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.

Arterial blood pressure (ABP) is an important vital sign from which it can be extracted valuable information about the subject’s health. After studying its morphology it is possible to diagnose cardiovascular diseases such as hypertension, so ABP routine control is recommended. The most common method of controlling ABP is the cuff-based method, from which it is obtained only the systolic and diastolic blood pressure (SBP and DBP, respectively). This paper proposes a cuff-free method to estimate the morphology of the average ABP pulse ($\overline{ABPM}$) through a deep learning model based on a seq2seq architecture with attention mechanism. It only needs raw photoplethysmogram signals (PPG) from the finger and includes the capacity to integrate both categorical and continuous demographic information (DI). The experiments were performed on more than 1100 subjects from the MIMIC database for which their corresponding age and gender were consulted. Without allowing the use of data from the same subjects to train and test, the mean absolute errors (MAE) were 6.57 ± 0.20 and 14.39 ± 0.42 mmHg for DBP and SBP, respectively. For $\overline{ABPM}$, R correlation coefficient and the MAE were 0.98 ± 0.001 and 8.89 ± 0.10 mmHg. In summary, this methodology is capable of transforming PPG into an ABP pulse, which obtains better results when DI of the subjects is used, potentially useful in times when wireless devices are becoming more popular.

In this paper, we analyze how elastic and viscoelastic properties differ across seven locations along the large arteries in 11 sheep. We employ a two-parameter elastic model and a four-parameter Kelvin viscoelastic model to analyze experimental measurements of vessel diameter and blood pressure obtained in vitro at conditions mimicking in vivo dynamics. Elastic and viscoelastic wall properties were assessed via solutions to the associated inverse problem. We use sensitivity analysis to rank the model parameters from the most to the least sensitive, as well as to compute standard errors and confidence intervals. Results reveal that elastic properties in both models (including Young's modulus and the viscoelastic relaxation parameters) vary across locations (smaller arteries are stiffer than larger arteries). We also show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics.

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.