# data[].attributes.body
-Microbubbles are utilized as a ultrasound contrast agent
-In vivo / Ex vivo in rats.
This was done in the mesentery
-The bubble will help with the ultrasound in the area and are also used in drug-delivery
-The bubbles may cause damage to the vessels
-https://asa.scitation.org/doi/full/10.1121/1.4817843

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- laser Doppler anemometry (LDA) measurements
- Left ventricle of jellyfish heart
Study done to enhance understanding of thrombus formation hemolysis in dynamic flow heart prosthesis

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Yos Morsi

Masahisa Kogure

Mitsuo Umezu

Abstract

Thrombus formation and hemolysis have both been linked to the dynamic flow characteristics of heart valve prostheses. To enhance our understanding of the flow characteristics past the mitral position of a jellyfish (JF) valve in the left ventricle under physiological pulsatile flow conditions, in vitro laser Doppler anemometry (LDA) measurements were carried out. The hydrodynamic performance of the JF valve was compared with that of a Bjork-Shiley tilting-disk valve (BS mono). The results indicated that both valves created disturbed flow fields and turbulence shear stress levels in the immediate vicinity and up to 1D (diameter of the valvering) downstream from the valve that were capable of causing lethal damage to blood elements. At a location further downstream, the JF valve showed better hydrodynamic performance than the BS in terms of back flow properties and velocity and turbulence stress characteristics. However, any imperfection in the manufacturing of the valve structure, particularly membrane thickness, adversely affected the performance of the JF valve.

Key words

Artificial heart valve Mitral position Hydrodynamics Pulsatile flow

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References

Schramm D, Baldauf W, Meisner H. Flow pattern and velocity field distal to human aortic and artificial heart valves as measured simultaneously by ultramicroscope anemometry in cylindrical glass tubes. Thorac Cardiovasc Surg 1980; 28(2):133-140

© The Japanese Society for Artificial Organs 1999

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In vitro laser Doppler anemometry of pulsatile flow velocity and shear stress measurements downstream from a jellyfish valve in the mitral position of a ventricular assist device

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Yos Morsi Masahisa Kogure Mitsuo Umezu Thrombus formation and hemolysis have both been linked to the dynamic flow characteristics of heart valve prostheses. To enhance our understanding of the flow characteristics past the mitral position of a jellyfish (JF) valve in the left ventricle under physiological pulsatile flow conditions, in vitro laser Doppler anemometry (LDA) measurements were carried out.

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Statistical wall shear stress maps of ruptured and unruptured middle cerebral artery aneurysms

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Statistical wall shear stress maps of ruptured and unruptured middle cerebral artery aneurysms

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-insilico
-MCA Aneurysms
-ZIBAmira software
-Animal and Human modeling

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1. Introduction

Blood flow-mediated structural changes of the parent vessel and the aneurysmal wall are associated with initiation, growth and rupture of intracranial aneurysms causing subarachnoid haemorrhage (SAH) [ 1]. SAH is associated with high mortality (up to 50%) and morbidity (25-50%) [ 2]. By means of modern non-invasive imaging modalities-three-dimensional rotational angiography (3DRA), computed tomography angiography (CTA) and magnetic resonance imaging (MRI)-more aneurysms without symptoms are detected incidentally. Since the aneurysm treatment options (microsurgical clipping or endovascular coil embolization) are not without risk [ 3], a treatment decision based on rupture risk analysis allows a trade-off between rupture risk and treatment risk and is expected to improve patient outcome. Current efforts focus on two groups of risk parameters: morphometric and haemodynamic [ 4- 7].

Haemodynamic parameters associated with the rupture risk are wall shear stress (WSS) and its derivatives. Based on a longitudinal study, it was hypothesized that aneurysmal growth occurs at regions exposed to low WSS [ 4]. By contrast, high WSS and WSS gradients were correlated with aneurysm initiation in an animal aneurysm model [ 8]. Significantly higher WSS [ 9, 10] and lower WSS [ 6, 11, 12] were both associated with ruptured aneurysms. Even more confusingly, Cebral et al. [ 13] found no correlation at all between WSS and rupture-only the impingement jet size correlated with rupture. Whereas Chien et al. [ 9] found no correlation for these proposed impingement jet parameters. Jou et al. [ 14] also found no correlation between maximum and mean WSS and rupture. They found, however, larger areas with low WSS in ruptured aneurysms. In a recently published analysis of 210 cerebral aneurysms, larger maximum WSS and concentrated inflow jets were observed in ruptured aneurysms [ 5].

Geometric parameters associated with aneurysm rupture are size and shape parameters. Size (aneurysm diameter) is now the only clinically used parameter for risk evaluation and treatment decision validated by the International Study of Unruptured Intracranial Aneurysms (ISUIA) [ 15]. The parameter is, however, controversial. ISUIA found a very low risk of rupture for aneurysms of the anterior circulation smaller than 13 mm. A lot of small aneurysms, however, rupture, whereas some giant aneurysms never rupture [ 16]. In clinical practice, the majority of ruptured aneurysms and unruptured aneurysms needing therapy decisions are of small and medium size (4.0-9.0 mm) [ 6, 7, 17]. This stimulated search and development of other geometric risk parameters, which are well described by Dhar et al. [ 7] and Lauric et al. [ 18]. The results of studies performing rupture risk analysis based on aneurysm morphometry are similarly confusing as the findings of studies based on haemodynamics. The general agreement is that uneven aneurysms are more prone to rupture [ 19].

Our hypothesis is that these controversial findings are due to the absence of a link between haemodynamic parameters and geometric locations. Aneurysm rupture, however, is a locally occurring event. Pathological studies revealed that most cerebral aneurysm ruptures (84% of 396) occur in the dome region (upper third part of the aneurysm height) [ 20, 21]. Only 2 per cent of ruptures take place in the neck region (lower third part). The purpose of this work is to establish and to include analysis of statistical WSS distributions of ruptured and unruptured aneurysm groups fixed in three-dimensional space into the rupture risk analysis. A point-to-point comparison of WSS distributions in different aneurysms is challenging owing to the high variability of aneurysm shapes (round, multi-lobular, elliptic and dumbbell) [ 22]. In order to circumvent this problem, we developed a tool transforming aneurysmal sacs with calculated WSS into a uniform shape. This is done after a uniform alignment of the aneurysms in the three-dimensional space, which is a part of the proposed method. Thereby, the statistical analysis of WSS distributions and the generation of statistical aneurysm shapes in 22 middle cerebral artery (MCA) aneurysms and separately for seven ruptured and 15 unruptured aneurysms became possible. The study was performed with aneurysms of the same location (MCA) as aneurysm site is a known rupture risk parameter [ 15, 17]. To the best of our knowledge, our study shows for the first time statistical WSS maps of ruptured and unruptured aneurysms.

2. Material and methods

During a period of 3 years (2008-2010), 3DRA data were collected from all patients with cerebral aneurysms (more than 90 cases) without vasospasms at the Helios Hospital Berlin-Buch, Department of Neurosurgery. The total database can be seen at http://www.charite.de/biofluidmechanik/downloads/Datenbank.pdf. Cases with vasospasms were not considered because vasospasms may significantly affect the intra-aneurysmal flow [ 23]. 3DRA acquires images of aneurysms with high contrast (signal-to-noise relation) and compared with CTA and MRI with higher space resolution. The geometric data for our study were acquired by means of the digital subtraction AXIOM Artis C-arm system with a rotational acquisition time of 5 s with 126 frames (190° or 1.5° per frame, 1024 × 1024 pixel matrix) with a post-processing using LEONARDO InSpace 3D (Siemens, Forchheim, Germany). Preliminary reconstruction of a volume of interest selected by a neurosurgeon generates a stack of 440 image slices with 512 × 512 pixels in-plane resolution resulting in an isovoxel size around 0.25 mm [ 3]. Thereafter, we performed the voxel labelling using simple thresholding with subvoxel accuracy combined with a region-growing technique [ 24], which implies an intensive manual interaction. The label field was then converted into a triangulated surface using a Marching Cubes [ 25] algorithm, which (surface) is smoothed using the Laplacian algorithm. The smoothing procedure is necessary to remove surface mesh artefacts (staircase effect) [ 3]. The reconstructions were performed using the software ZIBAmira (Zuse Institute Berlin, Germany). The final three-dimensional isosurfaces ( figure 1 a) were approved by the experienced clinician (neurosurgeon) that is considered to be the gold standard of a segmentation procedure [ 26].

Altogether 22 saccular MCA aneurysms acquired during the collection period with 3DRA images of sufficient quality for accurate segmentation were included in the study. Fusiform aneurysms were not included in the study owing to the basically different aneurysm shape. The analysed MCA aneurysms were from 19 patients (five male/14 female) 57.6 ± 10.64 years old (mean± standard deviation (s.d.)). Table 1 summarizes rupture state, patient age and sex, aneurysm radius, mean (time- and area-averaged) WSS and normalized area with WSS below 0.4 Pa, which is associated with rupture risk [ 14, 27]. The averaged radius of aneurysms was 3.17 ± 1.24 mm (mean ± s.d.). Rupture status was identified by the treating neurosurgeon or neuroradiologist. All MCA aneurysms are considered to be bifurcation aneurysms.

A tool to transform individual aneurysms into a uniform spherical shape ( figure 1 b) was developed as a component of the ZIBAmira software. First, the aneurysm sac is manually cut off the parent vessel at the aneurysm neck. The cut-off procedure is done freehand, but nevertheless operator-independent for the uniform shape generation: four operators including one clinician independently performed the cut-off procedure on five aneurysms with a mean radius of 3.35 ± 0.67 mm. The mean error (s.d.) of 0.015 mm or 0.45 per cent of the mean radius of 3.35 mm calculated for five aneurysms treated by four operators is negligible.

The aneurysm sac geometry is then automatically transformed into a spherical shape of identical volume and neck area. A neck plane approximating the neck cross section is computed by minimizing the distances between the aneurysmal neck edge and the plane using the least-squares algorithm ( figure 1 b). Normally, the neck edge has the shape of a saddle. The aneurysmal sac is then sheared such that the mass centre of the aneurysm sac is located perpendicular to the mass centre of the aneurysmal neck calculated at the neck plane ( figure 1 b). The shearing reduces the distortion of the surface at the subsequent projection to the spherical shape. The overall distortion d is defined as the accumulated change of area A over the aneurysm surface, i.e. for a surface consisting of n triangular surface cells t: .

To calculate the radius of the desired sphere, the volume of the aneurysm has to be determined. For that, the open neck area of the aneurysmal sac is closed by projecting each vertex of the edge to the neck plane and triangulating the hole. This closed aneurysm sac is then filled with tetrahedra in order to compute the exact volume and with it the necessary radius r of the sphere. The sphere is fixed in the three-dimensional space by keeping the neck plane and the neck mass centre the same as for original sac. Then, the vertices of the sheared aneurysmal sac together with their WSS data are radially projected onto the uniform sphere keeping the aneurysm volume constant. The projection for any point p is p′ = r × (( p − c)/| p − c|) (figures 1 b and 2 a). Theoretically, with non-convex aneurysm surfaces, this might lead to overlapping spherical shapes causing degenerated cells. However, the radial projection worked without any artefacts for the aneurysms investigated in this study. Figure 1 c shows exemplary WSS distributions of the original sac and the identical data projected onto the corresponding spherical shape.

The next step is the projection of the WSS data (scalar or vector) of all investigated aneurysms onto one sphere with a uniform surface mesh containing 5000 uniformly distributed vertices. For this purpose, each of these 5000 vertices is identified with that point on every aneurysms sphere, to which the distance is minimal. However, for some aneurysms, their spherical representation is closer to a complete sphere than for others. This is due to aneurysms with different aspect ratios (aneurysm height divided by aneurysm neck width), a parameter often used to describe aneurysm sacs [ 7, 16]. As a result, only data from a subset of the aneurysms are available for the neck region of the destination sphere (see §4). If the minimal distance from one vertex of the uniform sphere to a vertex on an aneurysms sphere exceeds a given threshold, this particular aneurysm is ignored for that specific data point (vertex).

The representation of data on the sphere is not favourable for static visualization, because spherical visualization hides the data on the hemisphere not aligned to the viewer. To overcome this drawback, the data represented on the uniform sphere are mapped onto a plane (disc) representation using the azimuthal equidistant projection known from Earth mapping ( figure 1 c). The centre of the two-dimensional disc corresponds to the dome point of the uniform aneurysm sac. This representation is equidistant for two points on a straight line through the centre point. The area distortion increases with increasing distances from the centre. From the sphere construction, the sphere centre point c and the neck plane normal n, defining where 'up' is on the sphere, are known. The point that intersects with n coming from c becomes the centre point of the plane. Any point on the surface is described by a vector p i relative to c with its length l and an angle α relatively defined to a fixed 0° vector corresponding with the 0X vector ( figure 2 b). The length l is measured on the spheres surface: l = ∡( n, p i) × r with r being the sphere radius and the angle given in radian. The angle α is measured between a projection of the vector p i to the neck plane and another arbitrary, but fixed vector parallel to that plane.

Owing to the projection of the original sacs onto a sphere, cell sizes have to be changed. These deformations were assessed in order to measure the deviation of the original aneurysmal sacs from the spherical shape. Finally, the average aneurysm surfaces were generated: all aneurysms and their corresponding spherical surfaces were scaled to an identical radius. Then, displacement vectors from each sphere vertex to its original aneurysm counterpart were computed. These displacements are mapped onto a single sphere and averaged for each of the 5000 vertices. Finally, the vertices on that sphere were transformed (normally shifted) according to the averaged displacements, which results in the mean aneurysm surface.

The statistical map generation needs a uniform alignment of all aneurysmal sacs in the three-dimensional space. During the transformation procedure, all aneurysms are automatically located (moved and rotated) in three-dimensional space in order to fulfil the following requirements: the aneurysm neck plane is aligned with the XY-plane ( figure 3 b) and the centre of coordinates is collocated with the centre of the uniform shape ( figure 1 b). The Z-axis (blue) is directed towards the dome. Then, the aneurysmal sac is rotated manually around the Z-axis in order to align the X-axis (red) with M2a and M2b, bifurcating branches of the first segment of the MCA. The M2a branch is the vessel topologically next to the anterior cerebral artery (ACA; figure 3 b). The direction of the X-axis is selected to be congruent with the axis of M2b. Aneurysms from left and right hemispheres were considered separately. Then, aneurysms of the right hemisphere were mirrored at the interhemispheric plane in order to study all cases together. Medians of WSS values calculated for each vertex of the uniform shape are shown in order to eliminate the impact of outliers owing to the small sample of ruptured cases.

Transient flow was calculated by a fully segregated pressure-based software Fluent 6.3 (ANSYS-Fluent Inc., USA) solving Navier-Stokes equations for incompressible flow. Fluent has been successfully used in biofluid mechanics studies and experimentally validated [ 28, 29]. A surface triangulated mesh with a vessel radius-dependent resolution of 0.15-0.25 mm node distance corresponding to the resolution of the 3DRA acquisition was generated. Then, a high-quality (maximal skewness less than 0.75 and aspect ratio less than 6.0) volume mesh including a boundary mesh layer consisting of three rows of wedges with an increasing depth of wedges by a factor of 1.2 (total depth of 0.3 mm) refining the mesh in the near-wall region was generated. Near-wall mesh refinement warrants the correct calculation of the local WSS. WSS were calculated by partial differentiation of near-wall local velocity fields perpendicular to the corresponding surface elements WSS = μ*(∂(velocity)/∂(↓surface)). The mesh procedure was based on results of our mesh independence study. Flow was assumed to be laminar. The non-Newtonian fluid was modelled using the generalized power-law model including haematocrit dependence [ 30]. All simulations were performed using one waveform obtained from an internal carotid artery (ICA) by means of a phase contrast MRI [ 31] and one mean flow rate of 222 ml min −1 [ 32]. The mean flow rate for the ICA was taken from the literature as patient-specific data were not available. ICA was the inlet segment in all investigated cases. The longest possible segments of ICA ( figure 1) were reconstructed in order to avoid the dependence of results from the reconstructed domain [ 33]. This is crucial owing to the complex course of the cavernous ICA generating swirling secondary flow. The flow ratio ( Q ₁/ Q ₂) at all bifurcations was split according to Murray's Law describing a relation between flow rate and vessel diameter ( Q ∼ d [ 3]), that is validated for cerebral arteries [ 34]. Diameters ( d) of branching segments were measured in three-dimensional reconstructions using the visual ZIBAmira measuring tools. The arterial walls were assumed to be rigid, and a no-slip condition at the wall was used. The pressure value at the outlet was not imposed. A second-order discretization scheme and a SIMPLEC (semi-implicit method for pressure-linked equations-consistent) model for pressure-flow coupling were used. The convergence limit for relative errors was set at 2 × 10 −5 . Unsteady flow simulations were performed through two pulsatile cycles to eliminate the influence of initial transients. Analyses of time-averaged WSS were performed for a second cycle. A small time step of 0.001 s assured a time-step independence of the solution. Statistical WSS maps of aneurysmal sacs were visualized on the two-dimensional planes (discs; figure 1 c) separately for all [ 22], unruptured [ 15] and ruptured [ 7] cases. Furthermore, the dome region corresponding to the upper third part of the uniform aneurysm sphere height was marked. Note that the visualization uses a nonlinear colour map. This is done normally to better visualize small variations. Taking into account the above-mentioned deformation of the cell sizes owing to the mapping procedure, the interpretation of coloured maps should be done with caution. In order to visualize and characterize WSS distributions accurately, we generated WSS histograms. The ranges of WSS values (0−WSS max) were divided into 100 classes. For each WSS class, the area corresponding to the respective class was calculated as the percentage of the total wall surface area of the uniform aneurysmal sac (sphere). Note that changes of cell sizes were taken in account during the area calculations and do not affect histograms. As described above, the whole uniform sphere contains 5000 WSS values, whereas the dome region contains about 1700.

The statistical analysis was performed using the statistical package SPSS V. 19. Significance was assumed at p ≤ 0.05 for all tests. A Kolmogoroff-Smirnov test was performed to assess deviations from a normal distribution. Group differences were assessed by paired t-Student's test in the case of normally distributed data. Otherwise, Mann-Whitney U-test was used in combination with the Levene test proving the equality of variances.

3. Results

The mean WSS of 22 MCA aneurysms ( table 1) varied between 0.28 (case A24) and 6.72 Pa (case A75-G) with a median/mean ± s.e.m. of 1.95/2.64 ± 0.38 Pa. Figure 4 shows statistical WSS maps for all 22 MCA aneurysms and separately for ruptured and unruptured cases.

Analysis of WSS maps for all cases ( figure 4 a) shows that higher WSS are found in two regions: in the neck area collocated with the M2a branch and in the corresponding half of the dome. Maximal values, however, are found in the neck region.

Mean WSSs in ruptured and unruptured aneurysms ( table 1) are not significantly ( p > 0.05) different (Mann-Witney U-test) with medians/means ± s.d.s of 1.85/2.01 ± 1.51 Pa versus 1.99/2.94 ± 1.85 Pa. In contrast, the normalized areas with WSS below 0.4 Pa approaches significance ( p = 0.06) with larger values for ruptured aneurysms (20.8 ± 27.2% versus 5.77 ± 8.48%, Mann-Witney U-test). No significant difference is found between ruptured and unruptured cases for aneurysm radius R (3.32 ± 1.53 mm versus 3.09 ± 1.13 mm). A significant inverse correlation with Pearson's correlation coefficient of 0.48 is seen between normally distributed WSS and radius R with WSS = 5.35 × exp(−0.3 × R) meaning lower WSS in larger aneurysms.

The statistical WSS maps ( figure 4 b) show that a larger continuous area of higher WSS values in the dome region is seen only in ruptured aneurysms. Ruptured aneurysms are also associated with larger areas of low WSS ( figure 4 b,c). WSS maps show geometrically linked differences between ruptured and unruptured aneurysms. A significantly lower WSS is found in ruptured aneurysms (1.4 ± 0.76 Pa versus 2.2 ± 0.66 Pa, p < 0.001) by a paired (5000 vertices of the uniform shape) Wilcoxon test. The same analysis of WSS maps of the dome region (region inside the black circle) reveals again an overall significantly lower WSS in ruptured aneurysms (1.89 ± 0.81 Pa versus 2.1 ± 0.49 Pa, p < 0.001). This result seems to be contrary to the WSS maps shown in figure 4 b. A large area with high WSS values colour-coded by red is seen in the dome region. This is due to the altered visualization of WSS distributions caused by the colour mapping and changes of the cell sizes described in §2. The quantitatively accurate visualization and characterization of WSS maps are done by WSS histograms. Histograms for the whole surface ( figure 4 c) show a left shift of the curve towards lower WSS for ruptured aneurysms (shift of the peak from 2.2 Pa towards 1.0 Pa). Histograms for the dome region ( figure 4 d) reveal a bimodal distribution for ruptured aneurysms with a first peak around 1.0 Pa and a second lower peak around 2.0 Pa. In ruptured aneurysms, both the areas of lower WSS and of higher WSS are larger compared with the histogram of unruptured cases showing only one taller peak around 2.0 Pa.

Figure 5 shows statistical WSS vector fields of 15 unruptured ( figure 5 a) and seven ruptured ( figure 5 b) aneurysms. WSS vector fields of ruptured and unruptured aneurysms are similar with a nearly unidirectional flow in the dome region, with the main flow direction along the X-axis. These WSS vector fields are formed by an intra-aneurysmal flow exemplified by two visualized velocity vector fields of one unruptured ( figure 5 c) and one ruptured ( figure 5 d) MCA aneurysms: the flow stream of the MCA segment directed towards the interhemispheric plane or an M2a vessel segment ( figure 3) enters the aneurysmal sac and forms the aneurysm filling vortex with the vortex core (axis of rotation) aligned with the Y-axis. The ends of the vortex core form critical points (points with zero WSS values). The angle of the stream entering the aneurysmal sac (impingement jet) may vary from case to case, forming a further critical point (impingement area) in the neck or the middle part of the aneurysmal sac ( figure 5).

Figure 6 a depicts the averaged deformations of cell areas owing to the transformation procedure of original sacs into the uniform shape. Deformation maps were also quantified using histograms ( figure 6 b). Unruptured aneurysms show significantly smaller absolute changes of cell areas (1.11 ± 0.15 versus 1.29 ± 0.29, p < 0.01, Mann-Whitney U-test), meaning a significantly larger deviation of ruptured aneurysm from a uniform spherical shape. This is also seen in averaged surfaces of ruptured and unruptured cases ( figure 6 c).

4. Discussion

A systematic review summarizes 24 risk factors associated with aneurysmal rupture [ 35], among them site and size of the aneurysm. Wall stress σ often described [ 7] by a simple Laplace law ( σ ∼ p × R/ s, with the intra-aneurysmal blood pressure p, curvature radius R and wall thickness s) is, however, the ultimate parameter defining the rupture of a vessel wall. The rupture location is a function of wall curvature, thickness, properties (elasticity) of the vessel wall and of the surrounding tissue [ 36]. Wall properties and thickness of vessels and aneurysms are still eluding modern imaging techniques. Nevertheless, aneurysm shape determines intra-aneurysmal flow defining the WSS distribution. WSS and its derivatives in turn determine structural changes [ 37] and hence properties and thickness of the aneurysmal wall defining the wall stress and thereby the rupture site and risk.

Consequently, many attempts were undertaken to correlate haemodynamic parameters with rupture risk [ 5, 8- 14, 38]. Our results reconcile seemingly inconsistent findings in the literature: the correlation of rupture risk with low WSS or larger areas with low WSS [ 11, 12, 14] and, controversially, with larger mean or maximal WSS [ 10, 38]. Analysis of areas with low WSS is highly interesting since aneurysm walls are exposed to significantly lower mean WSS compared with the parent vessel walls [ 6, 11, 22]. It was shown that the dome region is exposed to much slower flow [ 22]. Moreover, nearly stagnant flow was detected in the dome of dumb-bell-shaped and in daughter aneurysms [ 22]. In clinical practice, the dome is regarded as the rupture site [ 20- 22]. The exact threshold defining the range of low (non-physiological) WSS in the case of cerebral aneurysms is not yet exactly defined. In a first approximation, we use a threshold value of 0.4 Pa to define pathological low WSS. Such a threshold is regarded as responsible for endothelial cell dysfunction causing arterial wall remodelling [ 39]. The third group of parameters based on the analysis of intra-aneurysmal flow structure-larger impingement jet size or highly concentrated inflow jet [ 5, 13]-can also be linked to our finding of areas with higher WSS at the dome ( figure 4 b). As we found by statistical analysis that aneurysmal sacs of ruptured aneurysms are exposed to the lower area- and time-averaged WSS. This holds true also for the dome region in spite of the existence of a large uniform area with high WSS values (red coloured area in figure 4 b). Nevertheless, this finding should be considered with caution since the exact rupture sites are unknown and may correlate with areas of high WSS or with areas of low WSS (blue coloured area in figure 4 b) in the dome of ruptured cases. However, in contrast to the pattern in unruptured aneurysms, the statistical WSS map of ruptured aneurysms reveals only one quarter of the dome area exposed to the higher WSS ( figure 4 b). Function and survival of endothelial cells as well as molecular composition of vessel walls depend on the WSS and its derivates like WSS gradients [ 40]. Thus, it might be speculated that large areas with steep transitions between high and low WSS destabilize the aneurysm wall leading to weak points prone to rupture.

Owing to the generation of statistical WSS maps, individual aneurysms were transformed into the uniform shape. However, different aneurysms have different aneurysm aspect ratios (aneurysm height/neck width). As we noted above (see §2), this means that data for the neck region do not exist from all aneurysms. Figure 7 a shows the number of cases used for the statistical mapping of all aneurysms. Note, that for the dome region, all cases were available and could be analysed. This is valid for maps of ruptured and unruptured cases. The dome region is of greater importance, since 84 per cent of rupture sites are located in the upper third of the aneurysmal height [ 20, 21].

Cell size deformations and averaged surfaces ( figure 6) showed that ruptured aneurysms deviate more from the spherical shape. The averaged surface of unruptured aneurysms can be described as a round shape, whereas the shape of ruptured aneurysms can be described as multi-lobular. The deformation map of ruptured aneurysms indicates an area in the dome region corresponding to cells of double or more reduced area. Such regions correspond to lobes or blebs in original sacs. This is consistent with the general experience that aneurysms with more irregular shapes have a higher rupture risk [ 19, 22].

The relevance of WSS maps can be tested by visualizing the averaged WSS vector field. In the case of a high variability of intra-aneurysmal flow fields, as it has been noted in the literature [ 13], the averaged WSS vector field would be of stochastic nature with many critical points with zero WSS and many regions with different flow directions. We consider the relevance of findings based on such a stochastic field as questionable. However, the averaged WSS vector field presented in figure 7 b shows unidirectional flow in the dome underlining the relevance of our findings.

The goal of our study was to develop a method allowing visualization and analysis of averaged 2.5-dimensional fields of saccular aneurysms (distributions on non-plane surfaces), e.g. WSS values. A group of MCA aneurysms served as model population to test the performance and utility of the method. The method consists of three consecutive steps: uniform alignment of aneurysmal sacs in the three-dimensional space, calculation of the uniform (sphere) aligned sac with the centre located at the coordinate centre and projection of fields (e.g. WSS) onto the surface of the uniform shape. In foreground, the method was primarily developed in order to facilitate the retrospective analysis of rupture risk by incorporating locally bounded parameters (e.g. WSS or WSS space gradient) associated with aneurysm rupture. In an individual patient with an incidentally discovered, not yet ruptured aneurysm of small to medium size, it is difficult to decide if that individual aneurysm is prone to rupture. Therefore, a retrospectively validated method of rupture risk analysis is expected to facilitate therapy decisions. The advantage lies in the correlation of geometry data with haemodynamic parameters, e.g. the WSS-the 'link' to the elusive wall properties. The utility of such a rupture risk analysis in clinical practice can only be proven after a validation in a prospective clinical trial. In spite of the encouraging results of the presented study with MCA aneurysms, the advantage expected from the proposed method should be verified first in two further groups of cerebral aneurysms: ICA and anterior communicating artery (AComA) aneurysms. ICA, AComA and MCA aneurysms represent the majority (greater than 80%) of cerebral aneurysms in our clinical practice as well as in the aneurysm populations of other studies [ 6, 15]. Beside the generation and visualization of statistical WSS maps in a generalized manner ( figure 6) as done in our study, the method allows a point-to-point comparison of different patient-specific 2.5-dimensional fields. The alignment of aneurysmal sacs allows the generation of statistical shapes. In this study, we used a simple technique generating statistical shapes ( figure 6 c) of ruptured and unruptured aneurysms by averaging of local radii. Further statistical shape models may be generated as reviewed by Heimann & Meinzer [ 41]. Finally, a comparison of original and uniform sacs allows a development of new parameters to characterize aneurysm unevenness, which is associated with the rupture risk [ 7, 16, 18]. In this study, we analysed changes in cell size owing to projection ( figure 6 a). Further parameters as a Hausdorff distance [ 42] measured between surfaces of original and uniform shapes are under evaluation.

(a) Study limitations

With 22 cases, the number of investigated MCA aneurysms is limited. This is, however, a relatively large number for a CFD study of cerebral aneurysms of one vessel site. We know of only two other CFD studies in cerebral aneurysms of a defined location with study populations similar to our study: 20 MCA [ 11] and 26 AComA aneurysms [ 38]. Other studies contain significantly lower numbers of investigated cases (e.g. eight ICA-ophthalmic artery aneurysms [ 27]).

Patient-specific CFD calculation of WSS has some methodological limitations owing to information that is missing in clinical practice, (e.g. volume flow in the ICA). The acquisition technique with a segmentation and reconstruction procedure generating geometries has the greatest impact on simulation results in haemodynamic studies. We used a relatively simple segmentation technique. Some better segmentation techniques are available [ 18, 26]. There is, however, a direct correlation between the quality of vessel segmentation and the resolution of the acquisition method [ 18]. Since we used high-resolution image data obtained from 3DRA with a mean isovoxel size of 0.25 mm [ 3], the development of a complex segmentation technique was not necessary. Geers et al. [ 43] compared haemodynamic parameters in aneurysm reconstructions based on 3DRA or CTA images of the same patients. They concluded that although relatively large differences were found for quantitative haemodynamic parameters, the main flow characteristics were reproduced in the geometries obtained by both imaging techniques. The quantitative differences were produced by different flow rates at the aneurysm site owing to missing small (less than 1 mm diameter) branches in the CTA reconstructions. Our CFD model uses patient-specific vessel and aneurysm anatomy, pulsatile flow, and a non-Newtonian blood model with the patient-specific haematocrit. The inflow rate and waveform were based on literature data. Phase contrast MRI measurements found a relatively low difference of about 5 per cent between measured and literature data [ 44]. Flow rates of branches were calculated following Murray's Law or geometric information instead of the real, but unknown resistance of the peripheral vascular bed. Waveforms were found to be very important for time-varying parameters, as oscillating shear stress index (OSI) or standard deviation of the WSS [ 44]. Consequently, we analysed only time-averaged WSS, known to be independent from the limitations and assumptions of our study, as it was shown in other investigations [ 10, 13, 29, 45]. Finally, rigid vessel walls were assumed. Wall displacements measured in vivo are relatively small (0.2-0.3 mm) [ 46]. Simulations with compliant walls using fluid-structure interaction found a negligible impact of compliant walls on the calculation of the time-averaged WSS [ 47].

5. Conclusion

For the first time, statistical WSS maps and averaged surfaces in ruptured and unruptured aneurysms were visualized. Especially, the significant differences in the dome region (lower overall WSS in ruptured cases with larger areas with steep WSS transition), known to be associated with aneurysm rupture, show that the new analysis technique has predictive power that should be examined more closely in future studies. The differences in WSS distributions in ruptured and unruptured aneurysms visualized in a statistical manner help to better understand rupture risk parameters and can explain controversial findings in the literature. Rupture risk analysis is significantly improved owing to the statistical map linking WSS data to corresponding aneurysmal surface locations and owing to the separate consideration of the dome region. Next, we plan to perform similar analysis on other vessel sites (ICA and AComA) of the cerebral circulation.

Acknowledgements

This study was supported by the German Research Foundation (DFG project KE 900/9-1). We also thank Dr E. Wellnhofer from German Heart Institute of Berlin for supporting our statistical analysis.

Footnotes

References

# data[].attributes.attachment_link.title
Statistical wall shear stress maps of ruptured and unruptured middle cerebral artery aneurysms

# data[].attributes.attachment_link.description
Blood flow-mediated structural changes of the parent vessel and the aneurysmal wall are associated with initiation, growth and rupture of intracranial aneurysms causing subarachnoid haemorrhage (SAH) [ 1]. SAH is associated with high mortality (up to 50%) and morbidity (25-50%) [ 2].

# data[].attributes.body
- Fix erectile dysfunction
-THE penis
-To target the blood flow and study how pressure difference influences penis circumference
- More successful management of patients
- Limited number of patients available to study because of requirements required for the study

# data[].attributes.body
-Migrations of the stagnation points on the bottom of the anastomoses at mean Reynolds numbers
-transparent 1:1 casted replicas of distal vascular graft anastomoses created by conventional technique, Miller-cuff, Taylor- and Linton-patch were fabricated
-Vascular surgery
-To investigate flow patterns in four anastomotic types of femoral end-to-side distal bypass graft anastomoses
-Advantages: Miller-cuff has a wider cavity which shows the lower shift of the bottom stagnation point

https://www.sciencedirect.com/science/article/pii/S1078588498908024

# data[].attributes.body
Method: 2d model with immersed boundary, used Navier-Stokes Theorem, Lagrangian mesh
Area: sperm/bodily fluids
Purpose: to better understand mammalian reproduction and the roles of flagellar and ciliary beating
Advantage:
Disadvantage:
Information:

# data[].attributes.body
compare accepted CT angiography data to CT, MRI, 3DRA.
Test accuracy of these different methods

# data[].attributes.attachment_link.readable_text
J Neurol Surg A Cent Eur Neurosurg 2013; 74(05): 294-302
DOI: 10.1055/s-0033-1342937

Georg Thieme Verlag KG Stuttgart · New York

1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany

1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany

1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany

2  Scientific Visualization, Konrad Zuse Institute, Berlin, Germany

2  Scientific Visualization, Konrad Zuse Institute, Berlin, Germany

3  Department of Neurosurgery, Helios Hospital Berlin-Buch, Berlin, Germany
› Author Affiliations
Further Information

Abstract

Background and Study Aims Image-based computational fluid dynamics (CFD) provides a means for analysis of biofluid mechanical parameters of cerebral aneurysms. This may enable patient-specific rupture risk analysis and facilitate treatment decisions. Application of different imaging methods may, however, alter the geometrical basis of these studies. The present study compares geometry and hemodynamics of an aneurysm phantom model acquired by means of magnetic resonance imaging (MRI), computed tomography (CT), and rotational angiography (3DRA).

Materials and Methods The phantom model of a basilaris artery aneurysm was fabricated based on data generated by CT angiography. This model underwent imaging by means of CT, MRI, and 3DRA. We compared the geometrical reconstructions using the original dataset with those obtained from CT, MRI, and 3DRA. Similarly, CFD analyses were performed using the four reconstructions (3DRA, MRI, CT, and original dataset).

Results MRI and the 3DRA-based reconstructions yield mean reconstruction errors of 0.097 mm and 0.1 mm, which are by a factor of 2.5 better than the CT reconstruction. The maximal error for the aneurysm radius (7.11 mm) measurement was found in the 3DRA reconstruction and was 3.8% (0.28 mm). A comparison of calculated time-averaged wall shear stress (WSS) shows good correlations for the entire surface and, separately, for the surface of the aneurysmal sack. The maximal error of 8% of the mean WSS calculation of the whole surface was found for the CT reconstruction. The calculations of the aneurysmal sack mean WSS from the MRI reconstruction were estimated to have a maximal error of 7%.

Conclusion All three imaging techniques (CT, MRI, 3DRA) adequately reproduce aneurysm geometry and allow meaningful CFD analyses.

Keywords

cerebral aneurysm - geometry reconstruction - computational fluid dynamics - wall shear stress

# data[].attributes.attachment_link.title
Thieme E-Journals - Journal of Neurological Surgery Part A: Central European Neurosurgery / Abstract

# data[].attributes.attachment_link.description
J Neurol Surg A Cent Eur Neurosurg 2013; 74(05): 294-302DOI: 10.1055/s-0033-1342937 Georg Thieme Verlag KG Stuttgart · New York 1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany 1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany 1  Biofluid Mechanics Laboratory, Charité - Universitätsmedizin Berlin, Berlin, Germany 2

# data[].attributes.body
-3D Computer Modeling
-Data collected from patients undergoing Radioembolism set parameters for the simulation of blood vessels.
-The Hepatic Arterial System
-Understand blood flow when a tumor is present in the arterial system.
-Advantage: no need for a real person.
-Disadvantage: model may not apply to all cases.
https://www.sciencedirect.com/science/article/pii/S0360301609027205

# data[].attributes.headline
In silico modeling to predict drug-induced phospholipidosis

# data[].attributes.subject
In silico modeling to predict drug-induced phospholipidosis

# data[].attributes.body
-in silico quantitative structure–activity relationship (QSAR) modeling
-Quantitative structure–activity relationships (QSAR) are mathematical relationships linking chemical structure and pharmacological activity in a quantitative manner for a series of compounds. Methods which can be used in QSAR include various regression and

pattern recognition

techniques.
-predict drug-induced phospholipids
-Advantages: Provides invaluable data only easily obtainable with in silico testing
-https://www.sciencedirect.com/science/article/pii/S0041008X13001063?via%3Dihub

# data[].attributes.headline
Reproducibility of Image-Based Analysis of Cerebral Aneurysm Geometry and Hemodynamics: An In-Vitro Study of Magnetic Resonance Imaging, Computed Tomography, and Three-Dimensional Rotational Angiography

# data[].attributes.subject
Reproducibility of Image-Based Analysis of Cerebral Aneurysm Geometry and Hemodynamics: An In-Vitro Study of Magnetic Resonance Imaging, Computed Tomography, and Three-Dimensional Rotational Angiography

# data[].attributes.body
-computational fluid dynamics (CFD) modelling using Navier-Stokes equation
-steady laminar flow was simulated in reconstructions; blood was modeled as a non-Newtonian fluid;
-model of aneurysms in the brain
-purpose is to model cerebral aneurysms and compare different imaging methods of phantom models
-advantages: easily compare models to see if which imaging device is the best or if any alter the geometry of the aneurysm in any way
-disadvantages: doesn't propose a solution or have a way to treat the differences

# data[].attributes.headline
Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid–structure interaction approach

# data[].attributes.subject
Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid–structure interaction approach

# data[].attributes.body
In Silico
Method - Fluid Structure Interaction (FSI) Method
How - model created using GAMBIT software, using finite volume coding
Area of Body - heart valve
Purpose - showing how to reproduce the effects of a 27 mm mechanical heart valve
Advantage - "modeling a more realistic geometry"
Disadvantage - there was a much smaller magnitude gap between the fluid and the valve that was manufactured

# data[].attributes.attachment_link.readable_text
JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page.

Abstract

The main purpose of this study is to reproduce in silico the dynamics of a bileaflet mechanical heart valve (MHV; St Jude Hemodynamic Plus, 27 mm characteristic size) by means of a fully implicit fluid-structure interaction (FSI) method, and experimentally validate the results using an ultrafast cinematographic technique. The computational model was constructed to realistically reproduce the boundary condition (72 beats per minute (bpm), cardiac output 4.5 l/min) and the geometry of the experimental setup, including the valve housing and the hinge configuration.

The simulation was carried out coupling a commercial computational fluid dynamics (CFD) package based on finite-volume method with user-defined code for solving the structural domain, and exploiting the parallel performance of the whole numerical setup. Outputs are leaflets excursion from opening to closure and the fluid dynamics through the valve.

Results put in evidence a favorable comparison between the computed and the experimental data: the model captures the main features of the leaflet motion during the systole. The use of parallel computing drastically limited the computational costs, showing a linear scaling on 16 processors (despite the massive use of user-defined subroutines to manage the FSI process). The favorable agreement obtained between in vitro and in silico results of the leaflet displacements confirms the consistency of the numerical method used, and candidates the application of FSI models to become a major tool to optimize the MHV design and eventually provides useful information to surgeons.

Keywords

Cardiovascular biofluid mechanics

Fluid-structure interaction

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# data[].attributes.attachment_link.title
Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach

# data[].attributes.attachment_link.description
JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. The main purpose of this study is to reproduce in silico the dynamics of a bileaflet mechanical heart valve (MHV; St Jude Hemodynamic Plus, 27 mm characteristic size) by means of a fully implicit fluid-structure interaction (FSI) method, and experimentally validate the results using an ultrafast cinematographic technique.

# data[].attributes.body
-In silico
-Time resolved 3D-PIV technique used for measuring near wall flow field measurements
-Uses diffuse, monochromatic full-field illumination and optical flow algorithm to estimate near wall flow
-Circulatory system
-Advantage: more limited to near wall region through the use of a molecular dye
-Disadvantage: new technique

# data[].attributes.attachment_link.readable_text
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 106)

Abstract

This chapter describes the development of a new time resolved 3D PIV technique for near wall flow field measurements. This measurement technique, called wall-PIV, is based on Beer-Lambert's law. It substitutes the classical PIV laser sheet by a diffuse, monochromatic full-field illumination that is limited to the near wall region by an absorbing molecular dye in the fluid. Aimed range of applications is the investigation of flow fields next to one- or two dimensionally curved, possibly flexing surfaces. The three dimensional three component flow estimation uses a new optical flow algorithm, based on particle trajectories. Results of the measurement technique's application on a displacement pediatric blood pump are presented.

Keywords

Particle Image Velocimetry Wall Shear Stress Wall Shear Rate Tomographic Particle Image Velocimetry Wall Flow

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

1. Ethier, C.R., Steinman, D.A.: Exact fully 3D navier-stokes solutions for benchmarking. International Journal for Numerical Methods in Fluids 19(5), 369-375 (1994)

2. Hui, W.H.: Exact solutions of the unsteady two-dimensional navier-stokes equations. Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 38(5), 689-702 (1987)

3. Subramanian, G., Brady, J.F.: Trajectory analysis for non-brownian inertial suspensions in simple shear flow. Journal Of Fluid Mechanics 559, 151-203 (2006)

Authors and Affiliations

1. 1. Biofluid Mechanics Laboratory Charité - Universitätsmedizin Berlin

2. 2. Digital Image Processing Research Group, Heidelberg Collaboratory for Image Processing University of Heidelberg Heidelberg

# data[].attributes.attachment_link.title
The Wall-PIV Measurement Technique for Near Wall Flow Fields in Biofluid Mechanics

# data[].attributes.attachment_link.description
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 106) This chapter describes the development of a new time resolved 3D PIV technique for near wall flow field measurements. This measurement technique, called wall-PIV, is based on Beer-Lambert's law.

# data[].attributes.body
-heart pulsed flow simulator
-ventricle made of transparent silicone rubber connected to test valves and a standard 23 mm aortic value in mitral and aortic positions respectively in a way that they could open and close freely with flow
-heart
-to see how the profile height of the mitral bioprosthetic valve changes the blood flow behavior
-this method allows for a close model to actual blood flow in vivo and allows for various sized bioprosthetic valves to be tested
-this model is not involving the factors of platelet activation and aggregation which may result in high shear rates and deformation, so additional tests need to be done to establish the true character of the bioprosthetics

https://journals.lww.com/asaiojournal/Fulltext/2006/01000/An_In_Vitro_Study_of_Changing_Profile_Heights_in.7.aspx

# data[].attributes.body
https://www.sciencedirect.com/science/article/pii/S0041008X13001063?via%3Dihub

# data[].attributes.headline
The fluid mechanics of root canal irrigation

# data[].attributes.subject
The fluid mechanics of root canal irrigation

# data[].attributes.body
https://iopscience.iop.org/article/10.1088/0967-3334/31/12/R01/meta

-In Vitro
Method- Observing differing stagnation points with different insertion needles and methods
-Teeth, specifically the roots and canals inside the tooth
-Advantage- By maintaining a constant volume flow rate and with side-discharging needles, the effectiveness of canal cleaning is increased.
-Disadvantage- There remains a lack of clarity about the mechanisms of irrigant delivery, replenishment, mixing, flushing and wall erosion of the tooth

# data[].attributes.attachment_link.readable_text
Ulrich Kertzscher,

Torsten Schneider,

Leonid Goubergrits,

Klaus Affeld,

Daniel Hänggi,

Andreas Spuler

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Abstract

Background

Cerebral arterial vasospasm leads to delayed cerebral ischemia and constitutes the major delayed complication following aneurysmal subarachnoid hemorrhage. Cerebral vasospasm can be reduced by increased blood clearance from the subarachnoid space. Clinical pilot studies allow the hypothesis that the clearance of subarachnoid blood is facilitated by means of head shaking. A major obstacle for meaningful clinical studies is the lack of data on appropriate parameters of head shaking. Our in vitro study aims to provide these essential parameters.

Methodology/Principal Findings

A model of the basal cerebral cistern was derived from human magnetic resonance imaging data. Subarachnoid hemorrhage was simulated by addition of dyed experimental blood to transparent experimental cerebrospinal fluid (CSF) filling the model of the basal cerebral cistern. Effects of various head positions and head motion settings (shaking angle amplitudes and shaking frequencies) on blood clearance were investigated using the quantitative dye washout method. Blood washout can be divided into two phases: Blood/CSF mixing and clearance. The major effect of shaking consists in better mixing of blood and CSF thereby increasing clearance rate. Without shaking, blood/CSF mixing and blood clearance in the basal cerebral cistern are hampered by differences in density and viscosity of blood and CSF. Blood clearance increases with decreased shaking frequency and with increased shaking angle amplitude. Head shaking facilitates clearance by varying the direction of gravitational force.

Conclusions/Significance

From this in vitro study can be inferred that patient or head shaking with large shaking angles at low frequency is a promising therapeutic strategy to increase blood clearance from the subarachnoid space.

Citation: Kertzscher U, Schneider T, Goubergrits L, Affeld K, Hänggi D, Spuler A (2012) In Vitro Study of Cerebrospinal Fluid Dynamics in a Shaken Basal Cistern after Experimental Subarachnoid Hemorrhage. PLoS ONE 7(8): e41677. https://doi.org/10.1371/journal.pone.0041677

Editor: Robert Loch Macdonald, St Michael's Hospital, University of Toronto, Canada

Received: March 15, 2012; Accepted: June 24, 2012; Published: August 1, 2012

Copyright: © Kertzscher et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: No current external funding sources for this study.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Despite the elaborate current treatment strategies, cerebral arterial vasospasm leading to delayed cerebral ischemia constitutes the major delayed complication following aneurysmal subarachnoid hemorrhage (SAH). Vasospasm is associated with significant morbidity and mortality rates [1]. Independent predictors of cerebral vasospasm are clot volume in the subarachnoid space [2], [3] and clot clearance rate [4]. Being a function of the amount of subarachnoid blood, the incidence of vasospasm can be reduced by increasing blood clearance from the basal cerebral cisterns. This can be achieved by means of increased perfusion of the subarachnoid space with CSF alone [5] or combined with intracisternal thrombolysis [6].

Clearance of cisternal blood may also be facilitated by repeated head motion. Two different head motion strategies, translational movement [7], [8] and bidirectional rotation [9], have been applied clinically. Since in these studies head motion was combined with an intensified lumboventricular lavage [9], the contribution of bidirectional rotation to the clearance of the subarachnoid space is difficult to dissect from the effect of increased CSF flow. Furthermore, none of the studies of head motion investigated variations of head shaking parameters.

The aim of our study was to define clinically applicable settings for effective head shaking. Using a quantified dye washout technique in vitro, we visualized and analyzed CSF flow and cisternal blood clearance in the central basal cistern. In order to understand the basic blood washing process in the basal cistern, we investigated the clearance of a blood model during head shaking with a steady net CSF flow.

Materials and Methods

Phantom Model of the Basal Cistern

The study complies with the declaration of Helsinki. The study was done in a model constructed from human magnetic resonance imaging data of the brain. All data are from one single human who is co-author (DH) and gave written voluntary informed consent. Approval was given by the ethic committee of the Heinrich-Heine-University Düsseldorf, Germany. The model of the basal subarachnoid cistern consists of the prepontine cistern, the pontocerebellar cistern, and the pentagonal cistern. It was fabricated using a stereolithography (STL) geometry. Magnetic resonance imaging (MRI) data were acquired from the above mentioned healthy 35-year-old male volunteer using a 1.5 T scanner (Magnetom Avanto™, Siemens, Erlangen, Germany) by means of a spin echo (SE) sequence (sequence variant SK) with a slice thickness of 2.4 mm, a repetition time (TR) of 4,000.0 ms, and an echoing time (TE) of 250.0 ms. Data acquisition resulted in a stack of 180 slices with a voxel resolution of 0.82 mm×0.82 mm×1.2 mm. Three-dimensional segmentation of the subarachnoid cistern was done using the software Mimics™ (Materialise NV, Leuven, Belgium) ( Figure 1).

Segmentation was performed manually based on boundaries defined primarily by automatic segmentation using intensity signal thresholding. Finally, the reconstructed geometry was converted into a STL file format. This geometry served as physical model in our experimental study ( Figure 2A and B). The volume of the experimental basal cistern was 20 ml. Sizes of the cistern (length and width) are indicated in Figure 2B. Mean depth of the cistern was approximately 10 mm.

From the reconstructed surface geometry (STL file) a 1∶1 wax cast was fabricated by means of a rapid prototyping printer thermojet (PORTEC, Zella-Mehlis, Germany) with a spatial resolution of 0.1 mm ( Figure 2C). Thereafter, a transparent silicone phantom model of the basal cistern was generated as block cast. For this, the wax model with ducts representing the CSF inflow and outflow tracts was embedded in a mixture of Elastosil™ RT 601 A and B (Wacker Chemie, Munich, Germany). Inflow and outflow tracts were mounted along the longitudinal axis of the cistern model at the narrowest regions of the boundaries of the reconstructed basal cistern geometry. Inside diameters of inflow and outflow tracts were 4 mm each. The diameters were selected according to the cross-sectional areas at the respective regions (basal cistern inflow/outflow) identified on the MRI data. The wax was melted out in a furnace at 150°C resulting in the transparent silicone model of the basal cistern ( Figure 2D).

Experimental Setup

The study was performed in a custom-built experimental setup ( Figure 3). The setup was designed to allow flow visualization simultaneously with simulated head shaking: light source, phantom model and camera were combined in a rigid rotatable construction. The axis of rotation (x-axis) parallel to the horizon and the (longitudinal) center of the cistern model were mounted with an offset of 0.15 m to the longitudinal axis of the basal cistern (head) model ( Figure 3). The setup permitted an engine driven shaking with different speeds and different shaking angle amplitudes φ max. The assembly transmitting the drive mechanics into the shaking motion emulated sinusoidal deflection curves. Rotation of the cistern model around the y-axis ( Figure 3, right) simulated three head (patient) positions: α = 0° - supine patient with slightly reclined neck and x-axis of the basal cistern parallel to the axis of rotation, α = 30° - supine patient with normal head position and x-axis of the basal cistern deviating 30° from the axis of rotation, and α = 90° - semi-sitting patient and x-axis of the basal cistern deviating 90° from the axis of rotation.

Experimental CSF was a mixture of distilled water with glycerin in a concentration of 43.7% (by weight) glycerin, whereas experimental blood was a mixture in a concentration of 70.0% (by weight) glycerin.

This specific composition of the mixtures offers three major advantages: First, experimental CSF and blood have the same density ratio (ρ CSF/ρ blood) of 0.95 as known for physiological CSF and blood [10]-[12] at a temperature of 37°C (ρ CSF = 1.000 kg/l and ρ blood = 1.048 kg/l). Second, the refractive indices of experimental CSF (n = 1.3891) and experimental blood (n = 1.4274) measured with the refractometer DR201-95™ (A. Krüss Optronic, Hamburg, Germany) sufficiently approximate the refractive index of silicone (n = 1.409, manufacturer information). Third, one hour of in vitro measurement corresponds to four hours in vivo taking into account the laws of dimensionless flow similarity. This accelerates the time-consuming tests. The same scaling is valid for the shaking frequency: a frequency of 10 rpm in vitro is equivalent to 2.5 rpm in vivo. In vitro time scaling was achieved by increasing viscosities and flow rates according to the dimensionless Reynolds (Re  =  U. L/ν) and Strouhal (St  =  L/U. T) numbers with U as characteristic (mean) velocity (m/s), L as characteristic length of the flow model (m), ν as kinematic viscosity of the test fluid (m ²/s), and T as characteristic flow time (s). The resulting kinematic viscosities of experimental CSF and blood were 3.40·10 −6 m ²/s and 15.80·10 −6 m ²/s respectively at 24°C, the temperature of the fluids during experiments. Kinematic viscosities of the test fluids were measured by means of a SCHOTT Ubbelohde Viscometer™ 50101/0a and Ia (SCHOTT Instruments, Mainz, Germany) with a device accuracy of 1%. In vivo kinematic viscosities depend on various parameters (e.g. hematocrit, protein content and temperature) and were assumed to approximate 0.75·10 −6 m ²/s for CSF [13] and 3.50·10 −6 m ²/s for blood [14]. Thus, the ratio of CSF and blood viscosity is in vitro the same as in vivo (0.75∶3.50 and 3.40∶15.80).

The experimental setup allows also experiments simulating the pulsatile nature of CSF flow [15]. For this purpose a sinusoidal CSF flow was superimposed to the net flow at the inflow duct. The sinusoidal flow pulse was generated by means of a linear motor PS01-48×240F-C™ (LinMot™, NTI, Switzerland) attached to a 20 ml Original-Perfusor™ syringe (B. Braun, Melsungen, Germany) filled with experimental CSF ( Figure 3). A sinusoidal pulse with an in vitro frequency of 4 Hz (corresponding 1 Hz in vivo) and an in vitro amplitude of CSF flow rate of 4 ml/s (1 ml/s in vivo) was used according to CSF flow curves observed in phase-contrast MRI measurements [16] and used in a numerical study of CSF flow [17].

Dye Washout and Data Analysis

First, two reference experiments "CSF-washout" and "Blood-CSF-diffusion" were performed. The first experiment "CSF-washout" serves as the reference allowing a comparison of blood clearance with the dynamics of the CSF replacement without additional blood. The second reference experiment evaluates the impact of the diffusion between two fluid models (CSF and blood) affecting the kinematics of the CSF/blood mixing process. Second, experiments with eight different settings simulating blood washout were done ( Table 1).

The CSF-washout reference experiment with experimental CSF alone i.e. without injection of experimental blood was performed as follows: The cistern model was filled with dyed experimental CSF. Dye in a concentration of 0.5 g/kg (100% of dye concentration) of the food coloring dye Patent Blue V™ (Schumann & Sohn, Karlsruhe, Germany) was used. A syringe pump (Perfusor Secura™, B. Braun, Melsungen, Germany) generated flow of non-dyed experimental CSF with a rate of 80 ml/h. The flow rate was calculated taking into account the physiological CSF net flow rate of approximately 20 ml/h [18] and Reynolds similarity.

The model was illuminated from the backside by diffuse light emitted from a custom-made panel of "cold white" light-emitting diodes (ASMT-QWBB™, Avago Technologies, San José, CA USA). Light intensity was adjusted to avoid overexposure and to utilize the full range of illumination dynamics (gray values between 0 and 255). Washout was recorded by a charge-coupled device (CCD) color video camera (UI 6250SE-C™, IDS Imaging Development Systems, Obersulm, Germany) with a resolution of 1600×1200 pixels, a manually adjusted constant white balance and an exposure time of 21 ms.

In experiments with SAH modeling, the basal cistern model was filled with non-dyed experimental CSF first. Thereafter, 10 ml of dyed experimental blood (0.5 g/kg dye concentration) was injected with a flow rate of 100 ml/h into the cistern model ( Movie S1). This injection was generated by means of a syringe pump (R100EC™, Razel Scientific, St. Albans, VT USA) in order to minimize the variability of initial experimental conditions. Shaking and washout with non-dyed experimental CSF (flow rate of 80 ml/h) were started and recorded ( Movie S2) simultaneously. Experimental setup and settings of the camera and light source were the same as in the reference experiments. In vitro data acquisition time was one hour (corresponding to four hours in vivo).

Image analysis by means of MATLAB™ (The MathWork, Natick, MA USA) consisted in converting color images into gray scale images (gray values ranging from 0 to 255), setting the region of interest (ROI), averaging grayscale values in the ROI for each image, normalizing (0-1) the gray values according to images with 100% and 0% dye concentration, and smoothing the results by averaging periods of 1 min recording. A normalized gray value of 1 represents light absorption of the model completely filled with undiluted dyed experimental blood (100% dye concentration). A normalized gray value of 0 was assigned to the absorption of the model filled with non-dyed experimental CSF. Normalized gray values of 50%, 25% and 12.5% experimental blood concentration were determined in additional experiments because of the non-linear relationship between normalized gray value and dye concentration.

The resulting curve of the "CSF-washout" reference experiment (Exp. 9) describes washout (replacement) of CSF. In the other experiments, the curves describe mixing of CSF and blood combined with blood washout. The dye washout process of CSF was characterized by two periods: half dye time, which is the period to achieve a gray value corresponding to a dye concentration of 50% in the calibration (normalized gray value of 0.90), and quarter dye time, which is the period between half dye time and time to achieve a gray value corresponding to a 25% of the dye concentration (normalized gray value of 0.81).

There is an important difference between the reference experiment and blood washout experiments: The reference experiment starts with a normalized gray value of 1, i.e. 100% of the dye concentration in 20 ml of CSF. The injection of 10 ml experimental blood with a dye concentration of 100% simulated SAH. In the case of full mixing between experimental dyed blood and non-dyed CSF, the resulting normalized gray value would correspond to 50% dye concentration or a normalized gray value of 0.90. Blood injection, however, does not result in full homogeneous mixing with CSF. In the worst case (no mixing), half of the model's projected area (i.e. the ROI) represents dyed experimental blood (normalized gray value of 1) and the other half represents a non-dyed CSF model (normalized gray value of 0). In this case, the resulting mean normalized gray value (averaged over ROI) is equal 0.5.

After the blood washout was started, the mixing process first results in an increase of the normalized gray value meaning a homogenization of the blood/CSF mixture. Therefore, the curves for blood clearance are characterized by the mixing time T M - the time during which the normalized gray value is increasing or constant, and by the clearance time T C - the time between the end of mixing and the time to achieve a normalized gray value of 0.81 corresponding to a 50% reduction of the amount of blood (25% of dye concentration). In some cases this value was not reached during the experiment lasting one hour because the washout was so slow.

Additionally, we performed an experiment under pulsatile CSF flow conditions with settings corresponding to supine patient with slightly reclined neck (α = 0°) not treated with head shaking (Exp. 11).

Dye Washout Experiments Repeatability

In order to prove repeatability of the results in our experimental setup, we performed the dye washout experiment with one setting (Exp. 1, Table 1) six times. The high repeatability of our experiments illustrated in Figure 4 is characterized by the standard deviation of the gray values of less than 2%. This low variability of gray values results in slightly higher standard deviation (less than 9%) for the characteristic times defining the washout process. The high repeatability of the experimental setup was also proved in experiments with further three settings (Exp. 2, 4 and 6). These experiments were repeated 2 times each. The results (data not shown) confirmed the high repeatability observed in experiment with settings Exp.1.

Results

Figure 5A shows the images of experimental CSF washout (Exp. 9) without blood for five time steps. This washout process is also described by the CSF washout graph in Figure 6. The in vivo half dye time in this experiment was 12.7 min, whereas the quarter dye period was 11.5 min (period between half dye time and time to achieve a gray value corresponding to the 25% of the dye concentration).

Five in vivo time step images of four dye washout experiments. Settings of experiments are shown in Table 1.

Three experiments (Exp. 6-8, Table 1) simulated blood washout without shaking (static washout) for three different head positions (cistern orientation α = 0°, 30° and 90°). Figure 5D shows an example of static blood washout for a cistern position of α = 30° (Exp. 7). In experiments 6 and 7, only mixing (resulting in increasing normalized gray values, see Figure 6A, curve of experiment 6) and no washout were observed in the experimental 60 min corresponding to 240 min in vivo. Only for a semi-sitting patient (cistern orientation α = 90°, Exp. 8), a very slow washout (clearance time T C was not achieved) after a long period of mixing ( in vivo T M  = 208 min) was observed.

Normalized gray value curves quantifying the washout process of six of the eight washout experiments, of both reference experiments and of the experiment with pulsatile conditions. For a better clearness graphs were displayed in two groups (A and B) with identical scales. The horizontal lines labeled with 100%, 50%, 25% and 12.5% represent the normalized gray values from a calibration experiment with according blood model concentrations.

Of all five experiments (Exp. 1-5, Table 1) simulating blood washout with shaking, washout was seen in the experiments with higher shaking amplitudes (see Figure 6B, Exp. 1-3) after a faster mixing process with a mean mixing time of T M = 50±46.4 min. Table 2 summarizes mixing and clearance times for all five blood washout experiments simulating shaking.

In the two experiments (settings Exp. 4 and 5) with a small shaking angle (φ max = 20°) only a minor washout of experimental blood (clearance time was not achieved) was observed during an in vivo period of four hours. The mixing times of these two experiments (83 min and 51 min) were substantially higher than in the three experiments with higher amplitudes (mean T M  = 17±3.5 min).

Figure 5 (B and C) shows serial images of two washout experiments with higher amplitude shaking. In experiment 1 ( Figure 5B and Movie S2), the shaking frequency was 1 rpm in vitro (corresponding to 0.25 rpm in vivo) and the shaking amplitude was φ max = 70° for a cistern orientation of α = 0°. In experiment 3 ( Figure 5C) shaking was done with 10 rpm in vitro (corresponding to 2.5 rpm in vivo) and with a φ max = 45° for a cisternal orientation of α = 0°. The corresponding curves are shown in Figure 6B. The shortest (best) clearance time of steady CSF net flow experiments was achieved with the settings of Exp. 1 (α = 0°, φ max = 70°, shaking frequency f = 0.25 rpm in vivo).

Discussion

Clot clearance from the basal cisterns after subarachnoid hemorrhage has been studied by means of serial computer assisted tomography (CAT) [4]. To our knowledge, there are no MRI-based clearance studies available. CAT or MRI can be used to assess clot clearance only in limited i.e. larger time intervals. We established an in vitro model to continuously study dynamics of clot clearance from the basal cistern. Furthermore, this model allows us to deduce suitable parameters for head shaking, a promising, non-pharmacological and non-invasive therapy to enhance subarachnoid clot clearance. In vitro blood clearance by steady CSF net flow in the basal cistern with and without head shaking was visualized by means of quantified dye washout. Dye washout is an established method used in clinical medicine (e.g. X-ray angiography) and in experimental and numerical flow visualization [19]-[21]. Our dye washout experiments indicate that cisternal blood clearance due to CSF net flow (20 ml/h) without additional external head motion (head shaking) is a very long lasting process ( Figure 6A). In the basal cistern without blood, flow of CSF causes a relatively fast washout ( Figure 6, CSF-washout curve). This can be explained by the fact that CSF flow is a creeping (Stokes) flow - a flow where inertial forces are small compared with viscous forces. With the given hydrodynamic diameter of the middle cross-section (10 mm depth and 56 mm width) the calculated Reynolds number equals 0.27.

The cisternal flow dynamics are fundamentally changed after SAH. Directly after a SAH, CSF and blood are essentially separated in the basal cistern due to differences in viscosity and density (see Movie S1). A split fluid-layer system forms with blood beneath the CSF ( Figure 7A and B). Resistance of laminar duct flow is linearly proportional to viscosity. Therefore and since CSF has a kinematic viscosity of at least 3.5 times lower than blood, CSF flows round the cisternal blood via the paths of least flow resistance. Mixing of blood and CSF is required in order to increase the rate of blood clearance. Blood-CSF mixing due to diffusion corresponding to the blood-water diffusion process is very slow due the low diffusion coefficient of about D BW = 0.6·10 −9 m ²/s [22], corresponding to a characteristic diffusion time (T D =  R ²/4 · D BW) of about 650 min for a distance of R = 10 mm. To visualize blood clearance, dyed experimental blood was used. Diffusion between dyed experimental blood and non-dyed experimental CSF differs from diffusion in vivo and may alter experimental results. However, as found by the "Blood-CSF-diffusion" reference experiment the diffusion coefficient of the used dye is very low. Therefore, the results of blood washout experiments simulating head shaking are not affected. Figure 6A includes the curve of Exp. 10 simulating experimental blood/CSF diffusion. There is only slow mixing without washout.

Blood model distribution images (A) and schematic drawings (B) after injection (φ = 0°, T = 0 min). The g-arrows indicate the direction of the gravitational force, blue regions correspond to experimental blood, whereas white regions to experimental CSF. Different cistern orientations (α = 0°, 30°, 90°) cause different CSF-blood layers. (C) Schematic drawings of different shaking angles for a given cistern position (α = 0°). The complex shape of the basal cistern hampers extensive movement of cisternal blood if the shaking angle is too small.

Our experiments revealed enhanced longitudinal washout after transversal mixing generated by head shaking. Blood clearance in a supine patient with slightly reclined head (α = 0°) increases with slower shaking frequencies and with higher shaking angles φ max ( Table 2).

We see several possible explanations for our experimental findings:

First, the mixing process is driven by gravitational force. Shaking changes the orientation of the basal cistern relative to the direction of earth's gravitational force. The change in the direction of gravitational force causes movement (shifting) of the blood layer, which has a slightly higher density than CSF (ρ CSF/ρ blood = 0.95). This motion is, however, very slow due to blood viscosity and the relatively small difference in density. Mixing by centrifugal acceleration due to shaking is negligible for the same reasons. Thus, slower shaking frequencies and greater shaking amplitudes are more suitable for therapeutical applications. These findings stand in contrast to therapy strategies in previous studies, in which lateral head movements with high frequencies of 0.5 to 3.0 and of 1.0 to 1.5 cycles per second respectively [7], [8] and a small translational amplitude of 4 cm were used [7]. Kawamoto et al. compared two groups of patients with SAH with both groups receiving cisternal washing via external catheters [7]. Only one group underwent additional translational low amplitude shaking. The incidence of a permanent neurological deficit was reduced by shaking (significance level p of 0.061). Furthermore, interpretation of the effect of shaking is obscure because in both groups cisterns were irrigated with a solution containing urokinase. Nakgomi et al. compared two groups of patients with SAH, one treated with cisternal washing and shaking and the other one treated without these measures [8]. The group with cisternal washing and head shaking had a significantly (p<0.05) decreased incidence regarding cerebral infarction, mortality, and morbidity due to vasospasm compared to the group without shaking and cisternal irrigation. Therefore, the significant better results in the group with shaking might been caused by cisternal washing and irrigation with urokinase. Hänggi et al. compared a study group of patients with surgically obliterated aneurysms and treated with rotational head-motion combined with lumboventricular lavage and a control group of patients whose aneurysms had been endovascularly obliterated and who were treated without rotational head motion or lumboventricular lavage [9]. Thus the statistically positive outcome in the study group could also been attributed to the effect of cisternal irrigation during and after surgery and not to the rotational head motion. So far no study has been published in which head shaking alone is compared with conventional treatment without cisternal irrigation.

Second, the complex shape of the basal cistern containing cavities and regions of convex and concave surfaces ( Figure 7) may prevent movement of cisternal blood. With too small shaking angles (e.g. φ max = 20°, Figure 7C), one would expect no increase in mixing and hence no improvement of blood washout. Consequently, larger shaking angles remarkably improve washout ( Table 1 and Figure 7C, φ max  = 70°).

Third, we observed variations in blood distribution after injection due to the cistern orientation ( Figure 5 and 7 and Movie S1). Location of blood in the basal cistern might have an impact on the mixing process. In our study, we did not vary the location of the bleeding source, what might also affect location and distribution of the cisternal blood.

Our findings allow general statements and are independent of individual differences in geometry and blood viscosity, which of course might have an impact on the patient-specific effectiveness of shaking therapy and the outcome after cisternal bleeding.

Study Limitations

This study has limitations. Blood is a non-Newtonian fluid [23], a feature altering its characteristics due to the coagulation process in the CSF. However, sparse information is available about blood rheology in the CSF after a SAH. Naff et al. found a first-order kinetic of the blood clot resolution, which was independent from clot volume, age, sex and use of external drainage [24]. They noted also that the thrombolytic enzyme system seems to be saturated at 24-48 hours after SAH. An increased blood viscosity due to coagulation is expected to hamper blood/CSF mixing and hence blood clearance. On the other hand, naturally occurring thrombolysis results in a lesser difference between viscosities and densities of blood and CSF and would facilitate blood clearance. This might imply that a therapeutic intervention aiming a removing of cisternal blood should start within the first 48 hours after SAH.

Our anatomical model is based on MRI data from a 35-year-old male whereas the average male patient with a ruptured aneurysm is about 50 years old (49.4±12.2 mean±s.d., CLARITY study [25]). Furthermore there is an increase in total subarachnoid volume with age [26]. This age-dependent increase in total subarachnoid volume results in a decrease of CSF clearance rate [27] thus challenging subarachnoid blood clearance. This emphazises the importance of active subarachnoid clearance mechanisms as head shaking and increased CSF perfusion with or without cisternal thrombolysis. Nevertheless our study does not provide statistical data on the age-dependency but on basic mechanisms of subarachnoid clearance in head shaking.

We studied only the basal cistern and not the adjacent anterior and lateral cisterns. These more peripheral cisterns empty into the basal cistern. Therefore, unplugging the basal cistern by clearing it from blood enables a better clearance of the peripheral cisterns.

The patient-specific anatomic model based on MRI measurements does not incorporate arachnoid membranes. Due to their delicate structure still elusive to modern imaging, these membranes can be modeled only in numerical studies assuming the basal cavity as a porous volume. To the best of our knowledge, only one such computational fluid dynamics (CFD) study of CSF flow in the subarachnoidal space using an anisotropic porous model has been published [15]. A CFD study simulating blood clearance over many hours is possible but requires enormous computational time. One would expect that anisotropy of permeability coefficients (factor six higher in a longitudinal direction [15]) would hamper the transversal mixing process. But due to the very high porosity of 0.99 [28], the existence of arachnoid membranes does not affect significantly CSF flow dynamics and hence our findings. This hypothesis is supported by the good correlation between measured CSF flows and simulations using models without arachnoid membranes [29]. The impact of arachnoid membranes, which are known to increase the static pressure in the basal cistern [15], on CSF dynamics should be, however, investigated more detailed in a separate CFD study.

In our study, we model steady CSF net flow. Magnetic resonance imaging measurements showed the pulsatile nature of CSF flow with high flow rate amplitudes during the heart cycle [15]. Actually, CSF flow changes its direction during the heart cycle. MRI-measurements in the pontine cistern found a maximal positive flow rate of 100 ml/min and a maximal negative flow rate of 50 ml/min with an in vivo net CSF flow rate of only 20 ml/h. CSF flow oscillating with the heart rate also increases CSF/blood mixing and thereby blood clearance. In Figure 6B, the curve labeled with "pulsation" describes the blood washout in the experiment with pulsatile CSF flow, a cistern orientation of α = 0° and without shaking (Exp. 11). The effect is even slightly better than our best washout experiment (Exp. 1) with steady net CSF flow and shaking. The clearance time T C of 23 min was 30% shorter than T C of Exp. 1 ( Table 2). Since the aim of our study was to analyze the effect of head shaking apart of other factors, the pulsatile nature of CSF flow was not considered in the first step. Consequently, the majority of the washout experiments were performed assuming natural net CSF flow. Note that a study of shaking therapy under pulsatile CSF flow conditions is challenging. Head shaking may affect volumes of three compartments with CSF, arterial and venous blood, which define the CSF flow pulsatility [24] and in turn affect the CSF pulsatility by increasing or decreasing of the pulsation amplitude. This may hamper or facilitate blood clot clearance.

Increased CSF flow seems to be advantageous in the treatment of SAH [5]. In any case, increased CSF flow enhances subarachnoid blood clearance. The existence of a mixing effect due to head shaking is, however, independent from CSF flow rate or pulsation.

Conclusions

Quantitative dye visualization was used to study in vitro the effects of head shaking on blood clearance in a model of cisternal SAH. Our experimental study supports the clinical assumption that head shaking can increase the subarachnoid blood clearance significantly. Our results provide insights into the effects of different shaking strategies (with respect to shaking frequency and angle amplitude) upon the washout process in a model of the basal cistern.

Based on the results, we expect that head shaking with low shaking frequencies and high shaking angles (amplitudes) will improve cisternal blood clearance. This should be, however, tested in a clinical study.

Open questions include the influence of pulsatile CSF flow known from MRI measurements [15], the effect of increased CSF flow (simulating cisternal irrigation), and the implication of increased blood viscosity (simulating a delayed start of the shaking intervention). Experimental answers to these questions might refine a treatment protocol for cisternal SAH combining head shaking and cisternal irrigation with or without a thrombolytic agent.

Key Messages

the hypothesis that head shaking is a therapeutic strategy to increase blood washout in the subarachnoid space is supported by the presented experimental in vitro study

blood washout of the subarachnoid space consists of two distinct phases: Blood/CSF mixing and clearance

head shaking facilitates blood washout by varying the direction of gravitational force

blood washout increases with decreased shaking frequency and with increased shaking angle amplitude

Acknowledgments

The authors would like to thank Sebastian Vagt for his help in the construction and programming of the experimental setup and Hanns-Joachim Schmidt for his help in the experiments and the analysis of the results.

Author Contributions

Conceived and designed the experiments: KA UK DH AS. Performed the experiments: TS LG. Analyzed the data: KA LG DH AS. Contributed reagents/materials/analysis tools: DH. Wrote the paper: UK TS AS.

References

1. 6. Amin-Hanjani S, Ogilvy CS, Barker FG 2nd (2004) Does intracisternal thrombolysis prevent vasospasm after aneurysmal subarachnoid hemorrhage? A meta-analysis. Neurosurg 54: 326-334.

2. 14. Sequeira A, Janela J (2007) An overview of some mathematical models of blood rheology. In: Seabra Pereira M, editor. A Portrait of State-of-the-Art Research at the Technical University of Lisbon. Springer 65-87..

# data[].attributes.attachment_link.title
In Vitro Study of Cerebrospinal Fluid Dynamics in a Shaken Basal Cistern after Experimental Subarachnoid Hemorrhage

# data[].attributes.attachment_link.description
Background Cerebral arterial vasospasm leads to delayed cerebral ischemia and constitutes the major delayed complication following aneurysmal subarachnoid hemorrhage. Cerebral vasospasm can be reduced by increased blood clearance from the subarachnoid space. Clinical pilot studies allow the hypothesis that the clearance of subarachnoid blood is facilitated by means of head shaking.

# data[].attributes.headline
Role of Fluid Mechanics in Localization and Detection of Atherosclerosis

# data[].attributes.subject
Role of Fluid Mechanics in Localization and Detection of Atherosclerosis

# data[].attributes.body
-In Vitro
-Using Doppler velocimeter, measure velocity disturbance to find points of atherosclerosis.
- Carotid artery
-Non invasive

# data[].attributes.body
-In silico
-Method: CFD modeling
-How it works: CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured
-Area: cardiovascular system
-Purpose: To have a computational model of the cardiovascular system that physicians can use in clinical applications
-Advantage: provides data and understanding that cannot be found using any other method
-Disadvantages: There are very few government regulations concerning the validity, reliability, or accuracy of this information. Also the necessary information found from hospitals can be restrictive and hard to use.

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Abstract

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Introduction

Computational fluid dynamics (CFD) is a well-established tool used in engineering, in many areas of which it has become the primary method for design and analysis. Bioengineers have adopted CFD to study complex physiological flows and have demonstrated their potential. There is increasing interest in applying these methods in cardiovascular medicine. CFD-based techniques are being used to build complex computer representations (in silico models) of the cardiovascular system in health and disease. CFD modelling is a new field within cardiovascular medicine, enhancing diagnostic assessment, device design and clinical trials. It can predict physiological responses to intervention and compute previously unmeasurable haemodynamic parameters. As CFD modelling continues to translate into clinical tools, it is important that clinicians understand the principles, benefits and limitations of these techniques. This article explores these topics using state-of-the-art examples in key clinical areas, highlighting applications likely to impact clinical practice within the next 5 years ().

Table 1

Area

Clinical applications

Data and evidence

Potential clinical impact

Limitations and challenges

References

Native valve haemodynamics in health and disease

Non-invasive computation and quantification of trans-valvular pressure drop and regurgitant fraction from CT imaging

Accurate 3D simulations in patient-specific models with valves in open and closed states to predict transvalvular dynamics in diseased states

Improved objective assessment and surveillance of valve disease from non-invasive imaging data

Requires high quality 3D images of valve orifice-not routinely generated. Balancing the requirement for complex dynamic simulation (FSI) vs simpler models (valve open/closed)

Stent design

Prediction of WSS and related metrics that influence endothelial function and NH due to stent-induced haemodynamic disturbance

Turbulent or disturbed laminar flow reduces WSS stimulating adverse vessel remodelling. NH preferentially accumulates in these regions

Not possible to measure arterial WSS in vivo, especially in the vicinity of stent struts post-PCI. Modelling provides detailed analysis of flow, and the influence of stent design through patient-specific reconstructions, enabling the optimal stent design to be achieved

High resolution imaging, vessel reconstruction and boundary conditions are challenging. CFD simulations demand fine computational meshes and time-resolved pulsatility. Run-times are long, even with high performance computing

Heart failure

Models based upon CT and MR help compute haemodynamics and the spatio-temporal distributions of pressure and myocardial stress/strain

CFD/FSI models replicate realistic pathophysiology in models of health and disease (eg, HFREF, HFPEF, HCM, DCM, and RWMA post-MI)

Additional haemodynamic data potentially enables early diagnosis and stratifies disease phenotypes and severities. Characterising complex vortex flows identifies areas of flow stagnation and thrombus risk

Resolution of imaging and reconstruction (representing trabeculae and papillary muscles). Tuning with realistic boundary conditions. Requirement for FSI in many models

CRT

Coupled electro-mechanical models of the ventricle incorporating CFD (multi-physics models) used to investigate heart function

Published reports of accurate patient-specific haemodynamic simulations with sufficient detail to optimise CRT before surgical intervention

Improved selection of CRT responders. Simulation and selection of optimal tuning of device settings and lead placement on an individual case basis

Uncertainties and assumptions regarding boundary conditions and the range of clinical measurements required for parameterisation. Mesh generation, prolonged computation times

VADs

Generic optimisation of pump design. Patient-specific models can aid implantation strategy and tuning of output according to patient physiology

Published models describing haemodynamic influences of catheter placement and minimisation of adverse haemodynamic effects

Pump tuning to ensure periodic opening and closing of AV, preventing leaflet fusion. Personalised catheter placement planning (prediction and avoidance stasis and thrombus formation)

Post-implantation imaging artefact limits modelling. Optimising performance requires the balance of multiple competing factors. As for all cardiac electromechanical models, selection of appropriate patient specific parameters is difficult due to sparsity of data

What is CFD?

CFD is a specialist area of mathematics and a branch of fluid mechanics. It is used in the design of many safety-critical systems, including aircraft and vehicles, by solving differential equations to simulate fluid flow. A glossary of uesful terms is provided in .

Table 2

Analytical solution

Relatively simple models can be described by solving a number of equations using mathematical analysis techniques such as calculus or trigonometry. The solution is analytical because an exact solution can be obtained through algebraic manipulation of the equations ( cf. numerical solution).

Bernoulli equation:
Rearranged and simplified:

The Bernoulli equation relates blood pressure ( P) and flow velocity ( V). The total energy of flowing blood comprises hydrostatic (P), kinetic ((1/2)ρV ²) and potential (ρgh where ρ is fluid density, g is gravity and h is height) energies, the sum of which is conserved. Therefore, an increase in flow velocity must be accompanied by a decrease in pressure, and vice versa. Gravitational effects (ρgh) are usually neglected in a supine vessel. The simplified and rearranged equation is used routinely to calculate transvalvular pressure gradients from flow velocity. The Bernoulli equation ignores energy loss due to viscous friction (see Poiseuille equation) and turbulence, and assumes steady flow.

Boundary conditions

A set of parameters or relationships which describe the physiological conditions (haemodynamic or structural) acting at the boundaries of a modelled segment, representing the interaction of the model with its distal compartments.

Discretisation

To divide into discrete elements or time periods.

Electrical analogue

An electrical circuit design used to represent a compartment of the circulation, using, for example, 'voltages' (pressures), 'current' (flow) and resistors. They lack spatial dimensions and are therefore also referred to as dimensionless or ' zero-D ' (0D) models.

In silico

'Represented or simulated in a computer', comparable to in vivo and in vitro.

Multi-scale model

A model which integrates models of different length- and or time-scales.

Newtonian and non-Newtonian fluid

As blood is a suspension, non-Newtonian behaviour is particularly important within the capillaries where the size of (solid) blood cells is large relative to vessel calibre, resulting in a non-linear relationship between shear-stress and viscosity. In larger blood vessels Newtonian fluid behaviour is often assumed whereby viscosity is constant, independent of the shear-stress acting on the fluid.

Numerical solution

In more complex models the mathematics becomes too complicated for analytical techniques and numerical techniques are used instead. Rather than generating an exact solution, the result is an approximation, albeit within very close bounds under certain circumstances. Typically, iterative methods are employed to produce a solution to the equations that converges around the true values. Used to resolve complicated, non-linear, transient (time-varying) analyses for example, 3D-CFD models.

Poiseuille equation:

Rearranged:

The Poiseuille equation describes blood flow (Q), along a vessel in relation to viscosity (μ), vessel geometry (length (L) and radius (r)) and the driving pressure gradient (ΔP). According to Poiseuille, flow is strongly dependent upon vessel radius (fourth power). Poisuille's equation considers viscous (frictional) energy losses.

Segmentation

The process by which relevant structures in medical images are identified, isolated and converted into computer representations.

Windkessel

German for ' air-chamber '. Windkessel models are relatively simple zero-D models used to represent the resistive and compliant properties of the arterial vasculature.

Workflow

A sequence of applications (computational tools) which are executed sequentially to manipulate medical data to build a model and perform computational analyses. Typically this involves medical imaging, segmentation, discretisation, CFD simulation and post-processing, that is, from clinical imaging to results. Sometimes referred to as a tool-chain.

For incompressible flows, almost all CFD analyses solve the Navier-Stokes and continuity equations which govern fluid motion. These equations are non-linear, partial differential equations based upon the principle of conservation of mass and momentum. Simplification of these equations yields familiar formulae (eg, those of Bernoulli and Poiseuille); but for complex geometries analytical solutions are not possible, so specialised software applications (CFD solvers) calculate approximate numerical solutions. Non-linearity, due to convective fluid acceleration, makes this challenging, especially in three dimensional (3D) models; so CFD analyses require significant computational power and time.

CFD model complexity

The applications reviewed in this paper focus on 3D CFD analyses of local regions of the vasculature because this is where promising applications are beginning to translate and impact upon clinical medicine. There is a long history of simplification of the governing equations to lower spatial dimensions. summarises the relationship between these approaches and provides clinical examples of their use.

Table 3

Model

Figure

CFD solution

Description/examples

Typical solution time†

0D

*

No spatial dimension. Physiological variables such as pressure ( P), flow ( Q) and resistance ( R) are assumed spatially uniform within the model, varying only as a function of time ( t), eg,

Solved with ordinary differential (0D NS) equations

Lump together distributed physiological systems into a single description. They describe the global behaviour of the modelled segment. The 0D Windkessel model (pictured) is often used to represent the compliant and resistive nature of the arterial circulation. 0D models are frequently used to model components of the cardiovascular system or to improve boundary conditions for 3D models of arterial, ventricular or venous pathophysiology.5 47

Immediate solution

1D

Physiological variables are solved as a function of a single spatial variable, typically length ( x), eg,

Solved with partial differential (1D NS) equations

Used to represent wave propagation characteristics and wave reflection. 1D models may also be used to provide boundary conditions for higher order models in order to increase refinement of the solution, especially where the effects of wave reflection are significant.45 46

S (static)
Min (transient)

2D

Physiological variables are solved as a function of two spatial variables, typically length and distance from centreline ( r) eg,

Solved with axisymmetric NS equations

Able to resolve the solution in 2D. Used less often now than previously due to ready availability of improved computer processing and 3D solvers. Examples include the simulation of para-prosthetic valve haemolysis and improvement of the assessment of the proximal flow convergence zone in the clinical evaluation of regurgitant valve disease.48

3D

Physiological variables are solved as a function of all three spatial variables, including the angle around the centreline axis ( θ) eg,

Solved with full 3-D NS equations

Full 3D CFD can resolve the physiological solution in all dimensions including time. Examples are more widely reviewed in the main body of the text.

Order of minutes for steady- state
Order of hours or days for transient

2D analyses typically assume symmetry of the solution about the central axis, 1D models capture variation of the solution along the axial direction only, and 0D representations lump the behaviour of vascular regions into a model with no spatial dimensions, hence the term 'lumped-parameter models'. Due to the breadth of the literature covering application of these techniques to cardiovascular haemodynamics, the interested reader is referred to recent reviews of the state-of-the-art.

Model construction

CFD model construction and solution can be described in seven stages ():

A range of medical imaging modalities can be used, including ultrasound, CT, MRI and X-ray angiography. Imaging must provide sufficient anatomical and physiological detail, in an appropriate format and quality, to enable segmentation and data extraction.

Segmentation methods convert medical images to in silico geometries which define the physical bounds of the model region of interest. If images are acquired over a cardiac cycle, anatomical motion can be tracked over segmented regions.

Spatial discretisation, or 'meshing', divides the geometry into a number of discrete volumetric elements or cells. Temporal discretisation divides the solution into discrete time steps. The accuracy and numerical stability of the analysis are influenced by both spatial and temporal refinement. The fabrication of the mesh, and the level of mesh refinement, are influenced by case- and context-specific factors. The mesh and timestep (ie, spatio-temporal discretisation) must be refined enough to capture the important haemodynamic behaviour of the modelled compartment (the final solution should be independent of mesh parameters), but without excessive refinement because this impacts negatively on computational resource and solution time (see online supplementary table S1).

Because it is impossible to discretise the entire cardiovascular system, the region to be analysed will have at least one inlet and one outlet. To enable CFD analysis, the physiological conditions at the wall and inlet/outlet boundaries must be specified. Boundary conditions are a set of applied physiological parameters (which may vary over time) that define the physical conditions at the inlets, outlets and walls. They may be based on patient-specific data, population data, physical models or assumptions.

A computer file defining the physical parameters of the model is written. In addition to the geometric, discretisation and boundary data, this file must define properties including: blood density and viscosity (ie, the fluid model), the initial conditions of the system (eg, whether the fluid is initially static or moving), time discretisation information (time step size and numerical approximation schemes), and the desired output data (eg, number of cardiac cycles to be simulated). This information allows the CFD solver to solve the Navier-Stokes and continuity equations, proceeding incrementally towards a final solution ('convergence'). A typical 3D cardiovascular simulation involves >1 million elements run over several cardiac cycles, each divided into hundreds or thousands of individual time-steps. Millions of non-linear partial differential equations are solved simultaneously, and repeatedly, over all elements, at all time-steps. 3D CFD modelling is therefore time-consuming and computationally demanding.

Typically, the CFD solver produces the pressure and velocity field over all elements at each time-step. Only a small proportion of these data are of interest to the operator, so some post-processing is required to extract and display relevant data.

It is important that modelled results are validated against an acceptable standard. Commonly, this involves comparison with either values measured within an in vitro phantom or acquired during in vivo assessment. Validation generates confidence in the accuracy and reliability of a CFD model.

The workflow

Collectively, the steps outlined above are known as a workflow or toolchain (see and online supplementary video). Although there are many specialised software applications facilitating the construction and operation of CFD-based workflows, considerable skill and experience are required at each stage (especially steps 3-5) to ensure reliability of results.

Advanced boundary conditions

Rather than specifying pressure or flow at a boundary, an additional, lower-order model may be coupled to the 3D solver to generate more realistic conditions proximal and distal to the simulation domain (see and ). This method of modelling is efficient, because it allows detailed analysis in the 3D region without wasting high temporal and spatial refinement on regions beyond this. In some cases the model representing the distal boundary also provides proximal boundary condition. These closed-loop models, or system models, require very careful tuning.

Assumptions

Many CFD models assume that the segmented region has rigid walls. Although untrue in the cardiovascular system, this approximation is acceptable for some applications. Vessel compliance allows blood to be stored during systole and released during diastole. At the system level this results in a finite speed of pressure wave transmission and tends to reduce the peak pressures associated with the inertial acceleration of the blood. Compliance tends to reduce shear stresses because the vessels are slightly larger when peak flow occurs. It is possible to model deformation of the wall, due to cardiac and respiratory variation, in response to change in pressure using fluid-solid interaction (FSI) models. These are far more complex to solve, boundary conditions are a challenge, and many wall parameters remain unknown, which increases the number of assumptions. Furthermore, it is yet to be established for which applications a full FSI approach improves accuracy. An example of the increased computational cost of FSI is reported by Brown et al where 3D transient (time-varying) analysis of the aorta required 145 h (FSI) compared with 6.6 h (CFD). An alternative is to impose wall movement derived from imaging data (eg, gated MRI). There are exciting developments in the use of data assimilation techniques in which sparse clinical data, for example, from 4D imaging, are integrated with the analysis process so that material properties of tissues in individual patients are recovered as the simulation progresses. In biomedical workflows it is assumed the boundaries of the fluid geometry are smooth, yet medical images may not generate smooth surfaces due to poor resolution or imaging artefacts. Instead, structures may be smoothed in silico after segmentation. Typically, cardiovascular simulations assume blood behaves as an incompressible fluid. Although blood exhibits non-Newtonian behaviour (see glossary in table 2), which must be simulated for flow in small capillaries, in larger vessels these effects are often neglected and a Newtonian fluid model is assumed.

Benefits of cardiovascular CFD modelling

CFD modelling enables investigation of pressure and flow fields at a temporal and spatial resolution unachievable by any clinical methodology. Post-processing provides additional data, generating new insights into physiology and disease processes. For example, it is difficult, and invasive, to measure arterial wall shear stress (WSS), a key factor in the development of atherosclerosis and in-stent restenosis, whereas CFD models can compute WSS and map its spatial distribution. Such work has established the link between haemodynamic disturbance and atherogenesis and has explained the preferential deposition of atherosclerotic plaque at arterial bends and bifurcation regions. CFD modelling has been central to our current understanding of the effects of WSS on endothelial homeostasis: laminar, non-disturbed blood flow is associated with increased WSS which inhibits unnecessary endothelial cell activation; whereas turbulent or disturbed blood flow reduces WSS which stimulates adverse vessel remodelling. A complex series of WSS-related signalling pathways and interactions underlie this phenomenon. Before these pathways can be exploited to generate anti-atherosclerotic therapies their complexity needs to be better understood. Integrated multiscale CFD models provide a powerful tool to combine analysis of fluid mechanics and cellular response. Recently, the effect of disturbed WSS in stented vessels has been modelled to investigate the influence on both endothelial function and neointimal hyperplasia, which preferentially accumulates at regions of low and disturbed WSS (). Such models can be used to develop stents which minimise the risk of in-stent restenosis and thrombosis.

Device design

In silico methods allow rapid prototyping, with reduced risk to humans, so a priority for the medical devices industry is to replace expensive and time-consuming in vivo and in vitro experimentation with in silico testing. In recognition of this, the US Food and Drug Administration (FDA) issued draft guidance in 2014 on the use of modelling to support regulatory submissions. An example is the significant role which CFD plays in design optimisation of mechanical heart valves. While comparison of major flow features captured in vitro with predictions from CFD shows good agreement, simulation delivers 3D information at much higher resolution within critical regions (eg, the hinges) than flow visualisation, giving invaluable insight into design-related thrombogenic potential. Comprehensive simulation of heart valve mechanics, including the separation of the upstream and downstream fluid regions at closure and the structural instability and snap-through dynamics of tissue valves, remain computationally challenging but achievable.

CFD has been used in the optimisation of several commercial ventricular assist devices (VADs), investigating potential thrombogenicity by highlighting design-related regions of stasis and device characteristics resulting in high shear stress. A tool for optimising thromboresistance has been recently demonstrated in a comparative study of two continuous flow VADs, which combines experimental and numerical simulation. Numerical models can also contribute to the process of VAD implantation, informing the choice of catheter implantation site.

In the context of stent design, the greatest emphasis has been on modelling the mechanical integrity of the stent structure during and after deployment. However, CFD provides a valuable tool to assess the resulting haemodynamics within the stented lesion. This, in turn, has been associated with the biological response of the vessel wall and the development of restenosis.

Diagnostic tools and personalised medicine

Computing intravascular physiology, with the aim of minimising invasive instrumentation, is of major interest. A prime example is fractional flow reserve (FFR), an index of physiological (coronary atherosclerosis) lesion significance, measured with a pressure-sensitive angioplasty guidewire. FFR-guided therapy improves patient outcomes, reduces stent insertions, and reduces costs, yet it is used in <10% of cases due to a host of procedural and operator related factors. Several groups propose models for computing 'virtual' FFR from angiography to provide the benefits of physiological assessment without the practical drawbacks which limit the invasive technique (see online supplementary figure S1). The VIRTU-1 trial demonstrated the effectiveness of CFD-derived FFR using invasive angiography (diagnostic accuracy 97% vs invasive FFR). More recently, the HeartFlow-NXT trial demonstrated the performance of virtual FFR using CT coronary angiography (sensitivity 86%, specificity 79% vs invasive FFR). Both models offer a less invasive approach, neither requires hyperaemic flow induction nor the passage of an intracoronary wire, and taken together could offer the benefits of FFR to all patients being assessed for coronary artery disease (CAD). CT FFR (HeartFlow Inc) is now FDA approved for use as a class II Coronary Physiologic Simulation Software Device.

Recent in vitro work combining CFD, colour Doppler and simulated Doppler images demonstrates the potential to reduce Doppler inter-user variability and inform interpretation of complex regurgitant flow fields in valvular heart disease. In silico models of the right heart and pulmonary arteries using phase-contrast MRI capture anatomical and flow velocity data to simulate pulmonary artery physiology. It is hoped that these models will soon deliver a diagnosis of pulmonary hypertension without invasive catheterisation. Added value may come from wave analysis of these models to discriminate between the key aetiological sub-groups of pulmonary hypertension.

Treatment decisions are often based upon the 'gold standard' of randomised controlled trials. Everyday clinical practice, however, requires tailored treatment for individual patients. CFD modelling offers a patient-specific approach to management, in which an individual's unique anatomy and physiology are used to define the model. The impact of alternative interventional strategies can be compared and a personalised, optimised strategy selected. Patient-specific modelling will not diminish the need for clinical trials but will allow the delivery of truly objective, personalised management on a wide scale.

This approach is exemplified in aortic aneurysm management, where current simplistic guidelines use aneurysm diameter as the arbiter of treatment. The @neurIST project addresses this, and incorporates patient-specific anatomic, genomic and demographic data, with simulated flow patterns (), to calculate the risk of rupture. The optimal treatment of aortic type B dissections remains controversial. Thoracic endovascular aortic repair (TEVAR) carries a risk of spinal ischaemia, and multiple communicating channels between true and false lumens confer a risk of proximal rupture if only the primary entry is closed. Therefore, graft length is balanced against the risk of paraplegia. In this context, CFD modelling provides individualised risk stratification and optimised treatment delivery (). Similar simulations are useful in the context of abdominal aortic aneurysm.

Full system models: the Virtual Physiological Human

There is increasing interest in integrating multiple physiological models into comprehensive system models to simulate the impact of various conditions, pathologies and treatments across multiple organ systems. While this is ambitious, large, international, collaborative research projects under the umbrella of the Virtual Physiological Human (VPH) reflect the seriousness, legitimacy and rationale underlying this long-term vision. Full system models offer the possibility of understanding, holistically, the impact of cardiovascular disease upon individual patients.

In silico trials

In silico techniques can simulate measures of safety, accuracy, and efficacy of interventions, both pharmacological and mechanical, in large cohorts of virtual patient models which represent naturally occurring physiological and pathological variability. This minimises the time, cost, and risk associated with clinical trials. The Avicenna project leverages significant commercial interest and engagement to develop a 'roadmap' describing the route by which multi-scale in silico techniques can achieve this.

Challenges and limitations

CFD models in medicine have traditionally been used by two user groups: industrial medical device developers, in rapid, low-cost, device prototyping; and academics, to investigate cardiovascular physiology and compute parameters that cannot otherwise be obtained. Both groups construct models which are typically complex, involve multiple finely-tuned geometric, haemodynamic and material parameters and require long computation times. In contrast, clinicians are a third, emerging user group, who require rapid results with adequate accuracy.

Model accuracy is determined by model design and quality of input data. For CFD applications it is unclear how detailed the clinical data needs to be in terms of geometry (segmented from medical images) and parameterisation (variability described by the model and the tuning of patient-specific boundary conditions). Continuing improvements in imaging, image-registration and segmentation algorithms will augment accuracy. Model parameterisation is more challenging, because it requires detailed knowledge of physiological metrics in the proximal and distal circulations which may be inaccessible and variable in health and in disease, for example, microcirculatory resistance is a major determinant of coronary blood flow. Further understanding of the relative importance of physiological parameters is required to determine those which are most influential, and those which can be assumed or averaged. This allows unnecessary model complexity to be simplified, balancing computing speed against accuracy. A second challenge is the development of relevant industry standards. In the European Union and USA, diagnostic software is regulated via CE marking and FDA directives, respectively; but there are no industry standards governing accuracy, reliability or validation. The FDA is addressing this through benchmarking initiatives, in the same way that aviation authorities adopted computer-aided design over traditional physical testing. Third, large volumes of clinical data, of value for model development and validation, are stored in hospital systems. Access is variable and restrictive; although the VPH-Share project demonstrates how anonymised patient-specific data and in silico models can be shared securely. Access to such data supports model validation against long-term outcomes which may expedite clinical translation. Fourth, CFD modelling can be perceived as a 'disruptive technology', and a threat, especially by manufacturers of traditional hardware. Finally, the next generation of doctors will require training in in silico systems, and understanding their principles, methodologies and limitations. Several initiatives are attempting to address this, but in the longer term, in silico medicine may gain prominence in medical curricula.

Future directions

In the context of device development, the major computational modelling and technological challenges have already been addressed and the benefits of simulation are recognised by the regulatory authorities. Sustained investment will enable engineers to continue model refinement and the development of novel applications, specifically targeting increases in precision, personalisation and speed. Beyond technological development, and before these tools become established in routine clinical practice, the most immediate need is to demonstrate equivalence of in silico results relative to invasive measurements through observational trials. Beyond this, efficacy must be demonstrated in large multicentre clinical trials. It is clear that these techniques have the potential to change clinical practice. The beneficiaries will be patients, clinicians and healthcare providers.

Acknowledgments

Dr Morris is funded by a Clinical Research Training Fellowship from the British Heart Foundation. was kindly provided by Dr Alberto Marzo, University of Sheffield.

Footnotes

Contributors: All authors have made a substantial contribution to the conception or design of the work, the drafting and revision of the work and have made an intellectual contribution. All authors have given final approval of the version submitted and have agreed to be accountable for all aspects of the work.

Funding: British Heart Foundation (R/134747-11-1).

Competing interests: None declared.

Provenance and peer review: Not commissioned; externally peer reviewed.

References

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Computational fluid dynamics modelling in cardiovascular medicine

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This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system.

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Biofluid Biomarkers of Traumatic Brain Injury 

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Biofluid Biomarkers of Traumatic Brain Injury 

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Method:CNS-derived exosomes analyzed by ultra-high sensitivity detection
Area: Brain
Purpose: identifying, diagnosing, and treating the underlying individual pathobiological changes of traumatic brain injury
Advantage: noninvasive
Disadvantage: Blood biomarker still not available
Information: https://www.tandfonline.com/doi/full/10.1080/02699052.2017.1357836

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Biofluid Mechanics of the Pulmonary System

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Chris D. Bertram Donald P. GaverIII Presents an overview of leading areas of discovery in biofluid mechanics related to the pulmonary system, with particular reference to the airways. Areas briefly reviewed include airway gas dynamics, impedance studies, collapsible-tube studies, and airway liquid studies.

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in silico, in vitro, or in vivo biofluid mechanics study

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in silico, in vitro, or in vivo biofluid mechanics study

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