation of the components within the network, the control law is augmented with a model-reference adaptive strategy in an external loop. By imposing a control law on the system to obey first order dynamics, a calibrated transient response is ensured. The methodology enables feedback control of complex systems with emergent responses and is robust in the presence of measurement noise or under conditions of poor model identification. Furthermore, it is also applicable to systems that exhibit higher order fractional dynamics. Examples of feedback-controlled transduction include cantilever positioning in atomic force microscopy or the control of complex de-excitation lifetimes encountered in many types of spectroscopies, e.g., nuclear magnetic, electron-spin, microwave, multiphoton fluorescence, Förster resonance, etc. The proposed solution should also find important applications in more complex electronic, microwave, and photonic lock-in problems. Finally, there are further applications across the broader measurement science and instrumentation community when designing complex feedback systems at the system level, e.g., ensuring the adaptive control of distributed physiological processes through the use of biomedical implants