Distribution of wall shear rate throughout the arterial tree: a case study

Mechanosensory entities and functionality of endothelial cells

The endothelial cells of the blood circulation are exposed to hemodynamic forces, such as cyclic strain, hydrostatic forces, and shear stress caused by the blood fluid's frictional force. Endothelial cells perceive mechanical forces via mechanosensors and thus elicit physiological reactions such as alterations in vessel width. The mechanosensors considered comprise ion channels, structures linked to the plasma membrane, cytoskeletal spectrin scaffold, mechanoreceptors, and junctional proteins. This review focuses on endothelial mechanosensors and how they alter the vascular functions of endothelial cells. The current state of knowledge on the dysregulation of endothelial mechanosensitivity in disease is briefly presented. The interplay in mechanical perception between endothelial cells and vascular smooth muscle cells is briefly outlined. Finally, future research avenues are highlighted, which are necessary to overcome existing limitations.

Force balance ratio is a robust predictor of arterial thrombus stability

Thrombus formation on a damaged vessel wall can lead to the formation of a stable occlusive/subocclusive clot or unstable embolizing thrombus. Both outcomes can cause significant health damage. The mechanisms that regulate maximum thrombus size, its stability, and embolization in both micro- and macrocirculation are poorly understood. To investigate the impact of flow and intrathrombus forces on the stability of homogeneous and heterogeneous platelet thrombi in a wide range of thrombus geometries, critical interplatelet forces, vessel diameters, and hydrodynamic conditions, we took advantage of the recently developed in silico models. To perform analysis of thrombus stability/embolization in arterioles, we used our previously developed particle-based 2D model with a single-platelet resolution. Its results and predictions were further extended to a 3D case and the large spatial scales of arteries using novel particle-based and continuum 3D models. We found a robust quantitative parameter, termed force balance ratio, which quantifies the balance between destabilizing hydrodynamic and stabilizing interplatelet forces. This parameter predicts whether a homogeneous thrombus (or the shell of a heterogeneous thrombus) with a particular value of critical interplatelet forces will embolize under given hydrodynamic conditions. Our simulations also predict that, for a given magnitude of critical interplatelet forces, the longer thrombi are more stable than the shorter ones. Furthermore, the aggregates formed on top of the severe stenosis are more stable than thrombi formed at moderate stenosis. Taken together, our results give new insights into the interplay between critical interplatelet forces, local hydrodynamics, and overall thrombus stability against the flow.

Imperatives of Mathematical Model of Arterial Blood Dynamics for Interpretation of Doppler Velocimetry: A Narrative Review

Clinicians frequently study arterial Doppler velocimetric waveforms depicted by Doppler sonography of the kidneys, the heart, the brain, and the feto-maternal circulation to assess the well-being of the aforementioned vital organs. The waveform interpretation of the Doppler indices can be studied using a mathematical model. The developed models serve as teaching tools and for easy comprehension of the regulatory mechanism of the organs. It will also obtain accurate wall shear stress (WSS) and likely atherosclerotic sites can be predicted early. The aim of this review is to reveal the imperatives of mathematical models in the study of the physical interpretation of Doppler velocimetry. The models will explore sonographic Doppler velocimetry and computational fluid dynamics (CFD) in determining the segments of the arteries that are prone to the development of atheromatous plaque. It will be achieved by comparing and computing the measurement differences of the WSS. A thorough literature review was carried out between 1971 and 2021 on the mathematical modeling of blood dynamics and Doppler velocimetry of different blood vessels, across various electronic databases including NC AHEC Digital Library, PUBMED, ERIC, MEDLINE, Free Medical Journals, and EMBASE. The results of the literature search were presented using the PRISMA flow chat. The narrative review of the mathematical models of arterial blood dynamics is based on incompressible Navier-Stokes equations, the Windkessel model, and CFD. It was deduced that the blood flow velocity decreased with time across the varying frequency from 0.2Hz to 0.50Hz in the interlobar arterial channels. The review also revealed that adult humans' Doppler indices of the renal-interlobar artery agree with developed models of renal interlobar arterial blood dynamics. The mathematical model measurements of the great vessels matched the sonographic Doppler velocimetry with <15% variation. In our fast-paced world of epidemiological transition, the imperatives of mathematical modeling of arterial flow dynamics based on the Navier-Stokes equations to represent various physiologic and pathologic situations cannot be overstated. The practical consequences include the possibility of mathematical models to acquire precise WSS distribution and early detection of potential atherosclerotic sites during cardiovascular Doppler sonography.

Vascular regulation of disseminated tumor cells during metastatic spread

Cancer cells can travel to other organs via interconnected vascular systems to form new lesions in a process known as metastatic spread. Unfortunately, metastasis remains the leading cause of patient lethality. In recent years, it has been demonstrated that physical cues are just as important as chemical and genetic perturbations in driving changes in gene expression, cell motility, and survival. In this concise review, we focus on the physical cues that cancer cells experience as they migrate through the lymphatic and blood vascular networks. We also present an overview of steps that may facilitate organ specific metastasis.

Evaluation and manipulation of tissue and cellular distribution of cardiac progenitor cell-derived extracellular vesicles

Cardiac progenitor cell-derived extracellular vesicles (CPC-EVs) have been successfully applied via different delivery routes for treating post-myocardial infarction injury in several preclinical models. Hence, understanding the in vivo fate of CPC-EVs after systemic or local, i.e. myocardial, delivery is of utmost importance for the further therapeutic application of CPC-EVs in cardiac repair. Here, we studied the tissue- and cell distribution and retention of CPC-EVs after intramyocardial and intravenous injection in mice by employing different EV labeling and imaging techniques. In contrast to progenitor cells, CPC-EVs demonstrated no immediate flush-out from the heart upon intramyocardial injection and displayed limited distribution to other organs over time, as determined by near-infrared imaging in living animals. By employing CUBIC tissue clearing and light-sheet fluorescent microscopy, we observed CPC-EV migration in the interstitial space of the myocardium shortly after EV injection. Moreover, we demonstrated co-localization with cTnI and CD31-positive cells, suggesting their interaction with various cell types present in the heart. On the contrary, after intravenous injection, most EVs accumulated in the liver. To potentiate such a potential systemic cardiac delivery route, targeting the cardiac endothelium could provide openings for directed CPC-EV therapy. We therefore evaluated whether decorating EVs with targeting peptides (TPs) RGD-4C or CRPPR connected to Lamp2b could enhance EV delivery to endothelial cells. Expression of both TPs enhanced CPC-EV uptake under in vitro continuous flow, but did not affect uptake under static cell culture conditions. Together, these data demonstrate that the route of administration influences CPC-EV biodistribution pattern and suggest that specific TPs could be used to target CPC-EVs to the cardiac endothelium. These insights might lead to a better application of CPC-EV therapeutics in the heart.

Investigation on the differences of hemodynamics in normal common carotid, subclavian, and common femoral arteries using the vector flow technique

OBJECTIVES

To investigate the feasibility of the vector flow imaging (V Flow) technique to measure peripheral arterial hemodynamic parameters, including wall shear stress (WSS) and turbulence index (Tur) in healthy adults, and compare the results in different arteries.

MATERIALS AND METHODS

Fifty-two healthy adult volunteers were recruited in this study. The maximum and mean values of WSS, and the Tur values at early-systole, mid-systole, late-systole, and early diastole for total 156 normal peripheral arteries [common carotid arteries (CCA), subclavian arteries (SCA), and common femoral arteries (CFA)] were assessed using the V Flow technique.

RESULTS

The mean WSS values for CCA, SCA, and CFA were (1.66 ± 0.68) Pa, (0.62 ± 0.30) Pa, and (0.56 ± 0.27) Pa, respectively. The mean Tur values for CCA, SCA, and CFA were (0.46 ± 1.09%), (20.7 ± 9.06%), and (24.63 ± 17.66%), respectively. The CCA and SCA, as well as the CCA and CFA, showed statistically significant differences in the mean WSS and the mean Tur (P < 0.01). The mean Tur values had a negative correlation with the mean WSS; the correlation coefficient between log(Tur) and WSS is -0.69 (P < 0.05).

CONCLUSION

V Flow technique is a simple, practical, and feasible quantitative imaging approach for assessing WSS and Tur in peripheral arteries. It has the potential to be a useful tool for evaluating atherosclerotic plaques in peripheral arteries. The results provide a new quantitative foundation for future investigations into diverse arterial hemodynamic parameters.

Endothelial Glycocalyx

The glycocalyx is a polysaccharide structure that protrudes from the body of a cell. It is primarily conformed of glycoproteins and proteoglycans, which provide communication, electrostatic charge, ionic buffering, permeability, and mechanosensation-mechanotransduction capabilities to cells. In blood vessels, the endothelial glycocalyx that projects into the vascular lumen separates the vascular wall from the circulating blood. Such a physical location allows a number of its components, including sialic acid, glypican-1, heparan sulfate, and hyaluronan, to participate in the mechanosensation-mechanotransduction of blood flow-dependent shear stress, which results in the synthesis of nitric oxide and flow-mediated vasodilation. The endothelial glycocalyx also participates in the regulation of vascular permeability and the modulation of inflammatory responses, including the processes of leukocyte rolling and extravasation. Its structural architecture and negative charge work to prevent macromolecules greater than approximately 70 kDa and cationic molecules from binding and flowing out of the vasculature. This also prevents the extravasation of pathogens such as bacteria and virus, as well as that of tumor cells. Due to its constant exposure to shear and circulating enzymes such as neuraminidase, heparanase, hyaluronidase, and matrix metalloproteinases, the endothelial glycocalyx is in a continuous process of degradation and renovation. A balance favoring degradation is associated with a variety of pathologies including atherosclerosis, hypertension, vascular aging, metastatic cancer, and diabetic vasculopathies. Consequently, ongoing research efforts are focused on deciphering the mechanisms that promote glycocalyx degradation or limit its syntheses, as well as on therapeutic approaches to improve glycocalyx integrity with the goal of reducing vascular disease. © 2022 American Physiological Society. Compr Physiol 12: 1-31, 2022.

A Multiscale Approach for Predicting Certain Effects of Hand-Transmitted Vibration on Finger Arteries

Prolonged exposure to strong hand-arm vibrations can lead to vascular disorders such as Vibration White Finger (VWF). We modeled the onset of this peripheral vascular disease in two steps. The first consists in assessing the reduction in shearing forces exerted by the blood on the walls of the arteries (Wall Shear Stress—WSS) during exposure to vibrations. An acute but repeated reduction in WSS can lead to arterial stenosis characteristic of VWF. The second step is devoted to using a numerical mechano-biological model to predict this stenosis as a function of WSS. WSS is reduced by a factor of 3 during exposure to vibration of 40 m·s−2. This reduction is independent of the frequency of excitation between 31 Hz and 400 Hz. WSS decreases logarithmically when the amplitude of the vibration increases. The mechano-biological model simulated arterial stenosis of 30% for an employee exposed for 4 h a day for 10 years. This model also highlighted the chronic accumulation of matrix metalloproteinase 2. By considering daily exposure and the vibratory level, we can calculate the degree of stenosis, thus that of the disease for chronic exposure to vibrations.

Assessing mechanical vibration-altered wall shear stress in digital arteries

The aim of this study is to implement and validate a method for assessing acute vibration-altered Wall Shear Stress (WSS) in the proper volar digital artery of the non-exposed left forefinger when subjecting the right hand to mechanical vibration. These changes of WSS may be involved in Vibration White Finger. Hence, an experimental device was set-up to link a vibration shaker and an ultra-high frequency ultrasound scanner. The Womersley-based WSS was computed by picking up the maximum velocity from pulse Wave Doppler measurements and extracting the artery diameter from B-mode images through an in-house image processing technique. The parameters of the former method were optimised on numerical ultrasound phantoms of cylindrical and lifelike arteries. These phantoms were computed with the FIELD II and FOCUS platforms which mimicked our true ultrasound device. The Womersley-based WSS were compared to full Fluid Structure Interaction (FSI) and rigid wall models built from resonance magnetic images of a volunteer-specific forefinger artery. Our FSI model took into account the artery's surrounding tissues. The diameter computing procedure led to a bias of 4%. The Womersley-based WSS resulted in misestimating the FSI model by roughly 10% to 20%. No difference was found between the rigid wall computational model and FSI simulations. Regarding the WSS measured on a group of 20 volunteers, the group-averaged basal value was 3 Pa, while the vibration-altered WSS was reduced to 1 Pa, possibly triggering intimal hyperplasia mechanisms and leading to the arterial stenoses encountered in patients suffering from vibration-induced Raynaud's syndrome.

Measuring wall shear stress distribution in the carotid artery in an African population: Computational fluid dynamics versus ultrasound doppler velocimetry

INTRODUCTION

Computational fluid dynamics (CFD) and ultrasound Doppler velocimetry are diagnostic tools useful for determining carotid artery segments susceptible to atheromatous plaque development. This study computes and compares the difference in Wall Shear Stress (WSS) measurements between these two methods.

METHODS

The carotid artery of 204 volunteers selected using simple random sampling were scanned using standard carotid doppler protocols. Four segments of the carotid artery - the common, internal, external carotid, and the carotid bulb were sonographically assessed. The intima-media thickness, diameter, peak systolic velocity, and end-diastolic velocity were measured at a point 2 cm away from the carotid bifurcation for the three segments, while the carotid bulb was measured at the bifurcation. A 2D incompressible Navier-Stokes Equation for modelling Newtonian, pulsatile, and laminar flow in a viscoelastic pipe was applied to model velocity flow across the carotid artery using COMSOL software. WSS values were computed for experimental and CFD measurements and the results were compared.

RESULTS

The WSS values generated by the model had respectively peak and average values of 19.81 N/cm² and 15.76 ± 1.81 N/cm² for the common carotid, 10.77 N/cm² and 7.57 ± 1.66 N/cm² for the internal carotid, 11.51 N/cm² and 8.05 ± 1.65 N/cm² for the external carotid, 37.55 N/cm² and 26.55 ± 6.62 N/cm² for the carotid bifurcation, 1.39 N/cm² and 3.13 ± 1.34 N/cm² for the carotid bulb. The model measurements matched doppler velocimetry measurements with <15% variation.

CONCLUSION

Model based WSS values were higher but comparable with doppler velocimetry measurements. The carotid bulb had low WSS and is therefore the segment highly disposed to atheromatous plaque formation.

IMPLICATIONS FOR PRACTICE

Subject-specific mathematical models could be incorporated during cardiovascular scan work up for accurate WSS distribution and early prediction of possible atherosclerotic sites.

Endothelial Cell Targeting by cRGD-Functionalized Polymeric Nanoparticles under Static and Flow Conditions

Since α_vβ₃ integrin is a key component of angiogenesis in health and disease, Arg-Gly-Asp (RGD) peptide-functionalized nanocarriers have been investigated as vehicles for targeted delivery of drugs to the α_vβ₃ integrin-overexpressing neovasculature of tumors. In this work, PEGylated nanoparticles (NPs) based on poly(lactic-co-glycolic acid) (PLGA) functionalized with cyclic-RGD (cRGD), were evaluated as nanocarriers for the targeting of angiogenic endothelium. For this purpose, NPs (~300 nm) functionalized with cRGD with different surface densities were prepared by maleimide-thiol chemistry and their interactions with human umbilical vein endothelial cells (HUVECs) were evaluated under different conditions using flow cytometry and microscopy. The cell association of cRGD-NPs under static conditions was time-, concentration- and cRGD density-dependent. The interactions between HUVECs and cRGD-NPs dispersed in cell culture medium under flow conditions were also time- and cRGD density-dependent. When washed red blood cells (RBCs) were added to the medium, a 3 to 8-fold increase in NPs association to HUVECs was observed. Moreover, experiments conducted under flow in the presence of RBC at physiologic hematocrit and shear rate, are a step forward in the prediction of in vivo cell–particle association. This approach has the potential to assist development and high-throughput screening of new endothelium-targeted nanocarriers.

The relevance of shear, sedimentation and diffusion during spin freezing, as potential first step of a continuous freeze-drying process for unit doses

Recently, a continuous freeze-drying process for the production of unit doses was presented and evaluated. In this concept, the freezing step is modified compared to traditional batch freeze-drying, as glass vials filled with a liquid formulation, are rotated around their longitudinal axis while cooled and frozen with a cold, sterile and inert gas (i.e. spin freezing). Finally, a thin frozen product layer spread over the entire vial wall is achieved. The aim of this paper is twofold: firstly, the relation between the rotation velocity and the relative difference between top and bottom of the frozen product layer thickness was determined for different vial types. Secondly, the impact of shear and centrifugal forces generated during spinning was examined, to find out whether they might cause pharmaceutical instability and sedimentation, respectively. Mechanistic and experimental evaluation showed that shear has no effect on proteins. Calculations showed that the sedimentation and diffusion velocity is too low to cause inhomogeneity in the product layer. In addition, Global Sensitivity Analysis (GSA) and Uncertainty Analysis (UA) were performed in order to account for the uncertainty of the used mechanistic model.

Interaction between drug delivery vehicles and cells under the effect of shear stress

Over the last decades, researchers have developed an ever greater and more ingenious variety of drug delivery vehicles (DDVs). This has made it possible to encapsulate a wide selection of therapeutic agents, ranging from proteins, enzymes, and peptides to hydrophilic and hydrophobic small drugs while, at the same time, allowing for drug release to be triggered through a diverse range of physical and chemical cues. While these advances are impressive, the field has been lacking behind in translating these systems into the clinic, mainly due to low predictability of in vitro and rodent in vivo models. An important factor within the complex and dynamic human in vivo environment is the shear flow observed within our circulatory system and many other tissues. Within this review, recent advances to leverage microfluidic devices to better mimic these conditions through novel in vitro assays are summarized. By grouping the discussion in three prominent classes of DDVs (lipidic and polymeric particles as well as inorganic nanoparticles), we hope to guide researchers within drug delivery into this exciting field and advance a further implementation of these assay systems within the development of DDVs.

A novel non-invasive ultrasonic method to assess total axial stress of the common carotid artery wall in healthy and atherosclerotic men

In the present study, developing a new non-invasive method independent from blood flow, we estimated and compared the total axial stress of the common carotid artery wall in healthy and atherosclerotic subjects. Consecutive ultrasonic images of the common carotid artery of 48 male subjects including healthy, with less and more than 50% stenosis in carotid artery were recorded. Longitudinal displacement and acceleration was extracted from ultrasonic image processing using a block matching algorithm. Furthermore, images were examined using a maximum gradient algorithm and time rate changes of the internal diameter and intima-media thickness were extracted. Finally, axial stress was estimated using an appropriate constitutive equation. Statistical analysis results showed that with stenosis initiation and its progression, axial acceleration and stress increase significantly. According to the results of the present study, maximum axial stress of the arterial wall is 1.713±0.546, 1.993±0.731 and 2.610±0.603 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Whereas minimum axial stress is -1.714±0.676, -1.982±0.663 and -2.593±0.661 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Moreover, internal diameter and intima-media thickness of the artery also increase significantly with stenosis initiation and its progression. In this study, the feasibility of axial wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data is concluded. We found a strong and graded association between axial stress and severity of carotid stenosis, which might be used to discriminate healthy from atherosclerotic arteries.

Agitation of amyloid proteins to speed aggregation measured by ThT fluorescence: a call for standardization

This retrospective study of protein aggregation measured by Thioflavin T (ThT) fluorescence assay in published literature has assessed protein sensitivity to denaturing conditions that include elevated temperatures, fluctuations in pH, and concentration and, in particular, agitation to induce amyloid structure formation. The dynamic tracking of fluorescence shows a sigmoidal evolution as aggregates form; the resulting kinetics of association have been analyzed to explore the range of aggregation behavior which occurs based on environmental parameters. Comparisons between the experimental results of different groups have been historically difficult due to subtleties of experimental procedures including denaturing temperature, protein type and concentration, formulation differences, and how agitation is achieved. While it is clear that agitation has a strong influence on the driving force for aggregation, the use of magnetic stirring bar or shaker table rotational speed is insufficient to characterize the degree of turbulence produced during shear. The pathway forward in resolving dependence of aggregate formation on shear may require alternative methodologies or better standardization of the experimental protocols.

Considerations of blood properties, outlet boundary conditions and energy loss approaches in computational fluid dynamics modeling

Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies.

Radiative transport in large arteries

A refined model for the photon energy distribution in a living artery is established by solving the radiative transfer equation in a cylindrical geometry, using the Monte Carlo method. Combining this model with the most recent experimental values for the optical properties of flowing blood and the biomechanics of a blood-filled artery subject to a pulsatile pressure, we find that the optical intensity transmitted through large arteries decreases linearly with increasing arterial distension. This finding provides a solid theoretical foundation for measuring photoplethysmograms.

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Reduced heart rate and cardiac output differentially affect angiogenesis, growth, and development in early chicken embryos (Gallus domesticus)

An increase in both vascular circumferential tension and shear stress in the developing vasculature of the chicken embryo has been hypothesized to stimulate angiogenesis in the developing peripheral circulation chorioallantoic membrane (CAM). To test this hypothesis, angiogenesis in the CAM, development, and growth were measured in the early chicken embryo, following acute and chronic topical application of the purely bradycardic drug ZD7288. At hour 56, ZD7288 reduced heart rate (f(H)) by ~30% but had no significant effect on stroke volume (~0.19 ± 0.2 μL), collectively resulting in a significant fall in cardiac output (CO) from ~27 ± 3 to 18 ± 2 μL min(-1). Mean f(H) at 72 h of development was similarly significantly lowered by acute ZD7288 treatment (250 μM) to 128 ± 0.3 beats min(-1), compared with 174.5 ± 0.3 and 174.7 ± 0.8 beats min(-1) in control and Pannett-Compton (P-C) saline-treated embryos, respectively. Chronic dosing with ZD7288-and the attendant decreases in f(H) and CO-did not change eye diameter or cervical flexion (key indicators of development rate) at 120 h but significantly reduced overall growth (wet and dry body mass decreased by 20%). CAM vessel density index (reflecting angiogenesis) measured 200-400 μm from the umbilical stalk was not altered, but ZD7288 reduced vessel numbers-and therefore vessel density-by 13%-16% more distally (500-600 μm from umbilical stalk) in the CAM. In the ZD7288-treated embryos, a decrease in vessel length was found within the second branch order (~300-400 μm from the umbilical stock), while a decrease in vessel diameter was found closer to the umbilical stock, beginning in the first branch order (~200-300 μm). Paradoxically, chronic application of P-C saline also reduced peripheral CAM vessel density index at 500 and 600 μm by 13% and 7%, respectively, likely from washout of local angiogenic factors. In summary, decreased f(H) with reduced CO did not slow development rate but reduced embryonic growth rate and angiogenesis in the CAM periphery. This study demonstrates for the first time that different processes in the ontogeny of the early vertebrate embryo (i.e., hypertrophic growth vs. development) have differential sensitivities to altered convective blood flow.

In vivo vascular wall shear rate and circumferential strain of renal disease patients

This study measures the vascular wall shear rate at the vessel edge using decorrelation based ultrasound speckle tracking. Results for nine healthy and eight renal disease subjects are presented. Additionally, the vascular wall shear rate and circumferential strain during physiologic pressure, pressure equalization and hyperemia are compared for five healthy and three renal disease subjects. The mean and maximum wall shear rates were measured during the cardiac cycle at the top and bottom wall edges. The healthy subjects had significantly higher mean and maximum vascular wall shear rate than the renal disease subjects. The key findings of this research were that the mean vascular wall shear rates and circumferential strain changes between physiologic pressure and hyperemia that was significantly different between healthy and renal disease subjects.

Errors in the estimation of wall shear stress by maximum Doppler velocity

OBJECTIVE

Wall shear stress (WSS) is an important parameter with links to vascular (dys)function. Difficult to measure directly, WSS is often inferred from maximum spectral Doppler velocity (Vmax) by assuming fully-developed flow, which is valid only if the vessel is long and straight. Motivated by evidence that even slight/local curvatures in the nominally straight common carotid artery (CCA) prevent flow from fully developing, we investigated the effects of velocity profile skewing on Vmax-derived WSS.

METHODS

Velocity profiles, representing different degrees of skewing, were extracted from the CCA of image-based computational fluid dynamics (CFD) simulations carried out as part of the VALIDATE study. Maximum velocities were calculated from idealised sample volumes and used to estimate WSS via fully-developed (Poiseuille or Womersley) velocity profiles, for comparison with the actual (i.e. CFD-derived) WSS.

RESULTS

For cycle-averaged WSS, mild velocity profile skewing caused ±25% errors by assuming Poiseuille or Womersley profiles, while severe skewing caused a median error of 30% (maximum 55%). Peak systolic WSS was underestimated by ~50% irrespective of skewing with Poiseuille; using a Womersley profile removed this bias, but ±30% errors remained. Errors were greatest in late systole, when skewing was most pronounced. Skewing also introduced large circumferential WSS variations: ±60%, and up to ±100%, of the circumferentially averaged value.

CONCLUSION

Vmax-derived WSS may be prone to substantial variable errors related to velocity profile skewing, and cannot detect possibly large circumferential WSS variations. Caution should be exercised when making assumptions about velocity profile shape to calculate WSS, even in vessels usually considered long and straight.

Multifactorial determinants that govern nanoparticle uptake by human endothelial cells under flow

Vascular endothelium is a potential target for therapeutic intervention in diverse pathological processes, including inflammation, atherosclerosis, and thrombosis. By virtue of their intravascular topography, endothelial cells are exposed to dynamically changing mechanical forces that are generated by blood flow. In the present study, we investigated the interactions of negatively charged 2.7 nm and 4.7 nm CdTe quantum dots and 50 nm silica particles with cultured endothelial cells under regulated shear stress (SS) conditions. Cultured cells within the engineered microfluidic channels were exposed to nanoparticles under static condition or under low, medium, and high SS rates (0.05, 0.1, and 0.5 Pa, respectively). Vascular inflammation and associated endothelial damage were simulated by treatment with tumor necrosis factor-α (TNF-α) or by compromising the cell membrane with the use of low Triton X-100 concentration. Our results demonstrate that SS is critical for nanoparticle uptake by endothelial cells. Maximal uptake was registered at the SS rate of 0.05 Pa. By contrast, endothelial exposure to mild detergents or TNF-α treatment had no significant effect on nanoparticle uptake. Atomic force microscopy demonstrated the increased formation of actin-based cytoskeletal structures, including stress fibers and membrane ruffles, which have been associated with nanoparticle endocytosis. In conclusion, the combinatorial effects of SS rates, vascular endothelial conditions, and nanoparticle physical and chemical properties must be taken into account for the successful design of nanoparticle-drug conjugates intended for parenteral delivery.

Plaque characteristics and arterial remodeling in coronary and peripheral arterial systems

BACKGROUND

Few studies have examined plaque characteristics among multiple arterial beds in vivo. The purpose of this study was to compare the plaque morphology and arterial remodeling between coronary and peripheral arteries using gray-scale and radiofrequency intravascular ultrasound (IVUS) at clinical presentation.

METHODS AND RESULTS

IVUS imaging was performed in 68 patients with coronary and 93 with peripheral artery lesions (29 carotid, 50 renal, and 14 iliac arteries). Plaques were classified as fibroatheroma (VH-FA) (further subclassified as thin-capped [VH-TCFA] and thick-capped [VH-ThCFA]), fibrocalcific plaque (VH-FC) and pathological intimal thickening (VH-PIT). Plaque rupture (13% of coronary, 7% of carotid, 6% of renal, and 7% of iliac arteries; P = NS) and VH-TCFA (37% of coronary, 24% of carotid, 16% of renal, and 7% of iliac arteries; P = 0.02) were observed in all arteries. Compared with coronary arteries, VH-FA was less frequently observed in renal (P < 0.001) and iliac arteries (P < 0.006). Lesions with positive remodeling demonstrated more characteristics of VH-FA in coronary (84% vs. 25%, P < 0.001), carotid (72% vs. 20%, P = 0.001), and renal arteries (42% vs. 4%, P = 0.001) compared with those with intermediate/negative remodeling. There was positive relationship between remodeling index and percent necrotic area in all four arteries.

CONCLUSIONS

Atherosclerotic plaque phenotypes were heterogeneous among four different arteries; renal and iliac arteries had more stable phenotypes compared with coronary artery. In contrast, the associations of remodeling pattern with plaque phenotype and composition were similar among the various arterial beds.

Global sensitivity analysis of a wave propagation model for arm arteries

Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.

Shear flow induced changes in apolipoprotein C-II conformation and amyloid fibril formation

The misfolding and self-assembly of proteins into amyloid fibrils that occur in several debilitating diseases are affected by a variety of environmental factors, including mechanical factors associated with shear flow. We examined the effects of shear flow on amyloid fibril formation by human apolipoprotein C-II (apoC-II). Shear fields (150, 300, and 500 s(-1)) accelerated the rate of apoC-II fibril formation (1 mg/mL) approximately 5-10-fold. Fibrils produced at shear rates of 150 and 300 s(-1) were similar to the twisted ribbon fibrils formed in the absence of shear, while at 500 s(-1), tangled ropelike structures were observed. The mechanism of the shear-induced acceleration of amyloid fibril formation was investigated at low apoC-II concentrations (50 μg/mL) where fibril formation does not occur. Circular dichroism and tryptophan fluorescence indicated that shear induced an irreversible change in apoC-II secondary structure. Fluorescence resonance energy transfer experiments using the single tryptophan residue in apoC-II as the donor and covalently attached acceptors showed that shear flow increased the distance between the donor and acceptor molecules. Shear-induced higher-order oligomeric species were identified by sedimentation velocity experiments using fluorescence detection, while fibril seeding experiments showed that species formed during shear flow are on the fibril formation pathway. These studies suggest that physiological shear flow conditions and conditions experienced during protein manufacturing can exert significant effects on protein conformation, leading to protein misfolding, aggregation, and amyloid fibril formation.

Detecting the early onset of shear-induced fibril formation of insulin in situ

A new approach is presented for detecting the early onset of amyloid fibril formation of insulin in a fluidic environment. The fibrillogenesis of insulin in a well-characterized Taylor-Couette flow cell was analyzed in situ using Raman spectroscopy in combination with principal components analysis (PCA). Raman spectra recorded using a 532.5 nm excitation laser revealed a more rapid fibrillogenesis process during the first 90 min of shearing than previously reported for samples exposed to flow. Bands corresponding to intermolecular H-bonded β-sheet structure of insulin at 1678, 1630, and 1625 cm(-1) observed in the Raman difference spectra between unsheared insulin and sheared insulin show an increase in intensity as a function of shear exposure time, which is characteristic of fibril formation, with the first changes detected after 10 min. Additional analysis of samples removed from the flow cell after specific time periods provided conformation of the flow-enhanced fibrillogenesis process, including the detection of early fibril formation after only 1 min of shearing. FT-IR spectra of the insulin solutions showed evolution of bands at 1673 and 1633 cm(-1) from an increase in H-bonded β-turn and β-sheet structures, respectively, while fluorescence emission spectra detected the presence of a new emission band at 482 nm. TEM images confirmed the early onset of fibril formation at 1 min shear exposure, before a maturation and concentration increase of fibrils with further shearing. This study highlights the ability of fluid flows to accelerate insulin fibril formation, which has important implications for biotechnology applications such as the purification process of insulin therapeutic drugs in the pharmaceutical industry, as well as the use of optical-based methods for detecting fibrillogenesis.

Simplified particulate model for coarse-grained hemodynamics simulations

Human blood flow is a multiscale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well-established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long-range interactions and-in order to describe the more complex short-range behavior of cells-anisotropic model potentials known from molecular-dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. In this paper we present our model and demonstrate its applicability to conditions typical for the microvasculature.

Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way

To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0MPa with an average of (3.8±1.7)MPa at the brachial artery and from 1.2 to 7.8MPa with an average of (4.8±2.2)MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.

Fluid Flow in Tree-Shaped Constructal Networks: Porosity, Permeability and Inertial Parameter

This paper aims to contribute to the ongoing research on tree-shaped flow structures. First, it briefly traces the progress made on constructal tree-shaped flow networks. Then, the paper focuses on tree pattern of tubes connecting the centre and the rim of a circular area. It shows that the physical description underlying the classical Darcy-Forchheimer-Ergun equation may provide a legitimate correlation for this kind of flow structure. The porosity, hydraulic permeability and the inertial factor of the flow structure are also presented.

Shear stress regulation of nitric oxide production in uterine and placental artery endothelial cells: experimental studies and hemodynamic models of shear stresses on endothelial cells

Hemodynamic shear stress is the most powerful physiological regulator of endothelial Nitric Oxide Synthase (eNOS), leading to rapid rises in nitric oxide (NO). The substantial increases in uterine and placental blood flows throughout gestation rely heavily on the action of NO. We and others have investigated endothelial function in response to shear stress with cell culture models of shear stress. In order to apply the results of these studies more effectively, we need a more complete understanding of the origin and coupling of the hemodynamic forces and vascular tissue behavior. For example, equations commonly used to calculate in vivo shear stress incorporate assumptions of steady (non-pulsatile) blood flow and constant viscosity of blood (Newtonian fluid). Using computational models, we can estimate a waveform of shear stress over a cardiac cycle and the change in blood viscosity with shear rate and hematocrit levels, two variables that often change with size of vessel and location within a vascular tree. This review discusses hemodynamics as they apply to blood flow in vessels, in the hope that an integration of these fields can lead to improved in vitro shear stress experiments and understanding of NO production in uterine and placental vascular physiology during gestation.

Role of shear stress on nitrite and NOS protein content in different size conduit arteries of swine

AIM

Inherent fundamental difference exists among arteries of different sizes. The purpose of this study was to evaluate the relation between regional difference of wall shear stress (WSS) in various sizes arteries and contents of nitrite and NO synthase (NOS) isoforms.

METHODS

Five different conduit arteries in a wide range of diameter (1-8 mm) were examined in the hind limbs of 13 pigs. Blood flow rate and outer diameter were measured in vivo to determine WSS. Arterial tissues were harvested for the measurement of nitrite and NOS protein contents. The concentration of nitrite, a product of NO synthesis, was determined by high-performance liquid chromatography method. Western blot analysis was used to assess the protein contents of endothelial NOS (eNOS), inducible NOS (iNOS) and neuronal NOS (nNOS).

RESULTS

Our data show that WSS increases with a decrease in artery diameter. Nitrite level increases with increasing WSS and hence decreases with artery diameter. The eNOS protein contents decrease with an increase in diameter. No significant difference for iNOS and nNOS protein contents was found with different artery diameter. A significant positive correlation between tissue nitrite and eNOS protein contents was also observed. Finally, the WSS-normalized eNOS is not significantly different in various size vessels.

CONCLUSION

Regional difference in blood flow has no effect on iNOS and nNOS protein contents in these conduit arteries. Regional difference in eNOS expression and nitrite contents may be related to the WSS-induced NO by the endothelium under normal physiological conditions.

Stem cells, microenvironment mechanics, and growth factor activation

Physicochemical features of a cell's microenvironment can exert important effects on cell behavior and include the effects of matrix elasticity on cell differentiation processes, but molecular mechanisms are largely mysterious. Here we highlight recent reports of a mechanical dependence to growth factor activation, with a particular focus on release of TGFbeta (Transforming Growth Factor beta) from its large latent complex via forced unfolding. We discuss these processes and pathways in the contexts of matrix adhesion and fluid shearing as they might relate to stem cell differentiation and other mechanisms in development, disease, and repair.

Extension of Murray's law using a non-Newtonian model of blood flow

Background

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.

Modeling

In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. ΣR^c = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.

Results

We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.

Conclusion

It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Endothelial differentiation of adipose-derived stem cells: effects of endothelial cell growth supplement and shear force

BACKGROUND

Adipose tissue is a readily available source of multipotent adult stem cells for use in tissue engineering/regenerative medicine. Various growth factors have been used to stimulate acquisition of endothelial characteristics by adipose-derived stem cells (ASC). Herein we study the effects of endothelial cell growth supplement (ECGS) and physiological shear force on the differentiation of ASC into endothelial cells.

MATERIALS AND METHODS

Human ASC (CD13(+)29(+)90(+)31(-)45(-)) were isolated from periumbilical fat, cultured in ECGS media (for up to 3 wk), and exposed to physiological shear force (12 dynes for up to 8 d) in vitro. Endothelial phenotype was defined by cord formation on Matrigel, acetylated-low density lipoprotein (acLDL) uptake, and expression of nitric oxide synthase (eNOS), von Willebrand factor (vWF), and CD31 (platelet endothelial cell adhesion molecule, PECAM). Additionally, cell thrombogenicity was evaluated by seeding canine autologous ASC onto vascular grafts implanted within the canine arterial circulation for 2 wk.

RESULTS

We found that undifferentiated ASC did not display any of the noted endothelial characteristics. After culture in ECGS, ASC formed cords in Matrigel but failed to take up acLDL or express the molecular markers. Subsequent exposure to shear resulted in stem cell realignment, acLDL uptake, and expression of CD31; eNOS and vWF expression was still not observed. Grafts seeded with cells grown in ECGS (+/- shear) remained patent (six of seven) at 2 wk but had a thin coat of fibrin along the luminal surfaces.

CONCLUSIONS

This study suggests that (1) ECGS and shear promote the expression of several endothelial characteristics in human adipose-derived stem cells, but not eNOS or vWF; (2) their combined effects appear synergistic; and (3) stem cells differentiated in ECGS appear mildly thrombogenic in vitro, possibly related, in part, to insufficient eNOS expression. Thus, while the acquisition of several endothelial characteristics by adult stem cells derived from adipose tissue suggests these cells are a viable source of autologous cells for cardiovascular regeneration, further stimulation/modifications are necessary prior to using them as a true endothelial cell replacement.

A method to estimate wall shear rate with a clinical ultrasound scanner

A simple technique to estimate the wall shear rate in healthy arteries using a clinical ultrasound scanner has been developed. This method uses the theory of fully developed oscillatory flow together with a spectral Doppler trace and an estimate of mean arterial diameter. A method using color flow imaging was compared with the spectral Doppler method in vascular phantoms and found to have errors that were on average 35% greater. Differences from the theoretic value for the time averaged wall shear rate using the spectral Doppler method varied by artery: brachial -9 (1) %; carotid -7 (1) %; femoral -22 (4) %; and fetal aorta -17 (10) %. Test measurements obtained from one healthy volunteer demonstrated the feasibility of the technique in vivo.

Effects of posture on shear rates in human brachial and superficial femoral arteries

Shear rate is significantly lower in the superficial femoral compared with the brachial artery in the supine posture. The relative shear rates in these arteries of subjects in the upright posture (seated and/or standing) are unknown. The purpose of this investigation was to test the hypothesis that upright posture (seated and/or standing) would produce greater shear rates in the superficial femoral compared with the brachial artery. To test this hypothesis, Doppler ultrasound was used to measure mean blood velocity (MBV) and diameter in the brachial and superficial femoral arteries of 21 healthy subjects after being in the supine, seated, and standing postures for 10 min. MBV was significantly higher in the brachial compared with the superficial femoral artery during upright postures. Superficial femoral artery diameter was significantly larger than brachial artery diameter. However, posture had no significant effect on either brachial or superficial femoral artery diameter. The calculated shear rate was significantly greater in the brachial (73 +/- 5, 91 +/- 11, and 97 +/- 13 s(-1)) compared with the superficial femoral (53 +/- 4, 39 +/- 77, and 44 +/- 5 s(-1)) artery in the supine, seated, and standing postures, respectively. Contrary to our hypothesis, our current findings indicate that mean shear rate is lower in the superficial femoral compared with the brachial artery in the supine, seated, and standing postures. These findings of lower shear rates in the superficial femoral artery may be one mechanism for the higher propensity for atherosclerosis in the arteries of the leg than of the arm.