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

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 >.95) with experimental blood pressure data.Fil: Ventre, Jeanne. Centre National de la Recherche Scientifique; FranciaFil: Politi, Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fernández, Juan M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ghigo, Arthur R.. Université de Toulouse; FranciaFil: Gaudric, Julien. Centre National de la Recherche Scientifique; Francia. Université de Toulouse; FranciaFil: Wray, Sandra. Universidad Favaloro; ArgentinaFil: Lagaert, Jean Baptiste. Université Paris Sud; FranciaFil: Armentano, Ricardo Luis. Universidad de la República; UruguayFil: Capurro, Claudia Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fullana, José Maria. Centre National de la Recherche Scientifique; FranciaFil: Lagrée, Pierre Yves. Centre National de la Recherche Scientifique; Franci

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