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 alpha, called spring-pot. The stress-relaxation prediction was accurate and fast. Sensitivity plots for each parameter presented a minimum near their optimal values. Least-squares errors remained below 2%. Values of order alpha = 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.

New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues.

Damping is the conversion of mechanical energy of a structure into thermal energy, and it is related to the material viscous behavior. To evaluate the role of damping in the common carotid artery (CCA) wall in human hypertension and the possible improvement of angiotensin-converting enzyme (ACE) inhibition, we used noninvasive CCA pressure (tonometry) and diameter (B-mode echography) waveforms in normotensive subjects (NT group; n=12) and in hypertensive patients (HT group; n=22) single-blind randomized into HT–placebo (n=10) or HT-treated (ramipril, 5 to 10 mg/d during 3 months; n=12). Vascular smooth muscle (VSM) null tonus condition was achieved from in vitro pressure and diameter waveforms (Konigsberg microtransducer and sonomicrometry) measured in explanted human CCA (n=14). Arterial wall dynamics was described by viscous (η), inertial ( M ), and compliance ( C ) parameters, mean circumferential wall stress, viscous energy dissipation ( W _D ), peak strain energy ( W _St ), damping ratio (ξ= W _D / W _St ), and modeling isobaric indexes C _Iso and W _St(Iso) . The lack of VSM tonus isobarically increased wall stress and reduced η, C _Iso , and damping ( P <0.01). Wall stress, η, and W _D were greater in HT than in NT ( P <0.015) and arrived near normal in HT-treated ( P <0.032 respect to HT), with no changes in HT–placebo. Whereas C _Iso increased in HT-treated ( P <0.01) approaching the NT level, ξ did not vary among groups. During hypertension, because of the W _St increase, the arterial wall reacts increasing W _D to maintain ξ. ACE inhibition modulates VSM activation and vessel wall remodeling, significantly improving wall energetics and wall stress. This protective vascular action reduces extra load to the heart and maintains enhanced arterial wall damping.

Arterial pulse wave velocity (PWV) is associated with increased mortality in aging and disease. Several studies have shown the accuracy of applanation tonometry carotid-femoral PWV (Cf-PWV) and the relevance of evaluating central aorta stiffness using 2D cardiovascular magnetic resonance (CMR) to estimate PWV, and aortic distensibility-derived PWV through the theoretical Bramwell-Hill model (BH-PWV). Our aim was to compare various methods of aortic PWV (aoPWV) estimation from 4D flow CMR, in terms of associations with age, Cf-PWV, BH-PWV and left ventricular (LV) mass-to-volume ratio while evaluating inter-observer reproducibility and robustness to temporal resolution. We studied 47 healthy subjects (49.5 ± 18 years) who underwent Cf-PWV and CMR including aortic 4D flow CMR as well as 2D cine SSFP for BH-PWV and LV mass-to-volume ratio estimation. The aorta was semi-automatically segmented from 4D flow data, and mean velocity waveforms were estimated in 25 planes perpendicular to the aortic centerline. 4D flow CMR aoPWV was calculated: using velocity curves at two locations, namely ascending aorta (AAo) and distal descending aorta (DAo) aorta (S1, 2D-like strategy), or using all velocity curves along the entire aortic centreline (3D-like strategies) with iterative transit time (TT) estimates (S2) or a plane fitting of velocity curves systolic upslope (S3). For S1 and S2, TT was calculated using three approaches: cross-correlation (TTc), wavelets (TTw) and Fourier transforms (TTf). Intra-class correlation coefficients (ICC) and Bland-Altman biases (BA) were used to evaluate inter-observer reproducibility and effect of lower temporal resolution. 4D flow CMR aoPWV estimates were significantly (p < 0.05) correlated to the CMR-independent Cf-PWV, BH-PWV, age and LV mass-to-volume ratio, with the strongest correlations for the 3D-like strategy using wavelets TT (S2-TTw) (R = 0.62, 0.65, 0.77 and 0.52, respectively, all p < 0.001). S2-TTw was also highly reproducible (ICC = 0.99, BA = 0.09 m/s) and robust to lower temporal resolution (ICC = 0.97, BA = 0.15 m/s). Reproducible 4D flow CMR aoPWV estimates can be obtained using full 3D aortic coverage. Such 4D flow CMR stiffness measures were significantly associated with Cf-PWV, BH-PWV, age and LV mass-to-volume ratio, with a slight superiority of the 3D strategy using wavelets transit time (S2-TTw).