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Subjects with amputation of the lower limbs are at increased risk of cardiovascular mortality and morbidity. We hypothesize that amputation-induced alterations in the arterial tree negatively impact arterial biomechanics, blood pressure and flow behavior. These changes may interact with other biological factors, potentially increasing cardiovascular risk. To evaluate this hypothesis regarding the purely mechanical impact of amputation on the arterial tree, we used a simulation computer model including a detailed one-dimensional (1D) arterial network model (143 arterial segments) coupled with a zero-dimensional (0D) model of the left ventricle. Our simulations included five settings of the arterial network: (1) 4-limbs control, (2) unilateral amputee (right lower limb), (3) bilateral amputee (both lower limbs), (4) trilateral amputee (lower-limbs and right upper-limb), and (5) quadrilateral amputee (lower and upper limbs). Analysis of regional stiffness, as calculated by pulse wave velocity (PWV) for large-, medium- and small-sized arteries, showed that, while aortic stiffness did not change with increasing degree of amputation, stiffness of medium and smaller-sized arteries increased with greater amputation severity. Despite a staged decrease in cardiac output, the systolic and diastolic blood pressure values increased, resulting in an increase in both central and peripheral pulse pressures but with an attenuation of pulse pressure amplification. The most significant increase in peak systolic pressure and decrease in peak systolic blood flow was observed at the site of the abdominal aorta. Wave separation analysis indicated no changes in the shape of the forward and backward wave components. However, the results from wave intensity analysis showed that with extended amputation, there was an increase in peak forward wave intensity and a rise in the inverse peak of the backward wave intensity, suggesting potential alterations in cardiac hemodynamic load. In conclusion, this simulation study showed that biomechanical and hemodynamic changes in the arterial network geometry could interact with additional risk factors to increase the cardiovascular risk in patients with amputations.

During aging, systolic blood pressure continuously increases over time, whereas diastolic pressure first increases and then slightly decreases after middle age. These pressure changes are usually explained by changes of the arterial system alone (increase in arterial stiffness and vascular resistance). However, we hypothesise that the heart contributes to the age-related blood pressure progression as well. In the present study we quantified the blood pressure changes in normal aging by using a Windkessel model for the arterial system and the time-varying elastance model for the heart, and compared the simulation results with data from the Framingham Heart Study. Parameters representing arterial changes (resistance and stiffness) during aging were based on literature values, whereas parameters representing cardiac changes were computed through physiological rules (compensated hypertrophy and preservation of end-diastolic volume). When taking into account arterial changes only, the systolic and diastolic pressure did not agree well with the population data. Between 20 and 80 years, systolic pressure increased from 100 to 122 mmHg, and diastolic pressure decreased from 76 to 55 mmHg. When taking cardiac adaptations into account as well, systolic and diastolic pressure increased from 100 to 151 mmHg and decreased from 76 to 69 mmHg, respectively. Our results show that not only the arterial system, but also the heart, contributes to the changes in blood pressure during aging. The changes in arterial properties initiate a systolic pressure increase, which in turn initiates a cardiac remodelling process that further augments systolic pressure and mitigates the decrease in diastolic pressure.

[This corrects the article DOI: 10.1371/journal.pone.0221425.].

Decrease in arterial compliance leads to an increased pulse pressure, as explained by the Windkessel effect. Pressure waveform is the sum of a forward running and a backward running or reflected pressure wave. When the arterial system stiffens, as a result of aging or disease, both the forward and reflected waves are altered and contribute to a greater or lesser degree to the increase in aortic pulse pressure. Two mechanisms have been proposed in the literature to explain systolic hypertension upon arterial stiffening. The most popular one is based on the augmentation and earlier arrival of reflected waves. The second mechanism is based on the augmentation of the forward wave, as a result of an increase of the characteristic impedance of the proximal aorta. The aim of this study is to analyze the two aforementioned mechanisms using a 1-D model of the entire systemic arterial tree. A validated 1-D model of the systemic circulation, representative of a young healthy adult was used to simulate arterial pressure and flow under control conditions and in presence of arterial stiffening. To help elucidate the differences in the two mechanisms contributing to systolic hypertension, the arterial tree was stiffened either locally with compliance being reduced only in the region of the aortic arch, or globally, with a uniform decrease in compliance in all arterial segments. The pulse pressure increased by 58% when proximal aorta was stiffened and the compliance decreased by 43%. Same pulse pressure increase was achieved when compliance of the globally stiffened arterial tree decreased by 47%. In presence of local stiffening in the aortic arch, characteristic impedance increased to 0.10 mmHg s/mL vs. 0.034 mmHg s/mL in control and this led to a substantial increase (91%) in the amplitude of the forward wave, which attained 42 mmHg vs. 22 mmHg in control. Under global stiffening, the pulse pressure of the forward wave increased by 41% and the amplitude of the reflected wave by 83%. Reflected waves arrived earlier in systole, enhancing their contribution to systolic pressure. The effects of local vs. global loss of compliance of the arterial tree have been studied with the use of a 1-D model. Local stiffening in the proximal aorta increases systolic pressure mainly through the augmentation of the forward pressure wave, whereas global stiffening augments systolic pressure principally though the increase in wave reflections. The relative contribution of the two mechanisms depends on the topology of arterial stiffening and geometrical alterations taking place in aging or in disease.

Arterial rupture in horses has been observed during exercise, after phenylephrine administration or during parturition (uterine artery). In human pathophysiological research, the use of computer models for studying arterial hemodynamics and understanding normal and abnormal characteristics of arterial pressure and flow waveforms is very common. The objective of this research was to develop a computer model of the equine arterial circulation, in order to study local intra-arterial pressures and flow dynamics in horses. Morphologically, large differences exist between human and equine aortic arch and arterial branching patterns. Development of the present model was based on post-mortem obtained anatomical data of the arterial tree (arterial lengths, diameters and branching angles); in vivo collected ultrasonographic flow profiles from the common carotid artery, external iliac artery, median artery and aorta; and invasively collected pressure curves from carotid artery and aorta. These data were used as input for a previously validated (in humans) 1D arterial network model. Data on terminal resistance and arterial compliance parameters were tuned to equine physiology. Given the large arterial diameters, Womersley theory was used to compute friction coefficients, and the input into the arterial system was provided via a scaled time-varying elastance model of the left heart. Outcomes showed plausible predictions of pressure and flow waveforms throughout the considered arterial tree. Simulated flow waveform morphology was in line with measured flow profiles. Consideration of gravity further improved model based predicted waveforms. Derived flow waveform patterns could be explained using wave power analysis. The model offers possibilities as a research tool to predict changes in flow profiles and local pressures as a result of strenuous exercise or altered arterial wall properties related to age, breed or gender.

Identification of a Strain Energy Function (SEF) is used when describing the complex mechanical properties of soft biological tissues such as the arterial wall. Classic SEFs, such as the one proposed by Chuong and Fung (J. Biomech. Eng. 105(3) (1983) 268), have been mostly phenomenological and neglect the particularities of the wall structure. A more structural model was proposed by Holzapfel et al. (J. Elasticity 61 (2000) 1–48.) when they included the characteristic angle at which the collagen fibers are helically wrapped, resulting in an excellent SEF for applications such as finite element modeling. We have expanded upon the idea of structural SEFs by including not only the wavy nature of the collagen but also the fraction of both elastin and collagen contained in the media, which can be determined by histology. The waviness of the collagen is assumed to be distributed log-logistically. In order to evaluate this novel SEF, we have used it to fit experimental data from inflation–extension tests performed on rat carotids. We have compared the results of the fit to the SEFs of Choung and Fung and Holzapfel et al. The novel SEF is found to behave similarly to that of Holzapfel et al., both succeed in describing the typical S-shaped pressure-radius curves with comparable quality of fit. The parameters of the novel SEF obtained from the fitting, bearing the physical meaning of the elastic modulus of collagen, the elastic modulus of elastin, the collagen waviness, and the collagen fiber angle, were compared to experimental data and discussed.

Animal models of aortic aneurysm and dissection can enhance our limited understanding of the etiology of these lethal conditions particularly because early-stage longitudinal data are scant in humans. Yet, the pathogenesis of often-studied mouse models and the potential contribution of aortic biomechanics therein remain elusive. In this work, we combined micro-CT and synchrotron-based imaging with computational biomechanics to estimate in vivo aortic strains in the abdominal aorta of angiotensin-II-infused ApoE-deficient mice, which were compared with mouse-specific aortic microstructural damage inferred from histopathology. Targeted histology showed that the 3D distribution of micro-CT contrast agent that had been injected in vivo co-localized with precursor vascular damage in the aortic wall at 3 days of hypertension, with damage predominantly near the ostia of the celiac and superior mesenteric arteries. Computations similarly revealed higher mechanical strain in branching relative to non-branching regions, thus resulting in a positive correlation between high strain and vascular damage in branching segments that included the celiac, superior mesenteric, and right renal arteries. These results suggest a mechanically driven initiation of damage at these locations, which was supported by 3D synchrotron imaging of load-induced ex vivo delaminations of angiotensin-II-infused suprarenal abdominal aortas. That is, the major intramural delamination plane in the ex vivo tested aortas was also near side branches and specifically around the celiac artery. Our findings thus support the hypothesis of an early mechanically mediated formation of microstructural defects at aortic branching sites that subsequently propagate into a macroscopic medial tear, giving rise to aortic dissection in angiotensin-II-infused mice.

Background Several so-called loop-based methods, have been proposed to estimate local pulse wave velocity (PWV). However, previous studies have demonstrated inaccuracies in local PWV-estimates due to presence of reflections, which led to the proposition of a frequency-domain correction method [ 1 ]. The aim of this study is to assess the accuracy of PWV-estimates from different loop methods throughout the human arterial tree. Methods The output data of a validated one-dimensional (1D) model of the human systemic circulation [ 2 ] was used to simulate the physiological signals needed on the estimations of local PWV methods, and this for model settings representing a young and an aged individual (stiffness increased by factor 2). Local PWV by the PU-loop, ln(D)U-loop, ln(D)P-loop, QA-loop and the frequency-domain (PWV1-5) methods, were compared against the reference value obtained from the Bramwell-Hill equation. Results Figure 1 shows the deviation (%) of loop-based estimates of PWV and PWV1-5 from the reference. The PU-loop overestimates PWV by more than 20% for most arterial sites, while the ln(D)U- and QA-loop underestimate to the same extent at these same locations. The correction method performs acceptably well in most of the young configuration. Discrepancies increase significantly in the aged model configuration for every studied method (except the ln(D)P-loop method). Conclusion The accuracy of loop-based methods is highly dependent on the location where they are applied, and results should be interpreted with great caution. Best results were obtained for the reflection- insensitive ln(D)P-loop method, but this method does not really provide an alternative for the Bramwell-Hill equation. Figure 1 Deviation of the loop-based estimates of PWV (PU-, ln(D)U-, ln(D)P- and QA-loops) and the correction method (PWV 1–5 ) from the reference (Bramwell-Hill), for every location of the arterial tree in the young and aged configurations. Red and blue colors indicate over- and underestimation, respectively.

Growth and rupture, the two events that dominate the evolution of an intracranial aneurysm, are both dependent on intraaneurysmal flow. Decrease of intraaneurysmal flow is considered an attractive alternative for treating intracranial aneurysms by minimally invasive techniques. Such modification can be achieved by inserting stents or flow diverters alone. In the present paper, the effect of different commercial and innovative flow diverters’ porosity was studied in intracranial aneurysm models. Single and stent-in-stent combination of Neuroform II as well as single and stent-in-stent combination of a new innovative, low-porosity, intracranial stent device (D1, D2, D1 + D2) were inserted in models of intracranial aneurysms under shear-driven flow and inertia-driven flow configurations. Steady and pulsating flow rates were applied using a blood-like fluid. Particle image velocimetry was used to measure velocity vector fields in the aneurysm midplane along the vessel axis. Flow and vorticity patterns, velocity and vorticity magnitudes were quantified and their value compared with the same flows in absence of the flow diverter. In absence of flow diverters, a solid-like rotation could be observed in both shear-driven and inertia-driven models under steady and pulsatile flow conditions. The flow effects due to the insertion of low-porous devices such as D1 or D2 provoked a complete alteration of the flow patterns and massive reduction of velocity or vorticity magnitudes, whereas the introduction of clinically adopted high-porous devices provoked less effect in the aneurysm cavity. As expected, results showed that the lower the porosity the larger the reduction in velocity and vorticity within the aneurysm cavity. The lowest-porosity device combination (D1 and D2) reached an averaged reduction of flow parameters of 80% and 88% under steady and pulsatile flow conditions, respectively. The reduction in mean velocity and vorticity was much more significant in the shear-driven flows as compared to the inertia-driven flows. Although device porosity is the main parameter influencing flow reduction, other parameters such as device design and local flow conditions may influence the level of flow reduction within intracranial aneurysms. Die zwei wichtigsten Faktoren für die Entwicklung intrazerebraler Aneurysmen, nämlich Wachstum und Ruptur, hängen vom intraaneurysmatischen Blutfluss ab. Eine Verminderung des intraaneurysmatischen Blutflusses durch minimalinvasive Techniken wird als attraktive Behandlungsmethode erachtet. Eine solche Modifikation des Blutflusses kann durch das Einbringen eines Stents oder „flow diverter“ allein erzielt werden. In der vorliegenden Arbeit untersuchten die Autoren den Effekt der Porosität verschiedener handelsüblicher und innovativer „flow diverters“ an Modellen intrakranieller Aneurysmen. Sowohl einzelne oder Stent-in-Stent-Kombinationen des Neuroform II (NF) als auch einzelne oder Stent-in-Stent-Kombinationen von neuen innovativen, niedrigporösen intrakraniellen Stents (D1, D2, D1 + D2) wurden in Modellen intrakranieller Aneurysmen mit Eigenschaften von „shear-driven“ und „inertia-driven“ Fluss platziert. Flächen mit Geschwindigkeitsvektoren in der mittleren Ebene des Aneurysmas parallel zur Achse des Gefäßes wurden mit Hilfe der „particle image velocimetry“ (PIV) ermittelt. Eigenschaften von Fluss und Verwirbelungen, Geschwindigkeit und Ausmaß von Verwirbelungen wurden gemessen und mit Messwerten des gleichen Modells ohne „flow diverter“ verglichen. Ohne „flow diverter“ konnte eine beständige Rotation in beiden – „shear-driven“ und „inertia-driven“ – Flussmodellen beobachtet werden. Die Auswirkungen nach Platzierung eines niedrigporösen Modells wie D1 oder D2 riefen eine komplette Änderung der Flusseigenschaften und eine massive Verringerung der Geschwindigkeit und des Ausmaßes von Verwirbelungen hervor, wohingegen die Platzierung klinisch angewendeter hochporöser Modelle geringere Auswirkungen auf die Kavität des Aneurysmas hatte. Erwartungsgemäß haben die Ergebnisse gezeigt: Je kleiner die Porosität ist, desto größer sind die Auswirkungen auf Blutflussgeschwindigkeit und Verwirbelungen im Aneurysma. Die Kombination mit der geringsten Porosität (D1 und D2) erzielte eine durchschnittliche Reduktion der Flussparameter um 80% bzw. 88% bei konstanten und pulsatilen Flüssen. Die Verminderung von mittlerer Geschwindigkeit und von Verwirbelungen war beim „shear-driven“ Fluss deutlich signifikanter als beim „inertia-driven“ Fluss. Obwohl die Porosität der wichtigste Parameter zur Senkung des Flusses ist, können andere Parameter wie das Design des jeweiligen Modells oder lokale Flusseigenschaften die Wirksamkeit der Flussreduktion in intrakraniellen Aneurysmen beeinflussen.