Modeling of biofluid transport 1

Equivalent electrical circuits are a very commonly used tool in modelling of blood flow. However, it can be difficult to know which form of circuit to use and how to relate the equivalent electrical parameter values to the underlying blood and wall parameters, in particular those for inductance and capacitance. We have recently developed a novel first order method to relate the inlet and outlet flows to the inlet and outlet pressures in a blood vessel, using a perturbation approach (based on frequency) that is valid in small vessels (diameter < 1.4 mm).

We now show how this model can be compared directly to an electrical equivalent circuit, comprising resistance, inductance and capacitance. We consider a vessel of radius r and length L, containing blood of density ρ and viscosity μ and use the model for blood flow presented in Payne and El-Bouri, 2017. The vessel is assumed to have wall compliance C. Both the vascular model and the electrical equivalent circuit model are shown in Figure 1. The equations for both models relating flow to pressure in the frequency domain are expanded out to second order, based on a perturbation approach, as shown in Figure 1.

Through comparison of the two models, we then show how the zero and first order expansions (α₀ and α₁) can be exactly matched for both resistance (when R_e =  8μL/πr⁴, i.e. Poiseuille flow) and inductance (when I_e = 4ρL/3πr², i.e. very close to the standard expression), but that capacitance cannot be exactly matched (although the best approximation occurs when C_e = C, i.e. 8 times the wall compliance). We then show that whilst the second order terms (α₂) can be matched to a good degree of accuracy, the equivalent electrical parameter values are different from those obtained from first order matching. In the case of inductance the error is small (approximately 2 %), but for capacitance the difference is very substantial, being over one order of magnitude.

Thus whilst we can show a good agreement with the first order terms, the equivalent electrical circuit model cannot also match the second order terms. Thus only in the smaller vessels where the second order terms can be assumed to be negligible can the equivalent electrical circuit be used with accuracy. In these vessels, however the electrical equivalent circuit can provide a good approximation when the expressions quoted above are used. The expressions derived here can be considered to be the optimal values for calculation of the parameters in equivalent electrical circuits and should be used in future models. Future work will include the calculation of these equivalent electrical parameters for larger-scale networks.

Understanding how the cerebral vasculature behaves is made challenging by the complexity of the highly interconnected network of vessels across many different scales that is found in the human brain. In a recent paper we have presented a new model for simulating dynamic changes in blood flow and volume that is based on a rigorous mathematical analysis of the governing equations (Payne and El-Bouri, 2017). We have also developed a network model of the cerebral microvasculature that scales across 13 generations of blood vessels (Payne and Lucas, 2017), as shown in Figure 1; since these are the generations that predominantly contribute to oxygen delivery from blood to tissue, this section of the microvasculature is key to understanding the relationship between flow and metabolism. We have previously shown that oxygen delivery from this section of the microvasculature to the surrounding tissue is governed by a single time constant of approximately 6 seconds; however, we now consider the blood flow and volume response of this network to changes in pressure.

We consider changes to the network in terms of the inlet blood pressure, where we simulate a sharp drop of 20 % after 1 second, with the results shown in Figure 1. The total volume as a function of time is then calculated and a first order response is fitted using a least squares fitting procedure. The resulting model values are found to be approximately 1.5 x 10^-15 m³/Pa and 0.62 seconds. A similar approach is used for the outlet flow, giving values of approximately 0.85 x 10^-15 m³/Pa.s and 0.62 seconds, but with a delay of approximately 0.4 seconds; the overall delay is thus approximately 1 second. Both the outlet flow and volume responses of this section of the cerebral microvasculature can thus be accurately summarised using a first order response.

Comparison of our results with those presented earlier shows that the flow and volume responses are governed by time constants that are an order of magnitude faster than those for oxygen transport. The coupling between flow and metabolism is thus predominantly limited by the oxygen transport across the vessel walls, with the other responses being significantly faster. This opens up interesting questions about the nature of regulation, since the local flow response is very rapid in response to changes in pressure, but much slower in response to changes in tissue oxygenation; other pathways must be involved in signalling ischaemia.

Introduction
An arterio-venous fistula (AVF) is the preferred method of vascular access for hemodialysis. However AVFs have high failure rates owing to failure to mature and vascular occlusion. It is believed that the hemodynamics play an important role in failure as the creation of an AVF results in disturbed hemodynamics, leading to abnormal wall shear stress patterns. Particle image velocimetry (PIV) is used to compare the flow field in steady (Re = 1742) and pulsatile flow conditions (, ) within a rigid patient-specific brachio-cephalic AVF phantom to determine if it is necessary to model the pulsatile transient nature in CFD phantom.  The objective is to assess the influence of pulsatility on the flow from a modelling and maturation perspective.

Materials and Methods
A commercial PIV system (LaVision) was used to record measurements in the AVF anastomosis region [1]. The system was designed to allow 95% of the flow to exit the venous outlet and the other 5% to leave the distal arterial outlet. The working fluid used was a mixture of water-glycerol-sodium iodide seeded with 10 µm fluorescent particles. Cross-correlation was performed on the images pairs using interrogation windows of 32x32 pixels with a 50% overlap resulting in a vector spacing of 0.12mm. Particle streaks were also recorded.

Results and Discussion
Planar PIV measurements were recorded parallel to each other and the out-of-plane component was extracted using integration. The average pulsatile and steady streamlines exhibited a high degree of similarity, as seen in figures 1 (a) and (b). The velocity magnitudes were within 90% of each other and the extent of the recirculation regions lay within 37% of each other. The results from this study showed that steady flow results in larger fluctuations in velocity magnitudes and flow direction than pulsatile flow urging caution for oversimplification in numerical simulations. It was also seen that the maximum flow disturbance under pulsatile flow conditions occurs after the peak in the velocity waveform.

Figure 1: (a) Streamlines of Steady and (b) Pulsatile flow measurements.

The results from this study determine that a complex flow structure is present. From the steady and pulsatile streamlines it is clear that there is flow separation in the distal artery and in the proximal vein resulting in flow recirculation. However there is also a difference in steady and pulsatile boundary conditions results determining that it is necessary to model the pulsatile transient flow in CFD. These 3D-3C results will be used to validate numerical simulations as well as serve as a reference data set to assess the feasibility of ultrasound imaging velocimetry as an in-vivo validation technique.

REFERENCES

[1] S. Drost, B.J.de Kruif and D. Newport. Arduino Control of a Pulsatile Flow Rig. Medical Engineering and Physics, 2017

Vasomotion, the rhythmic oscillation of vessel walls, has been found within the cerebral microvasculature for many years. It has been proposed that, as it appears to be found more under conditions of hypoxia, it could be a protective mechanism. This is also supported by the fact that the time-averaged resistance of a vessel to flow is reduced from the steady state value when the walls exhibit a periodic oscillation, due to the strong non-linearity of the Poiseuille equation. However, changes in the resistance of one vessel will affect the flow and hence oxygen transport through potentially the whole of the microvasculature. Despite this, no study has examined the effects of vasomotion on a network model.

We thus considered our existing model of the cerebral microvasculature, Payne and Lucas, 2017: this considers 13 generations of vessels, 6 arterial, 1 capillary and 6 venous, Figure 1a. Since these are the generations that predominantly contribute to oxygen delivery from blood to tissue, this section of the microvasculature is key to understanding the relationship between flow and metabolism in the cerebral microvasculature. Using the modelling approach set out in Payne and Lucas, 2017, we calculated the baseline mean tissue partial pressure of oxygen. We then simulated vasomotion of varying amplitude in each generation and calculated the change in time-averaged partial pressure. We found that there is a peak value of vasomotion amplitude at which the rise in partial pressure is greatest, with this value being typically close to 0.5, Figure 1b.

We then considered the response to changes in both baseline flow (set by adjusting the pressure differential across the network) and baseline metabolism. For each condition, we calculated the rise in partial pressure caused by vasomotion of amplitude 0.5, Figure 1c. Finally, we considered the amplitude of vasomotion in each generation to be a variable and optimised over all 13 of these variables to obtain the highest rise in partial pressure that can be achieved, and then repeated this for a range of values of baseline flow and metabolism, Figure 1d.

From these results, it is clear that vasomotion has the capacity to increase the partial pressure of oxygen in tissue very significantly; it is also clear that there is a maximum capacity, which can be found by adjusting the amplitudes of vasomotion in each generation appropriately. This was designed to be based on a feedback mechanism (which we do not attempt to describe in any further detail here). Our model simulations thus support the hypothesis that vasomotion is a response to hypoxia and show that there is a significant capacity for increased oxygen delivery to tissue.

Introduction

Many cardiovascular diseases, like atherosclerosis [1], are associated with the dynamics of the endothelial glycocalyx under flow shear stresses, as glycocalyx plays a prominent role in orchestrating multiple biological processes occurring at the plasma membrane. Reliable prediction of the dynamics of the glycocalyx under blood flow is of great importance for understanding the pathodology of cardiovascular diseases, helping to form therapetic strategies. However, detailed mechanisms behind the interactions between blood flow and the glycocalyx at the molecular level are still poorly understood, despite numerous studies via classical theoretical or experimental methods.

Methods

In this research, large-scale molecular dynamics (MD) simulations are conducted on the UK’s national supercomputing service, ARCHER, to study the interactions between the flow and glycocalyx. An all-atom flow/glycocalyx system (Fig.1) is adopted [2] with the bulk flow velocity set in the realistic physiological range. The system is simulated by MD using  ~ 6 million atoms..

Fig.1  An all-atom glycocalyx/flow system containing ~ 6 million atoms.

Results and Discussion

The simulation results include detailed velocity distribution and time evolution as well as the dynamics of the glycocalyx constituents under the flow shear stresses. Comprehensive analysis leads to a new model for predicting the glycocalyx behaviours. The model reconciles a longstanding debate about the force transmisson mode via the glycocalyx. Furthermore, the biological significance behind the coupled dynamics between the flow and the bio-complex is discussed in order to further understanding of mechanisms for mechanotransduction of the endothelial glycocalyx.

Conclusions

For the first time, flow in the physiologically relevant range is realized in a most detailed atomistic model of the glycocalyx. The intricate dynamics of the glycocalyx biomolecules revealed have potential applications in the pathologies of glycocalyx-related diseases, for example in renal or cardiovascular conditions.

Acknowledgement

The research is supported by the UK Engineering and Physical Sciences Research Council under the project (EPSRC) “UK Consortium on Mesoscale Engineering Sciences (UKCOMES)” Grant No. EP/L00030X/1.

References

[1] T.J. Rabelink, D. de Zeeuw, Nature reviews. Nephrology, 11 (2015) 667-676.

[2] X.Z. Jiang, H. Gong, K.H. Luo, Y. Ventikos, Journal of The Royal Society Interface, 14 (2017).

Introduction

In many computational and experimental flow studies in models of the circulatory system the non-Newtonian flow behavior of blood is often ignored. Moreover, fundamental fluid mechanics definitions such as laminar and turbulent flow are unprecise, unclear or sometimes even wrong [1]. In this study we investigate the flow dynamics in a bifurcation under different flow conditions with Newtonian and non-Newtonian fluids and give definitions of flow regimes presented in the circulatory system.

Methods

A rigid glass model of a 90° bifurcation, beside an elastic one, was used for the flow studies. To visualize the flow under steady flow conditions we used the experimental set up including three injection needles with different dyes. The needles were located upstream of the bifurcation at the different positions. The flow ratio into the branch to the total flow proximal to the bifurcation was variable. For an unsteady flow conditions a photoelasticity apparatus with a birefringent fluid was used. The measured viscosity curve of the non-Newtonian fluid (polyacrylamide solution) was used to calculate the representative viscosity [2]. Flow studies with Newtonian and non-Newtonian fluids were performed with the same Reynolds and Strouhal numbers [3].

Results

The clear definitions of flow regimes are given based on results of the experimental studies: laminar flow, nominal laminar flow, transitional flow and turbulent flow. Flow visualizations show that at bifurcation the flow is neither a Poiseuille laminar nor a fully developed turbulent one. Flow disturbances and the flow separation region can be clearly seen. This is a typical example for a nominal laminar flow and a beginning of a transitional flow over a very small area. The velocity fluctuations occur over an area of about 2-3 diameter distal to the branch as shown by the dyes at different flow-rate ratios from 0 to 1 (Fig. 1). It is clearly demonstrated that no turbulent flow exists; otherwise the dyes would spread out and cannot be observed as lines. The flow behaviors of Newtonian and a non-Newtonian fluid are significantly different at bifurcation where recirculation zones are created at special flow-rate ratios.

Discussion

This study has demonstrated that no fully developed turbulent flow exists in the circulatory system – only nominal laminar or transitional flow are present. The use of “turbulent flow” in many numerical flow studies is ambiguous and misleading. Also the significant differences between Newtonian and non-Newtonian flow behavior in recirculation zones are clearly shown, which should be considered in the future studies more precisely.

Acknowledgements

This work was supported by Russian Science Foundation (Project 16-15-10327).

References

1. Andersson, M., et al., (2017). J Biomech, 51 pp8–16

2. Giesekus, H., Langer, G., (1977). Rheol Acta, 16(1) pp1-22

3. Liepsch, D.W., (1986). Biorheology, 23(4) pp395–433

It is well documented that atherosclerosis is much more prone to occurring in particular regions of the arterial system where the geometry changes sharply, which is referred to the localization of atherosclerosis. Two mechanisms of shear stress and mass transport have been recognized to play an important role in the development of localized atherosclerosis. However, their relationship and roles in atherogenesis are still obscure. It is necessary to investigate quantitatively the correlation among lowdensity lipoproteins (LDL) transport, haemodynamic parameters and plaque thickness. We simulated blood flow and LDL transport in rabbit aorta using computational fluid dynamics and evaluated plaque thickness in the aorta of a high-fat-diet rabbit. The numerical results show that regions with high luminal LDL concentration tend to have severely negative haemodynamic environments (HEs). However, for regions with moderately and slightly high luminal LDL concentration, the relationship between LDL concentration and the above haemodynamic indicators is not clear cut. Point-by-point correlation with experimental results indicates that severe atherosclerotic plaque corresponds to high LDL concentration and seriously negative HEs, less severe atherosclerotic plaque is related to either moderately high LDL concentration or moderately negative HEs, and there is almost no atherosclerotic plaque in regions with both low LDL concentration and positive HEs. In conclusion, LDL distribution is closely linked to blood flow transport, and the synergetic effects of luminal surface LDL concentration and wall shear stress-based haemodynamic indicators may determine plaque thickness. This research may provide a theory basis for the mechanism of atherosclerosis as well as clinical diagnosis.

It is pivotal that Nitric Oxide (NO) produced in endothelium was consumed by hemoglobin wrapped in red blood cells (RBCs) membrane in regulating the vascular tone. Thus, the form of RBCs in capillary is a vital factor in determining NO distribution in microcirculation. However, the whole process of NO transport in vessel containing flowing RBCs is still not clear so far. The objective of this study is to investigate the influence of the movement and deformation of biconcave disc shape RBCs on NO transport in a impermeable capillary with various hematocrit.

In this work, the motion of RBCs in a 2D capillary is investigated by using immersed boundary lattice Boltzmann method firstly and the deformability of RBC is expressed by spring network model which is based on the minimum energy principle. Furthermore, the interaction between RBCs is considered. The computational domain is a segment of capillary with 9in diameter and 40in length. It is worth noting that we employed periodic boundary condition relating to RBC movement, indicating that the RBC comes out of outlet completely and then enters into inlet, and pressure boundary conditions relating to flow flied. The initial biconcave shape of RBC put in capillary was obtained from circular based on minimum energy principle. Based on the flow field, we will calculated NO production rate from endothelium through wall shear stress (WSS) based on hyperbolic model. NO distribution in capillary within flowing deformable RBCs was obtained using immersed boundary finite difference method.

A 2D model about NO transport in capillary containing RBCs with different Hct value has been developed in this work, including the computation of blood flow velocity, RBC deformation and movement, NO production rate, and NO concentration distribution. The results show that RBCs gradually transform from biconcave disc shape to convex shape similar to parachute shape driven by plasma flow. And with the transforming of RBC shape, the width of RBC-free layer near vascular wall will increases over time. Thus, NO concentration in vascular wall increases with increasing thickness of RBCs-depleted layer when RBCs flow with plasma and deform from biconcave shape to parachute shape. In addition, RBCs show less deformation in high Hct value resulting from more powerful mechanical interaction among RBCs and plasma. NO concentration distribution reduces in vessel along with increasing Hct value and the decrease extent of NO centration in lumen is larger than vascular wall.

This work is financially supported by National Science Foundation of China NSFC NO. 51576033 and Dalian Science and Technology R & D program (2015F11GH092).

Introduction

Diffuse Coronary atherosclerosis is frequent in humans [1]. It is important to understand how serial stenoses interact hemodynamically to affect atherosclerotic progression and potentially plaque rupture. The objective of the study is to investigate the hemodynamic distribution in patient-specific epicardial LMCA tree with serial stenoses.

Methods

The 3D geometry of patient epicardial LMCA tree was reconstructed from CTA images.  Navier-Stokes and continuity equations were solved using a transient method [2].  The inlet and outlet boundary conditions were the aortic pressure wave and flow resistance, respectively.  Hemodynamic parameters were determined based on the computed flow field. 

Results

A stenosis at a mother vessel mainly deteriorated the hemodynamics near the bifurcation while a stenosis at a daughter vessel affected the remote downstream bifurcation.  In comparison with a single stenosis, serial stenoses increased the peak pressure gradient along the main trunk of the epicardial left anterior descending arterial tree by > 50%.  An increased distance between serial stenoses further increased the peak pressure gradient.  

Discussion

Serial moderate stenoses along the LAD main trunk increased the peak pressure gradient by > 50% in comparison with a single stenosis, where the increased distance between serial stenoses increased the peak pressure gradient. The hemodynamic analysis in multiple stenoses of the epicardial coronary arterial tree improves our understandings of diffuse atherosclerotic progression.

References

1. X. Chen, et al., (2016), PLoS ONE, 11: e0163715
2. Y. Huo, et al., (2009), Journal of Biomechanics, 42: 594-602

Lung protective mechanical ventilation (LPMV) is a mean to avoid acute respiratory distress syndrome (ARDS) during artificial respiration. Patients undergoing LPMV tend to suffer from hypercapnia and hypercapnic acidosis. These side effects can be compensated by a novel approach, intracorporal CO₂ removal (ICCO2R). ICCO2R devices are hollowfiber membrane catheters inserted into inferior vena cava and thus do not require high blood priming volume or an external blood flow loop. Due to their implantation ICCO2R devices face anatomical and physiological constraints as restricted membrane area, catheter diameter or flow resistance.

To meet these constraints and the required metabolic CO₂ removal demand, highly efficient devices need to be developed. Experimental methods are usually very time consuming, expensive and provide a few number of point data, mostly limited to easily accessible regions of the catheter. Computational fluid dynamics (CFD) allows a three dimensional and time dependent description of the CO₂ removal, respectively transport, in the membrane catheter and enables to investigate phenomena like local dead zones, wall effects or bypassing, as well as other flow irregularities. Furthermore, the diffusive boundary layer (concentration polarization layer), representing a major part of the total CO₂ transport resistance, can be examined. Consequently, information gained by CFD simulations can be used to effectively optimize ICCO2R devices.

In the scope of this research an inhouse solver membraneFoam, based on the open source CFD code OpenFOAM®, was utilized. Additionally, a membrane permeance model for the main blood gas (BG) components CO₂ and O₂ has been developed and implemented. On the blood side, adapted diffusion and partial pressure models to describe the BG transport as well as the driving force responsible for transmembrane flux were incorporated. To be able to account for the complex saturation behavior of CO₂ and O₂ in blood, a multispecies approach for the single BG components was chosen. The solver, membraneFoam, not only allows investigations of BG transport on the blood-, respectively shell-side of the fibers but also in the fiber lumen.

In this study, the performances of the described models were tested by simulating flow structure and BG transport in a hollow fiber packing, which allows basic studies of flow pattern and concentration polarization layers. By means of such results and further simulations we can investigate device design improvements like optimization of the fiber packing, introduction of static mixing, reduction of concentration polarization, prevention of bypassing and minimizing of flow resistance.

Acknowledgment

FFG 857859 MILL – Minimal invasive liquid

Background: A functioning vascular access is indispensable for hemodialysis and is often provided by prosthetic arteriovenous grafts (AVGs) when a native arteriovenous fistula cannot be created. An AVG provides a low resistance connection between an artery and a vein that bypasses the peripheral resistance, thereby facilitating the high blood flow required for hemodialysis. AVG creation results in disturbed flows and non-physiological wall shear stresses (WSS) near the venous anastomosis, leading to vessel wall damage, which initiates stenosis development, ultimately resulting in AVG patency loss. Graft hemodynamics is influenced by both graft design and in-vivo graft configuration. Typically, AVGs lose patency after two years, despite multiple interventions to maintain its patency.

To optimize graft hemodynamics and thus improve AVG longevity, computational fluid dynamics (CFD) studies have explored the impact of different graft designs. Highly idealized parametrizations of AVG geometry are often used for this purpose (Figure 1A) as straightforward creation of such geometries in computer aided design software facilitates quick evaluation of possibly beneficial graft modifications. Because these parametrizations neglect in-vivo configuration, hemodynamic characteristics might not be accurately represented.

This study proposes a framework for creating more realistic AVG parametrizations that allow for graft design optimization. We demonstrate how hemodynamics in these parametrizations differ from those in idealized ones.

Methods: The proposed framework is illustrated in Figure 1B. AVG geometries were segmented from a computed tomography angiography scan of a patient with functioning AVG, using the segmentation software VMTK¹. The in-vivo path of the segmented vessels was computed by means of centerline extraction. Post-operative ultrasound measurements were used to estimate arterial and venous diameter, and time-dependent velocity boundary conditions for CFD simulations. The inner graft diameter was assumed to be 6 mm. Based on these data a realistic and an idealized AVG parametrization were created in SolidWorks (Dassault Systèmes 2017). Differences in flow patterns and WSS between both parametrizations were assessed by CFD simulations using the Navier-Stokes solver OASIS². Both simulations used equal boundary conditions.

Results: We observed irregular, asymmetrical flow patterns at the venous anastomosis of our proposed parametrization, whereas smoother and symmetrical flow was observed in the idealized geometry (Figure 1). WSS patterns at the venous anastomosis of the idealized geometry were symmetric and mainly unidirectional during the cardiac cycle, whereas non-symmetric and oscillating patterns were observed in the proposed parametrization. Maximum observed WSS magnitude was approximately double in the proposed geometry compared to the idealized one.

Conclusion: We developed a framework for creating AVG parametrizations that both resemble the in-vivo situation and still allow for hemodynamic evaluation of different graft designs. We showed that relevant hemodynamic phenomena are oversimplified in idealized AVG geometries compared to the proposed parametrizations.

¹ http://www.vmtk.org/

²M. Mortensen et al., Computer Physics Communications, 2015.

Introduction

Evidence suggests that hemodynamics plays a key role in vascular disease. In particular, in the carotid bifurcation (CB) the initiation/progression of atherosclerosis has been associated with flow disturbances. Moved by the complexity of arterial flow, here we apply for the first time the Complex Networks (CNs) theory [1] to the human CB hemodynamics, challenging its ability in detecting peculiar fluid structures. The adoption of CNs approach is due to its efficiency in exploring complexity of physical systems with a huge number of interacting elements. Technically, a dataset of 10 patient-specific computational hemodynamic (CH) models of human CB presented elsewhere was considered [2] and a two-points velocity magnitude-based correlation strategy was proposed to test CNs ability in detecting disturbed flows.

Methods

For each of the 10 investigated models, a correlation matrix was built up considering two-points velocity magnitude time histories along the cardiac cycle at all nodes of the discretized fluid domain, as obtained from CH. Then, a spatial network was built establishing a link between the pair of nodes whose velocity magnitude time histories were correlated with R>0.8. This information was used to build the adjacency matrix A, on which CNs metrics were applied to measure: the Degree Centrality (DC) of a node inside the network, in terms of correlation with the hemodynamics in the rest of the bifurcation; the Average Euclidean Distance (AED) of each node from its ”neighbours” (identified by A), as a measure of physical path length over “neighbour” pairs of velocity magnitude time histories in the bifurcation.

Results

A proof of the ability of CNs in detecting hemodynamic structures is given in Fig. 1, where the DC volumetric maps in the investigated models are shown. In general, regardless of the specific bifurcation: highly correlated hemodynamic structures with high number of links are mainly located in the common carotid artery; regions characterized by flow disturbances [2] - i.e., carotid bulb and the proximal internal carotid artery - are characterized by poorly linked correlated hemodynamics. Low DC regions exhibit the lowest values of AED, suggesting that there the path length of highly correlated velocity time histories is very short. Interestingly, regions exposed to low and oscillatory shear at the luminal surface (identified by high relative residence time (RRT) maps [2]) are co-localized with regions characterized by low DC (Fig. 1).

Discussion

The proposed integrated CH & CNs-based approach has demonstrated to be a promising tool for detecting flow disturbances at the CB. Based on the applied strategy, fluid structures weakly linked and connected mostly with short physical path lengths co-localize with disturbed shear regions.

References

[1] Boccaletti, S., et al. Phys Rep, 424:175–308,(2006).

[2] Gallo, D., et al. J Biomech, 49(12), 2413–2419,(2016).

Introduction: Obstructive coronary artery disease (CAD) is a leading cause of death globally. CAD patients can develop collateral vessels which are the heart’s natural bypass grafts.  There is a correlation between well-developed collateral vessels and lowered frequency of downstream myocardial infarction [1].  Coronary artery bypass graft (CABG) surgery is one CAD treatment option.  Computational fluid dynamics (CFD) has been used to model CABG blood flow, but not with collateral vasculature.  The objective of this study is to assess the effect of collateral flow variation on CABG hemodynamics using CFD.

Methods:  Idealized models of the CABG anastomosis site with variable stenosis and collateral vessels were made with SOLIDWORKS.  First, the number of collateral vessels was increased from zero to three with a 75% stenosis to investigate the impact of collateral flow and location.  Second, the flow rate was increased in a single collateral vessel for four levels of stenosis (0 - 100%) to focus on the impact of collateral flow alone.  The models were imported into ANSYS Workbench for meshing which included increased mesh density near the wall.  Simulations were conducted using ANSYS Fluent with transient, laminar flow. The boundary conditions at the graft and artery inlets were based on velocity waveforms from literature [2] and the outlets were pressure outlets.  The collateral flow increased from 5 to 15 ml/min by adding additional vessels or increasing the flow from a single vessel. 

Results: A total of 16 simulations were conducted with combinations of stenosis levels, collateral flow rates, and collateral vessel counts.  As the number of collateral vessels increased, the skewed velocity profile due to the bypass graft was pushed back toward the center of the native vessel (Figure 1).  As expected, there was a decrease in WSS immediately following each collateral location.  Based on the streamlines, the increasing collateral flow rate (in a single collateral) had limited impact on the patterns in the anastomosis region.  However, downstream effects were seen which were consistent for each stenosis level.


    

Discussion:  This study represents the first investigation of the impact of collateral flow on CABG hemodynamics.  The boundary conditions varied for each stenosis level making interpretation of the results complicated.  Further study is needed with more consistent boundary conditions and the incorporation of downstream resistance at the outlets.  In conclusion, collateral flow affects the hemodynamics downstream of the anastomosis, however more research is needed to fully understand the effect of collateral flow on CABG.

Acknowledgements: NSF EEC-1659796, NIH/NIGMS MARC – U*STAR Program 1T34GM105551 (N. Francis Fisk University), and NC Summer Ventures in Science and Math.

References: 

1) Zhang, J., et al., (2014), Radiology, 271(3) p703-710.

Introduction:

The cerebral circulation maintains blood flow constant in spite of wide variations in blood pressure, but also react dynamically after neuronal firing events. The control mechanisms during homeostasis (autoregulation) and after neuronal firing (functional hyperemia) are poorly understood. We propose to study blood flow control based on fairly complete representation of the entire circulation of the brain ranging from the large arteries (carotid, Circle of Willis) to the pial network connected to the cerebral  microcirculation composed of the capillary bed, arterioles, venules and draining out through the veins.

Methods:

An artificial vessel growth algorithm was used to construct the entire cerebral angioarchitecture in mouse spanning  large arteries to the microcirculation in 12 specimen. The topological data for the synthetic whole mouse vascular network were acquired from micro-CT (main arteries, pial vessels) and 2-Photon imaging (microcirculation). Topological analysis shows the statistical equivalence of synthetic and real vascular trees as shown in Fig 1. Biphasic blood (pressure, flow, hematocrit) was modeled using a kinematic plasma skimming law¹. Dynamic simulations of blood flow, hematocrit, blood saturation, oxygen tension in tissue are used to elucidate perfusion changes in autoregulation and functional hyperemia.

Results:

The model predicted cerebral blood flow (CBF) and pressure ranges in agreement with a vast body of experimental data. Our predictions of functional hyperemia revealed a reasonable change in blood flow and also changes in hematocrit distribution in response to vasodilatory signals. Vasodilatory signals from neuronal firing events in simulated functional hyperemia triggered spatially distributed perfusion changes and its timing. Autoregulatory control maintained constant cerebral blood flow despite varying perfusion pressure.

Conclusion:

The complete cerebral vascular model is capable of predicting hemodynamic states over all length scales requiring only arterial pressure at the carotid arteries and jugular veins as input (boundary conditions). This biomechanical modeling approach provides plausible mechanistic explanations for autoregulation and functional hyperemia.  Our model demonstrates biomechanic actuation (vasodilation, vasoconstriction) during functional hyperemia and autoregulation over the entire cerebral angioarchitecture. A global model for blood flow is necessary to quantify the relative contributions of arteries, arterioles and capillaries (pericytes) to blood flow control.  A biomechanical model of cerebral blood flow control for the entire mouse brain was presented.

Acknowledgements:

This project was supported by NIH-1R21NS099896 and NSF-CBET-1301198.

References:

1. Gould et al. (2017) J. Cereb Blood Flow & Metab.
2. UCDavis KOMP Phenotyping, www.kompphenotype.org.

The use of Computational Fluid Dynamics (CFD) has proven to be of great benefit for blood oxygenators design, and different methods have been described in literature ⁽¹⁾. The oxygenation occurs in a hollow fiber bundle, which carry O2 inside (intraluminar flow) while blood circulates externally around them (extraluminar flow). The O2 and CO2 exchange is allowed by the microporous nature of the fibers membrane. Due to the hindering computational cost of accounting for all the fibers description, a traditional approach consists in an extrapolation of microscale characteristic values (i.e. permeability and porosity) to a homogenized porous media model. Broadly speaking, limitations of this technique could be associated to the boundary effects, and the suitability of the micro-scale structure considered. Although some studies have explored these limitations ⁽²⁾, the investigated fiber domains were significantly smaller and simpler than those typical of a commercial device.

In this work, a parametric model of fiber bundles with an optimal meshing strategy is defined to be applied to larger domains (both stacked and wounded membranes); its use as a gold standard allows to properly assess the porous media limitations, even in presence of complex flow paths (i.e. multiple inlet/outlet configurations). The predicted flow distributions by the porous and fiber models were compared, considering bundle perfusion, pathlines and residence times. Aiming for further reductions in the computational cost, fiber models with coarser meshes were investigated, assessing the amount of significant information that can be extracted from such models.

The proposed method is able to generate a mapped mesh of complex fiber bundles automatically, greatly reducing the required number of elements and optimizing their quality. The considered parameters depict remarkable deviations of porous model predictions that could affect the reliability of device performance evaluation. On the contrary, the suggested coarse mesh allows to accurately describe the flow distribution at reasonable computational cost and potentially study fiber bundles up to an infant device scale.

The proposed approach can be of usefulness during the designing phase of a blood oxygenator, in cases where the porous media fails to predict accurately the flow distribution inside the device.

Acknowledgements

This work was funded by the EU-MSCA. GA No 642612 (www.vph-case.eu).

References

(1) Zhang, J., Nolan, T. D., Zhang, T., Griffith, B. P., & Wu, Z. J. (2007). Characterization of membrane blood oxygenation devices using computational fluid dynamics. Journal of Membrane Science, 288(1-2), 268-279. doi:10.1016/j.memsci.2006.11.041

Introduction

Surgical valve replacement is the most common procedure for aortic stenosis treatment. Novel bioprostheses which allow a rapid implantation with a minimum number of sutures (i.e. “sutureless valves”) have reduced the invasiveness and time of the procedure. According to clinical studies, the haemodynamics related to this recent technology have also improved suggesting a benefit related to the absence of the pledget-armed sutures used in the traditional valve anchoring method [1,2,3]. The aim of this study was to verify this hypothesis by assessing the performance of rapidly implanted bioprostheses against standard device with experimental and computational analyses.

Method

Two commercially available bioprosthetic valves were included in this study: Magna Ease (Edwards) valve with sewed-in pledgets sutures and Intuity (Edwards) sutureless valve system. The two valves have identical design apart from the anchoring system. In addition, the Magna Ease was tested also in a configuration without sutures. Five different valve size ranging from 19 to 27 mm and three cardiac outputs were initally tested in an experimental bench work connecting a pulse duplicator (Vivitro System) to reproduce physiological conditions. Computational fluid dynamics (CFD) analyses were then set up to replicate the systolic flow phase with the valve leaflets in open configuration. Flow boundary conditions for each cardiac output were derived from the experimental data and imposed on the inlet of each valve configuration across all sizes. For each test, trans-valvular pressure drop, effective orifice areas and wall shear stress (WSS) were determined together with computed flow and turbulence fields.

Results

Results of both in vitro and in silico analyses showed how the presence of pledget-armed sutures negatively affected the performance of the bioprosthesis. This was mainly caused by local flow disturbances which in turn increase mean pressure gradient and decreased effective orifice area. Non-uniform distribution of turbulent kinetic energies (Figure) and WSS for the valve with pledgets was highlighted by the computational model. As expected, a decrease in pressure gradient was found as the valve diameter increased. It has also been observed that Intuity valve with smaller diameter showed similar hemodynamic performance as a Magna Ease model with bigger size.

Discussion

CFD analyses in combination with experimental results have helped to assess the local flow characteristics and conclude that the absence of sutures is beneficial for an improved hemodynamic performance of the bioprosthetic valve.

Figure: Turbulence kinetic energy field and streamlines for Intuity (left) and the Magna Ease (right) valves.

References:

[1] K. Phan et al. Ann Cardiothorac Surg.(2015);4(2):100-11

[2] F. Pollari et al. Ann Thorac Surg.(2014);98(2):611-6

[2] A.W. Wallner et al. Interact Cardiovasc Thorac Surg.(2016);22(6):799-805

The effect of the macromolecular layer covering the luminal surface of the vascular endothelium, called glycocalyx, on microcirculation has received increasing attention, since it has been described as the main mechanosensor and transducer of fluid shear-stress on endothelial cells [1]. In this study, we investigate the ability of glycocalyx to allow fluid permeation (permeability) through an extensive multiscale simulation of blood flow in capillaries. To this end, we introduce a two-phase moving interface model with the rich-in-RBCs core represented by the Viscoplastic Quemada (VQ) constitutive equation, a dynamically predictable cell-free layer (CFL) thickness and a porous medium of about 500 nm in thickness, which corresponds to the glycocalyx layer, based on the theoretical approach of Shiram et al [2]. Modelling the glycocalyx as an ideal spatial arrangement of protein fibers we accurately calculate the shear stress at the core-plasma interface, as well as the macroscopic geometry-defined permeability. The investigation is extended to a more realistic model through a microscopic approach incorporating the interaction between blood plasma and glycocalyx fibers. The latter are assumed to be composed of elastic deformable solids described by shear stress-induced porosity properties. The fluid-structure interaction problem is defined on a two-dimensional periodic domain utilizing the shear stress and the CFL thickness extracted from the 1D simulation. These microscopic fluid-structure interaction simulations allow for more accurate determination of the shear stress, but are more costly than the macroscopic, one-dimensional calculations. Comparison between the two approaches in terms of quantitative determination of the permeability reveals that for small arteries there is a significant deviation between the results, but for blood flows in capillaries over 100 μm in diameter this deviation between the two methods diminishes. By weighing the computational cost of the FSI method and the accuracy of the two models, we conclude that the permeability of the sieve porous layer can be efficiently determined by the versatile 1D model for blood flow situations where the intensive hemodynamical phenomena are absent and the role of the glycocalyx is relatively inconspicuous.

References

[1]. Pries A, Secomb T, Gaehtgens P. The endothelial surface layer. Pflugers Arch. 440:653-66, 2000

[2]. Shiram K, Intaglietta M, Tartakovsky DM. Non-Newtonian Flow of Blood in Arterioles: Consequences for Wall Shear Stress Measurements Microcirculation 21: 628:639, 2014

Introduction

Blood is a multiphase, non-Newtonian fluid which exhibits shear-thinning behaviour at low shear rates. It is often simplified as Newtonian, but this results in incorrect predictions of behaviour in blood contacting medical devices, and in diseased arteries, where flow becomes turbulent and eddies orders of magnitude larger than red blood cells (RBCs) are present [1]. The purpose of this project is to consider the multiphase nature of blood and create a numerical model for the design and analysis of medical devices. The aim of this work was to calculate the velocity fields over a backward facing step of two blood analogs, finding the transition in both.

Methods

A backward facing step [2] was modelled using open source finite volume software OpenFOAM. Large eddy simulation (LES) was performed using a Smagorinsky eddy viscosity model as a means to predict transitional flow. A Newtonian and shear-thinning blood analog was considered. The Newtonian analog assumed a constant viscosity µ=0.0035kg/m/s whilst the shear-thinning analog was implemented using a Carreau rheology model with viscosity µ_∞=0.0035kg/m/s [3]. Transitional behaviour was observed by varying the Reynolds number from Re=50 to Re=3400 for both analogs. Velocity fluctuations were plotted over time at the reattachment point to observe the transition to turbulence.   

Results

For Re=50, the recirculation length was reduced by 56% in the shear-thinning analog compared to the Newtonian, in fair agreement with [3] (difference 7%). Velocity traces showed that at low Re both analogs were very similar without fluctuations. Increasing Re to 1200 resulted in small velocity fluctuations for both analogs. At Re=1800 fluctuations were much greater in the Newtonian analog, which was assumed to mean transition to turbulence had occurred. The fluctuations were smaller and less frequent with the shear-thinning analog, assumed to mean transition had not yet occurred. Qualitative comparison of velocity fields showed that the flow fields were the same, but at different Re. 

Discussions

The transition to turbulence was delayed by Re=300 for the shear-thinning fluid. Hence, the velocity fields were similar at Re=1800 and Re=2100 for the Newtonian and shear-thinning analogs respectively. To conclude, accounting for the transition to turbulence using an LES model with a shear-thinning blood analog may clearly present the damaging shear stresses present in transitional blood flow. The shear-thinning property of blood is a result of both RBCs and proteins. Currently the LES method is being extended for multiphase fluids, to include RBCs. The model will be validated experimentally, with the aim of simulating flow through real medical devices.

References

[1] L. Antigua and D. Steinman, (2009). Biorheology, 46(2)

[2] B. F. Armaly et al, (1982). J. Fluid Mech, 127

[3] H. Choi and A. I. Barakat, (2005). Biorheology, 42

Acknowledgements

EPSRC

Introduction: Mitral valve insufficiency (MI) is the second most common acquired heart defect. Due to an impaired function of the mitral valve, blood flows from the left ventricle into the left atrium during systole. Since the heart has to compensate for this regurgitant flow, the left ventricle becomes volume overloaded. Furthermore, the high pressures generated by the left ventricle propagate into the pulmonary circulation causing typical symptoms as pulmonary hypertension and left atrial hypertrophy.

Usually, MI is diagnosed and quantified using transthoracic echocardiography [1]. However, quantification of MI is complex and based on several parameters as for example: the left atrial volume, the regurgitant jet width, the regurgitant jet volume as well as the mitral valve regurgitant orifice area.

In this study, the feasibility of calculating the regurgitant flow across the mitral valve using computational fluid dynamics is investigated.

Methods: Transesophageal echocardiography and computed tomography data of the left heart of a 64 year old female patient were acquired. Using the software ZIBAmira (Version) the patient-specific anatomy of the left ventricle, the left atrium and the beginning of the aorta were segmented manually. The mitral valve was segmented using and automatic segmentation provided by TomTec Arena. While the general shape of both mitral valve leaflets were detected by the shape model based algorithm, the residual gap during diastole had to be specified manually.

Flow simulations were performed using StarCCM+. Blood was modelled as Carreau-Yasuda type fluid [2]. Transient pressure boundary conditions were set at the left ventricle and the left atrium as well as the aorta. To determine, whether the main systolic flow passing through the aorta has an impact on calculation of regurgitant flow across the mitral valve, one additional simulation without the aorta was performed.

Results: The regurgitant volume calculated was 56 ml. The total stroke volume was 101 ml, resulting in a regurgitant fraction of 36 percent. Reducing the model by neglecting the main systolic flow passing through the aorta had no effect on the regurgitant flow across the mitral valve, the value calculated remained 56 ml. This agrees well to the regurgitation reported during echocardiography. Validation against 4D flow MRI is planned, but was not available as of yet.

Discussion: Even though this investigation is limited to one patient as of yet, the results are promising and indicate that simulation of regurgitant blood flow across the mitral valve during systole is feasible. This could allow for a robust assessment of MI and even prediction of changes in MI due to different treatment modalities, since mitral valve repair could be performed on the segmented geometry virtually.

References

1. Monin et al, 2005; DOI: 10.1016/j.jacc.2005.03.064
2. Karimi et al, 2014; DOI: https://doi.org/10.1016/j.jnnfm.2014.03.007

Joint replacements have been performed since the 1960s, the most common being hip and knee implants. Data collected from 2014 shows that, across the EU, on average 319 hip and knee replacements are carried out per 100 000 people. This equates to over 1.6 million surgeries annually. A number of factors including ageing populations, increasing life expectancy and improving joint designs mean that the number of replacement and revision procedures is only set to continue rising.

Current computational models for hip and knee prostheses utilise the Elasto-Hydrodynamic Lubrication (EHL) equations to predict fluid pressure and lubricant film thickness within the joints. Experimental results, show that these models are not solving the problem in its entirety when used to describe synovial joints because of the complex and multi-component nature of the fluid. Synovial fluid is protein rich and these proteins induce complex rheological behaviour which appears to be geometry specific where the length scale of the protein is of the same order as the fluid film thickness. A number of approaches have been considered in the field to improve the accuracy of simulations such as including non-Newtonian behaviour, piezo-viscosity or fluid compressibility, however further improvements are still needed.

It can be seen in the experimental work of others that protein matter collects at the inlet of the lubricated contact area and this aggregated matter drives rheological changes locally within the fluid. In this work, to model this behaviour computationally, protein concentration is tracked using an advection-diffusion equation with modified terms to simulate aggregation. Concentration predictions are used to alter the local viscosity of the fluid via a number of rheological models, giving rise to observed rheopectic behaviour. This study captures the nature of Protein-Aggregation Lubrication (PAL) alongside EHL to obtain computational results that better agree with observed phenomenon.

Arteriovenous fistulas (AVFs) are the preferred type of vascular access to facilitate dialysis. Despite this AVFs suffer from high primary failure rates of 18%–28%¹. Unphysiological flow and complex geometries associated with fistulas are implicated in the initiation of Intimal hyperplasia (IH). Numerous studies employ computational models to identify hemodynamic characteristics responsible for AVF dysfunction. Current research utilises MRI to acquire patient-specific AVF geometries for analysis. Scanning fistulas with MRI requires lengthy scans, making the acquisition of AVF geometries difficult. Such limitations prevent the enrolment of patients into long-term longitudinal studies. Fortunately, AVF geometries can be reconstructed using ultrasound^2,3 which is routinely performed. However, the spatial resolution of ultrasound is considerably lower, resulting in lower quality reconstructions. This study aims to determine the degree to which progressive idealisation of a patient-specific AVF geometry impacts the computational results.

A 3D image stack was obtained of a patient-specific AVF geometry using MRI. Segmentation software was used to compile the image stacks and develop a 3D model. The Vascular Modelling Toolkit was utilised to compute centreline data and record diameter readings from the fistula. These readings were used to recreate a pseudo-realistic AVF model. A second model was created using the mean diameter for the artery and vein, therefore removing tapering. Finally, planar models were developed to examine the impact of torsion on hemodynamics. All geometries were discretised with swept blocking techniques using linear hexahedral elements. Discretisation error was estimated using the grid convergence index method ensuring solution accuracy. Resulting meshes were imported into Star CCM+ for analysis. To replicate pulsatile flow, a parabolic waveform was applied at the arterial inlet. The arterial and venous outlets were modelled using a flow split condition. Blood was modelled as an incompressible Newtonian fluid with a constant density of 1050kg/m³ and a dynamic viscosity of 3.5mPas.

If these geometries adequately capture key hemodynamic features believed to impact AVF dysfunction, ultrasound may be used as a reliable imaging technique for the large-scale acquisition of geometries. A major limitation of computational studies that analyse AVFs is the transverse nature of such analyses. If computational modelling is to contribute in evaluating the physiological response that initiates IH, longitudinal analysis should become the focus, which analyses the morphological and hemodynamic changes during fistula maturation. Ultrasound would greatly reduce the complexity in longitudinal data acquisition. Therefore, allowing hemodynamics at one time point to be correlated to morphological changes at later time points, could aid in identifying the hemodynamic characteristics responsible for AVF maturation and failure.

Acknowledgements

SFI Career Development Award 15/CDA/3323

References

[1] Al-Jaishi., et al.,(2014) AJKD.

[2] McGah, P., et al.,(2013) Biomech Model Mechanobiol.

[3] McGah, P., et al.,(2012) J Biomech Eng.

Introduction

Image-based computer modeling has profound importance to biomedical research.  Generating a computer model from medical image data involves image segmentation that often results in a discrete boundary representation of the anatomy [1]. However, an analytic representation can significantly facilitate engineering design, analysis and computation.  Moreover, if the parameterization is analysis suitable, it can enable direct simulation using isogeometric analysis (IGA). Robustly converting a discrete model into an analysis suitable representation is highly challenging and an active area of research [2]. We present a robust and automated method to convert discrete image-based models, particularly for cardiovascular applications, into analysis suitable CAD representations, and demonstrate resulting IGA analysis.

Methods

Our framework to convert an image-based triangulated surface to a non-uniform rational b-spline (NURBS, the CAD industry standard) volume can be summarized by the following steps: (1) Centerlines of the discrete input model are generated based on an automated cell thinning method (Fig. 1B) creating a graph topology of the model (2) A polycube structure that mirrors this graph topology is generated, providing domains on which NURBS parameterizations can be formed (Fig. 1C). (3) The input model surfaces are partitioned into patches using the centerlines and centroidal voronoi clustering techniques (Fig. 1D). (4) Each model patch is mapped conformally to each polycube patch, while ensuring global consistency. (5) The structured parameterizations on the polycube are then mapped back to the original dataset to provide a structured quadrilateral surface mesh. (6) Interpolation of this surface mesh provides a structured hexahedral mesh volume, which acts as a scaffold onto which an analytic (volumetric NURBS) representation can be formed (Fig. 1E).

Results

The automatic conversion procedure has been tested on a variety of vascular models from vascularmodel.org.  An example demonstrating the ability of the method to provide a quality analytic volume representation is show in Fig. 1. Final volumetric conversions have been verified with quality metrics such as Hausdorff distance. With a volumetric analytic representation, IGA can be performed (Fig. 1F), and we will present examples of IGA simulation of blood flow and compare with finite-element modeling.

Discussion

We have developed a novel and automatic method to convert discrete image-based models into analysis-suitable volumes capable of being used for IGA. Although these methods were developed primarily for vascular models, they can be utilized on non-vascular geometries that have an identifiable centerline structure. Future work includes extending these methods to even more complex anatomies (e.g. aortic dissection).

Acknowledgements

This work was supported by the NSF (award 1407834 and GRFP).

References

1. Updegrove et al. ABME. 45(3), 525-541, 2017.
2. Zhang. Geometric Modeling and Mesh Generation from Scanned Images (Vol 6). 2016.

Background
     Ureteroscopy is a procedure to examine the urinary tract, and is often used for kidney stone removal surgery. Successful ureteroscopy relies on a good intrarenal view, which is in turn dependent on having constant irrigation of the system, both to clear the field of view of debris, and to open up the ureter to provide access for the scope. Successful irrigation is determined by properties of the ureteroscope and the operating room set-up. Mathematical modelling can be used to predict the impact of different ureteroscope designs, as well as the effect of working tools (laser fibres and baskets), on flow.

Methods
     We constructed a mathematical framework, based on systematic reductions of the Navier Stokes equations, to relate pressures and volumetric flow rates throughout the urinary system during ureteroscopic procedures with straight and curved ureteroscopes, with and without working tools. We focused on analysing how working tools and the extent of scope deflection affect the flow rate of irrigation fluid through the ureteroscope. We validated these theoretical models via comparison with wet-lab experiments. Additionally, we considered how having elliptical, instead of circular, cross-sections for the working tools and channel would affect the flow of irrigation, and also modelled the effect of varying the position of the working tool within the channel.

Results
     The model for flow rate in a straight and deflected flexible ureteroscope demonstrated an excellent correlation with the wet-lab findings. The impact of working tools on flow can also be accurately modelled, when considering the working tool to lie non-concentrically within the channel. Elliptically shaped channels and tools lead to higher flow rates under certain conditions.

Discussion
     Mathematical modelling is applied in many industry settings to improve efficiency. Mathematical models can be used to understand the impact of using different ureteroscopic equipment, to optimise the use of existing equipment and to guide the design of the next generation of instruments.

Introduction

Chiari malformation is a neurological disorder where the cerebellar tonsils herniate through the foramen magnum, obstructing and altering normal cerebrospinal fluid (CSF) flow. It is currently unclear why a substantial number of Chiari patients also develop fluid filled cavities (syrinxes) within the spinal cord.

Experimental studies have established that CSF in the subarachnoid space can flow into the spinal cord via perivascular spaces which surround penetrating arteries, driven by arterial pulsations [1]. It is hypothesised that the arteries may act as ‘leaky valves’, varying the resistance to flow over the cardiac cycle [2]. As such, the perivascular flow may depend on the relative timing of the subarachnoid and arterial pressures [2,3]. This study used computational models to characterise how Chiari malformation, with and without a syrinx, influences the subarachnoid CSF pressures and perivascular flow.

Methods

A series of subject-specific CFD models (9 controls, 7 Chiari patients with and 8 without a syrinx) were generated from anatomical and phase-contrast MRI to calculate the subarachnoid CSF pressures. The pressures were applied to an idealised model of the perivascular space to evaluate how variation in the pressure profile affected perivascular flow. The onset of systolic uptake, (relative to the R-wave) measured in the C5 vertebral artery, was used to estimate the phase difference between the arterial and subarachnoid pressures.

Results

The peak pressures in Chiari patients without a syrinx were elevated compared with controls (46% increase; p=0.029), and were shown to occur earlier in the cardiac cycle than both controls (2.58% earlier; p=0.045) and patients with a syrinx (2.85% earlier; p=0.045). The perivascular model showed that on average patients without a syrinx had the greatest net flow into the cord, when systolic uptake occurred 4-10% of the cardiac cycle after the R-wave. Flow measurements found systolic uptake to occur at 4.7±0.2%. The increase in net flow into the spinal cord was related to periods of sustained high pressure occurring earlier in the cardiac cycle (Fig.1; Adjusted R²=0.85; p<0.0001).

Fig.1: Relationship between the timing (A) and magnitude (B) of CSF pressures and the net perivascular flow.

Discussion

These results demonstrate that the temporal offsets required to facilitate the ‘leaky valve’ mechanism are physiologically feasible. Therefore the changes in CSF dynamics introduced by Chiari malformation may increase fluid flow into the spinal cord and contribute to syrinx formation. Additionally, the presence of a syrinx acts to normalise CSF dynamics, which could hinder further syrinx growth.

Acknowledgments

Column of Hope Foundation & NHMRC

References

1. Stoodley, M. A., et al., (1997). J Neurosurg. 86(4) p686.
2. Bilston, L. E., et al., (2010). J Neurosurg. 112(4) p808.
3. Clarke, E.C., et al., (2017). Comput. Meth. Biomech. Biomed. Eng. 20(5) p457.

Introduction

    The investigation of interaction between the inhaled nanoparticles (NPs) and pulmonary membrane can not only reveal the mechanisms for nanoparticles interacting with the pulmonary membrane but also can provide suggestion valuable to nanoparticle design for pulmonary drug delivery.

Method

    A new model of pulmonary membrane containing proteins and cholesterols was established in this work to simulate the transmembrane behaviors of different NPs in different breathing states using the molecular dynamic (MD) method. The coarse-grained (CG) models of three representative NPs in the atmosphere were established, as well as the pulmonary membrane CG model, which contained 1086 CG Dipalmitoyl Phosphatidylcholine (DPPC), 17 cholesterols, and 2 SP-B and 2 SP-C surfactant proteins^[1]. The NPs and the pulmonary membrane were placed in a 20× 40× 80 nm cuboid which contained 46634 CG water and one nanoparticle, as shown in Fig (1), and all simulations were conducted using the MARTINI force filed^[2].

Results

    The simulation results indicated that the Na₂SO₄ NP could translocate across the membrane during the expansion process, but could only absorb on the surface of the membrane during the compression process and in the static state as shown in Fig.2(a). The C₈H₁₄O₂ NP could translocate across the membrane relatively easily in three states while the C NP could not penetrate through the membrane and had remarkable effects on the structure and phase of the membrane (Fig.2(b)). The higher compression pressure increased the difficulty of the C₈H₁₄O₂ NP translocation across the pulmonary membrane. Moreover, it was found the semi-hydrophilic and semi-hydrophobic NPs totally embedded in the membrane while the hydrophobic NP embedded in the membrane partially, but the hydrophilic NP can penetrate through the membrane spontaneously. The hydrophilic NPs had less impact on the membrane no matter it translated across the membrane or not (Fig.2(c)). For the spherical, plated-shaped, and rod NPs, the plate-shaped NP had the best penetration ability and the rod-shaped NP came second. In addition, higher level of the cholesterol content in the membrane could change the fluidity of membrane, and subsequently improve the NP translocation across the pulmonary membrane.

Discussion

    This study has concluded that it is more efficient to translocate across the pulmonary membrane for the smaller hydrophilic NP with plate shape, and it has a smaller impact on the membrane structure. The effects of NP surface properties, shape, and the component of membrane should be comprehensively considered for the impact analysis of haze NPs and the carrier selection for pulmonary drug delivery.

Acknowledgements

National Natural Science Foundation of China (Grant No. 51276013).

References

1. Guoqing H., et al., (2013), Acs Nano, 7(12) p10525

2. Wong-Ekkabut, J., et al., (2008), Nature Nanotech, 3(6) p363

Introduction

Shear induced multimerisation of von-Willebrand-factor (vWF) is supposed to play an important role in coagulation inside extracorporeal membrane oxygenators [2]. However, there is no proof that links observed vWF structures to computed or measured flow conditions.

Methods

The structures of multimeric vWF fibers, observed in clinically used membrane oxygenators is examined using immunofluorescence microscopy (IFM) using Carstairs’ staining method (positive ethics committee vote). The flow around the membrane fibres inside the oxygenator is investigated in terms of shear rate, wall shear velocity and streamlines by using CFD (RANS, Carreau-Yasuda viscosity, geometry remodelled after high-resolution µCT-scans). By interpreting the histological and numerical results in this common context, indications for shear induced coagulation mechanisms can be identified.

Results

The fibre structures of multimeric vWF build regular but not exactly symmetric formations around the contact face (CF) between the crosswise stacked oxygenator fibres (OF), see fig.1B, vWF marked red. Annular around the CF arranged, cells are likely to be found, see fig.1B, nuclei marked blue. The computed streamlines around the OF show attached flow around the circular fibres. However, the irregular arrangement of real OF produce considerable cross flow between the interconnected neighbouring channels, in contrast to previous 2D-simulations. Thus, the CF are washed around closely by blood, also from neighbouring channels. The wall shear velocity streamlines form regular, slightly asymmetric shapes around the contact faces, see fig.1A. The occurring maximum shear rates are in the range of 1,000 1/s.

Fig.1: Wall shear contours and wall-shear-velocity-streamlines around oxygenator fibers from CFD (A) and observed von-Willebrand-factor multimeres (B)

Discussion

The shapes of vWF structures found in clinically used oxygenators match the computational results in terms of wall shear velocity and streamlines well. The accumulation of cells close to the CF can also be explained by fluid mechanics, as there are small shear gradients and slow velocities. However, occurring shear rates between OFs are too low to trigger multimerisation of vWF [1]. That raises the question where in the circuit the actual activation of vWF is started and how, at least partly chained, vWF multimeres are attracted towards the OF surface. A next step will be the investigation of the actual shear rate triggered (or mediated) multimerisation of vWF. Towards this end, microfluidic experiments with shear triggered coagulation will be performed. Also of big interest is the computation of the flow situation in the oxygenator in proximity to chaining threads, which have been ignored in computations so far. However, first a realistic representation of the effective viscosity in computations is needed, which is not available yet.

References

1. Herbig, Diamond, (2015). JThrombHaemost, 13(9)pp1699-1708
2. Malfertheiner, et al., (2016). CritCareMed, 44(4)pp747-754

The contribution of nitric oxide (NO) to myogenic response and vasodilation effects is at the forefront of scientific research in the endeavor of deeply understanding the mechanisms of autoregulation and mechanotransduction control in the vasculature [1]. To this end, we present an augmented model, in order to couple the hemodynamics with solid mechanics of vessel walls combined with the wall shear stress-induced NO production and the complex biochemical path of eNOS release in endothelial cells. In particular, a time-dependent fully coupled model is derived from the fusion of three sub-models, namely a blood flow model for the RBC distribution, a convection-diffusion model for the NO/O₂ transport, and a biochemical model for the synthesis of eNOS. Τhe accurate prediction of wall shear stress (WSS) on the endothelium surface, which is the signal for NO production, is based on a two-phase moving interface model with the rich-in-RBCs core represented by a thixotropic constitutive model, a dynamically adjustable cell-free layer (CFL) thickness, and a porous medium of about 500 nm of thickness, which represents the glycocalyx layer based on the theoretical approach of Shiram et al [2]. We further consider the existence of three additional adjoining connective layers corresponding to endothelium, vascular wall and smooth muscle tissue, which are assumed to be elastic and to exhibit both active and passive response to blood flow. In order to define the activation path of NO into the endothelial cells, we introduce a time-dependent biochemical model incorporating three major synthesis mechanisms including mechanosensing ion channels, integrins, and G protein-coupled receptors. The dynamically shear-induced NO diffusion both into the vessel lumen and to the surrounding tissue is described through a versatile diffusion-reaction model that accounts even for the NO scavenging from the RBCs hemoglobin. An extensive parametric analysis portrays the dynamically related hemodynamics quantities in a complex manner, which originates from the highly nonlinear biphasic transient behavior of eNOS activation and NO production. The radial diffusion model is certainly adequate for elucidating the role of each compartment in the microvessel and its surrounding tissue with regard to NO/O₂ exchange. Vascular wall elasticity was found to present an appreciable implication to WSS variation leading to a new configuration of NO activation and hence a modification to the diffusion and scavenging rates inside the lumen. This novel combination of individual models, which essentially incorporates all the major mechanisms of autoregulation, proves particularly advantageous compared to the existing incomplete models.

References

[1]. Tousoulis D, Kampoli, Tentolouris, Papageorgiou, Stefanadis. The Role of Nitric Oxide on Endothelial Function. Curr Vasc Pharm., 10 4-18, 2012.

[2]. Shiram K, Intaglietta M, Tartakovsky DM. Non-Newtonian Flow of Blood in Arterioles: Consequences for Wall Shear Stress Measurements. Microcirculation 21: 628:639, 2014.

What governs the supply of a human fetus with oxygen from the mother? We address this question with a model of the human feto-placental microvasculature. The physical setup in the human placenta is unique: the maternal and fetal blood supplies are separated by a thin layer of villous tissue (the syncytiotrophoblast), through which oxygen is exchanged by diffusion. Compared to other vasculatures, the capillaries are unusually loopy and bulged. Oxygen transfer from mother to fetus can be estimated using 3D finite-element simulations on realistic geometries obtained from confocal microscopy [1, 2]. However, owing to the computational expense of such calculations, it is infeasible to perform them on entire feto-placental capillary networks. Instead, we introduce a reduced 1D network model to simulate blood flow and oxygen transfer in feto-placental capillary networks efficiently. The model is used to study how network topology and vessel geometry affect oxygen transfer to the fetus.

For model input and validation we use several three-dimensional feto-placental geometries, obtained by confocal microscopy (see Figure 1 below). These geometries allow us to extract properties such as network connectivity, average vessel radius and length, and vessel distance from the villous membrane.

Our model uses the topology and spatial properties extracted from real 3D data to construct a 1D reduction which captures the flow and oxygen transfer of the full 3D geometry, exploiting an approximation derived in [1]. We validate the reduced 1D model against full 3D computational fluid dynamics. In contrast to 3D finite element models, our 1D model reduces flow and transport to linear algebraic equations and has virtually no computational cost. This allows us to relate oxygen transport to different network topologies, different vessel resistances, and to assess the impact of blood rheology on oxygen transport. This reduced 1D flow and transport model of the feto-placental microvasculature may contribute to multiscale models of the placenta and other biological systems.


Figure 1: Pipeline from 3D confocal microscopy (a) to 1D network (c). (a) Image of vascular endothelium from [2]. (b) 3D segmentation of confocal image, with capillary surface shown in yellow and villous surface in blue. (c) Vessel centrelines serve as foundation for spatial statistics and 1D network model.

This work is supported by the UK Medical Research Council grant MR/N011538/1.

References:
[1] Pearce, et al. (2016) PLoS ONE 11(10): e0165369.
[2] Plitman Mayo, et al. (2016) Journal of Biomechanics 49(16), 3780-3787.

Introduction

Fluid homeostasis in the limbs is relevant to numerous pathologies and treatments that have significant impacts on quality of life. For example, edema may arise from elevated vascular pressures due to failure of venous valves, elevated capillary permeability from local inflammation or insufficient fluid clearance by the lymphatic system due to disease or removal of lymph nodes during cancer surgery. Common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy.

Methods

To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of the limb that includes the effects of gravity. Our model is based on a poroelastic representation of the soft tissue where the fluid subvolume is further subdivided into arterial, venous, capillary, interstitial and lymphatic subvolumes. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due the initial lymphatics, and movement through the interstitial space due to gravity and gradients in the interstitial fluid pressure (IFP). A key feature of the model is that the hydraulic conductivity of the interstitial space can increase by orders of magnitude when the soft tissue dilates in response to increases in IFP of only a few mmHg above normal. We have implemented the physics of our model in COMSOL® with a simplified geometry of the lower leg. We can model inflammation by increasing the capillary permeability, lymphatic dysfunction by reducing the fluid clearance by the initial lymphatics, venous valve failure by introducing a hydrostatic pressure gradient in the capillary pressure and a compression wrap with increased boundary pressures.

Results

Figure 1 shows an example result where a compression wrap is used to treat venous valve failure where the capillary pressure increases linearly down the leg due to an uninterrupted standing column of blood in the veins.  

Fig. 1: IFP in mmHg in the leg and foot with venous valve failure without a compression wrap (left) and with a 30 mmHg compression wrap on the dashed region (right). Gravity acts downward.

Discussion

We find that gravity can have dramatic effects on the fluid balance in the limb. Any disturbance that alters the interstitial fluid balance can cause a runaway effect wherein increased fluid leads to increased tissue dilation which in turn increases the hydraulic conductivity. When the hydraulic conductivity increases too much, the swelling which is initially localized can spread vertically throughout the leg due to gravity. The presence of a compression wrap appears to offset this feedback loop. Our example demonstrates that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema in the limb.  

Acknowledgments

NIH grant R01-HL128168