WO2017148836A1 - A device for maintaining vascular connections - Google Patents

A device for maintaining vascular connections Download PDF

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WO2017148836A1
WO2017148836A1 PCT/EP2017/054420 EP2017054420W WO2017148836A1 WO 2017148836 A1 WO2017148836 A1 WO 2017148836A1 EP 2017054420 W EP2017054420 W EP 2017054420W WO 2017148836 A1 WO2017148836 A1 WO 2017148836A1
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supporting section
vein
centreline
device according
artery
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PCT/EP2017/054420
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French (fr)
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Peter Vincent
Lorenza GRECHY
Richard Corbett
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Imperial Innovations Limited
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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61MDEVICES FOR INTRODUCING MEDIA INTO, OR ONTO, THE BODY; DEVICES FOR TRANSDUCING BODY MEDIA OR FOR TAKING MEDIA FROM THE BODY; DEVICES FOR PRODUCING OR ENDING SLEEP OR STUPOR
    • A61M1/00Suction or pumping devices for medical purposes; Devices for carrying-off, for treatment of, or for carrying-over, body-liquids; Drainage systems
    • A61M1/36Other treatment of blood in a by-pass of the natural circulatory system, e.g. temperature adaptation, irradiation ; Extra-corporeal blood circuits
    • A61M1/3621Extra-corporeal blood circuits
    • A61M1/3653Interfaces between patient blood circulation and extra-corporal blood circuit
    • A61M1/3655Arterio-venous shunts, fistulae
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/11Surgical instruments, devices or methods, e.g. tourniquets for performing anastomosis; Buttons for anastomosis
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/11Surgical instruments, devices or methods, e.g. tourniquets for performing anastomosis; Buttons for anastomosis
    • A61B2017/1107Surgical instruments, devices or methods, e.g. tourniquets for performing anastomosis; Buttons for anastomosis for blood vessels
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/11Surgical instruments, devices or methods, e.g. tourniquets for performing anastomosis; Buttons for anastomosis
    • A61B2017/1135End-to-side connections, e.g. T- or Y-connections
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/11Surgical instruments, devices or methods, e.g. tourniquets for performing anastomosis; Buttons for anastomosis
    • A61B2017/1139Side-to-side connections, e.g. shunt or X-connections
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61MDEVICES FOR INTRODUCING MEDIA INTO, OR ONTO, THE BODY; DEVICES FOR TRANSDUCING BODY MEDIA OR FOR TAKING MEDIA FROM THE BODY; DEVICES FOR PRODUCING OR ENDING SLEEP OR STUPOR
    • A61M2206/00Characteristics of a physical parameter; associated device therefor
    • A61M2206/10Flow characteristics
    • A61M2206/20Flow characteristics having means for promoting or enhancing the flow, actively or passively

Abstract

There is provided a device for maintaining a vascular connection comprising a vein- supporting section and an artery-supporting section. The centreline of the vein-supporting section and the centreline of the artery-supporting section meet at an intersection point which defines the origin of a right-handed Cartesian coordinate system. The centreline of the artery-supporting section is arcuate and lies in the region y<=0 and has a tangent parallel to the x axis at the origin and wherein the artery-supporting section is configured to carry blood flow in a direction from negative x towards positive x. A tangent of the centreline of the vein-supporting section at the origin has direction [cos (Θ) sin (Φ), sin (Θ) sin (Φ), ± cos (Φ)], where Φ is in the range 225 to 270 degrees and Θ is in the range 200 to 300 degrees.

Description

A Device for Maintaining Vascular Connections

Field

The present disclosure relates to vascular connections such as arterio-venous connections, particularly arterio-venous fistulae, and a device for maintaining the same. In particular, but not exclusively, the present disclosure relates to a device which can fix the geometry of such a fistulae in a designed configuration.

Background

End-Stage Renal Disease (ESRD) causes patients to suffer an irreversible reduction in kidney function. Without renal replacement therapies, such as haemodialysis, ESRD is terminal. However, with these therapies the prognosis for patients can be radically improved. For example, during haemodialysis blood is drawn from the patient through vascular access and circulated through a dialysis filter to remove metabolic waste before being returned to the body.

In order to draw blood from a patient for haemodialysis, an appropriate connection must be formed. While catheter access to a vein is possible, this is associated with drawbacks including the possibility of infection and venous stenosis. It is currently recognised that the provision of arterio-venous fistulae (AVF) represents a superior solution.

AVF are arterio-venous connections commonly formed surgically in the wrist or upper arm by connecting or "anastomosing" a vein onto an artery. AVF offer significant benefits over catheter access to existing veins, including increased blood flow which improves the effectiveness of the haemodialysis process. In particular, the large pressure difference between the artery and vein leads to increased blood flow through the vein, which in optimum cases then causes the vein walls to strengthen and the vein itself to enlarge. AVF can take various forms, including end-to-end (where the vein and artery are connected end-to-end), side-to-side (where the vein and artery are connected side-to- side) and end-to-side (wherein the end of the vein is connected onto the side of the artery).

AVF can thus form an enlarged "arterialised" vein with strengthened walls and a high blood flow rate. In such circumstances, an excellent outcome is provided for haemodialysis, as the AVF may accommodate large gauge needles to withdraw and return blood. When successful, AVF may provide excellent access for haemodialysis over a period of several years. However, a significant percentage of AVF fail shortly after they are created, causing unfavourable clinical outcomes and significant additional costs for healthcare systems worldwide. One common reason for failure is an adverse inflammatory process called Intimal Hyperplasia (IH), which causes the intimal layer of the artery and/or vein to grow inwards, reducing the size of the lumen and dramatically reducing blood flow through the AVF.

There is an ongoing need to improve AVF to reduce such outcomes and thus improve clinical results. Summary

According to a first aspect, there is provided a device for maintaining a vascular connection comprising a vein-supporting section and an artery-supporting section, wherein

a centreline of the vein-supporting section and a centreline of the artery-supporting section meet at an intersection point which defines the origin of a right-handed Cartesian coordinate system;

the centreline of the artery-supporting section is arcuate and lies in the region y<=0 and has a tangent parallel to the x axis at the origin and wherein the artery- supporting section is configured to carry blood flow in a direction from negative x towards positive x; and

a tangent of the centreline of the vein-supporting section at the origin has direction [cos (Θ) sin (Φ), sin (Θ) sin (Φ), ± cos (Φ)], where Φ is in the range 225 to 270 degrees and Θ is in the range 200 to 300 degrees.

The geometry of the first aspect allows an arterio-venous fistula to be maintained in a position to reduce unsteadiness in the blood flow. It is considered that this may reduce the possibility of failure of the AVF and thus improve clinical outcomes. The centreline of the artery-supporting section may be an arc within the x-y plane.

In preferred embodiments, the vein-supporting section has a diameter D and passes through an intermediate point having coordinates (xp1 , yp1 , ±zp1 ), wherein:

xp1 lies in the range -6D to 4D, preferably -5.5D to 0.5D; and/or

yp1 lies in the range -4D to 5D, preferably -0.5D to 3.5D; and/or

zp1 is less than 5D, preferably in the range -5D to 5D.

D may be the internal diameter of the vein-supporting section. In preferred embodiments, the vein-supporting section is parallel to the x axis at a distal point. Preferably, the distal point of the vein-supporting section has coordinates (-Xd, Kd cos (ξ), ± Kd sin (ξ)). More preferably, Xd is twice Kd. In preferred embodiments, Xd equals 10D and Kd equals 5D, where D is a diameter of the vein-supporting section, ξ may take any value.

The length of the vein section from the intersection point to the distal point is preferably less than 25D, more preferably less than 20D, where D is a diameter of the vein- supporting section. Preferably, the centreline of the vein-supporting section is a two-piece cubic hermitian spline.

In preferred embodiments, the minimum radius of curvature of the vein-supporting section is 1.8D, where D is a diameter of the vein-supporting section. Preferably, the vein- supporting section is constrained within a cylinder of radius 7.5D centred on the x axis, where D is a diameter of the vein-supporting section. The geometry may be constrained such that there is no self-intersection. In some preferred embodiments, the device comprises or is formed from silicone such as a bio-compatible silicone. In alternative embodiments, the device may alternatively or additionally comprise or be formed from a bioresorbable hydrogel. Alternative materials or combinations of materials may also be envisaged. Brief Description of the Figures

A preferred embodiment of the present disclosure will now be described with reference to the accompanying drawings, in which:

Figures 1 (a) and 1 (b) illustrates different views of a device for maintaining the geometry of an arterio-venous fistula (AVF);

Figure 2 illustrates the geometry of the AVF;

Figure 3 shows the value of the objective function F against the simulation number;

Figure 4 shows the value of the objective function F and other parameters against the simulation number;

Figure 5 shows the median values of parameters, their upper and lower quartile ranges and their total ranges for the sets of parameters resulting in F<0.1 ;

Figure 6 illustrates the effect of modifying individual parameter values on predicted values of F, along with dashed lines indicating parameter values associated with the optimal configuration;

Figure 7 illustrates five identified geometries having the lowest value of the objective function F; and Figure 8 illustrates a further five identified geometries having the 6 to 10 lowest values of the objective function F;

Figure 9 illustrates a flow waveform applied at an artery inlet in a pulsatile simulation, together with outflow waveforms at artery outlet and venous outlet;

Figure 10 illustrates velocity magnitude on the arterial symmetry plane at (a) t=1.0s, (b) t=1.13s, (c) t=1.3s and (d) t=1.6s during a pulsatile simulation;

Figure 1 1 illustrates plane-normal vorticity on the arterial symmetry plane at (a) t=1.0s, (b) t=1.13s, (c) t=1.3s and (d) t=1.6s during a pulsatile simulation;

Figure 12 shows streamlines, originating from the artery inlet, shaded by velocity magnitude, at (a) t=1.0s, (b) t=1.13s, (c) t=1 .3s and (d) t=1.6s during a pulsatile simulation

Figure 13 shows the Power Spectral Density (PSD) of a first temporal mode of a Proper

Orthogonal Decomposition (POD) on a semi-log scale (a) and log-log scale (b) and of a fifth temporal mode of a POD on a semi-log scale (c) and a log-log scale (d);

Figure 14 shows the PSD of the input flow rate at the artery inlet on a semi-log scale (a) and a log-log scale (b);

Figure 15 shows a left-handed device (a) and a right-handed device (b) used in a porcine model;

Figure 16 shows a left-side AVF prior to implantation of the device;

Figure 17 shows a left-side AVF after implantation of the device;

Figure 18 shows a right-side AVF after implantation of the device;

Figure 19 shows a PSD computed with a Burg Autoregressive (AR) model of three stethoscope recordings from the left-side AVF prior to implantation of the device;

Figure 20 shows a PSD computed with a Burg AR model of three stethoscope recordings from the left-side AVF after implantation of the device; and

Figure 21 shows a PSD computed with a Burg AR model of three stethoscope recordings from the right-side AVF after implantation of the device.

Detailed Description Referring to Figures 1 (a) and 1 (b), there is illustrated a device 10 for maintaining an arterio-venous fistula (AVF) with a defined geometric configuration. The device 10 may be located internally or externally to the vasculature. The device 10 comprises a vein- supporting section 20 and an artery-supporting section 30. Figure 1 also illustrates the direction of blood flow within the device 10. The vein-supporting section preferably has an internal diameter of 2mm to 1.5cm. The internal diameter of the artery supporting section may be similar.

In the example shown in Figure 1 , the device has a central section disposed between the artery-supporting 30 and the vein-supporting section 20. This provides structural rigidity. In other embodiments, this central section may not be required. The device showing Figure 1 provides "guttering" in the artery-supporting section and vein-supporting section into which the AVF may be received after it is created. Alternative embodiments may be disposed within artery and/or vein during creation of the fistula (for example as a stent). In one alternative embodiment, the device may be formed of a silicone tube which can be pre-shaped using a nitinol (or other suitable material) wire having the desired curvature, before either being applied internally to the AVF as a stent or externally after the AVF is formed. In some preferred embodiments, the device is fabricated from a bio-compatible silicone. In alternative embodiments, the device may be alternatively or additionally fabricated from a bioresorbable hydrogel. Alternative materials or combinations of materials may also be envisaged. For example, in some embodiments, the device may be formed through 3D printing techniques and may be fabricated from appropriate materials for such techniques.

The defined geometry is designed to minimise oscillatory blood flow patterns within the AVF. This has been shown to reduce the risk of failure of the AVF. The defined geometry achieved by the device 10 of Figure 1 has been shown to achieve a reduction in unsteadiness through undertaking of computational fluid dynamics (CFD) simulations in a parameterised AVF model as will be discussed below.

The AVF comprises a vein section and an artery section corresponding with geometry matching the vein-supporting and artery supporting sections 20, 30 of the device 10 respectively. The geometry of the AVF and the device 10 can be further understood with reference Figure 2. This illustrates the centrelines of the vein supporting section and the artery supporting section; these centrelines may be projected beyond the vein supporting section and artery supporting sections themselves. The intersection of the centrelines of the vein-supporting section 20 and artery-supporting section 30 is at point pO = [xpO, ypO, zpO] = [0,0,0]. This is the proximal point of vein-supporting section 20, while the distal or final point is p2. Intermediate point p1 of the vein-supporting section 30 is also illustrated.

The artery-supporting section 20 is formed as a planar arc of a circle, having equations:

Figure imgf000009_0002
Figure imgf000009_0001

s e [-30,30]

Here, ra is the radius of curvature of the centreline of the artery supporting section. Preferably, ra is less than 20D, where D is a diameter of the vein-supporting section. D may be the internal diameter of the vein-supporting section.

The centreline of the vein-supporting section 20 is built as a two-piece cubic Hermitian spline, which can be written as the sum of two polynomials:

Figure imgf000010_0001
mi+i

+s2(-2s + 3) Vpi+i + s2(s - l)

ZPi+i Z, mi+i

Where pO = [xpO, ypO, zpO] = [0, 0, 0] and is the location of the start of the centreline of the vein supporting section (which is at the intersection of the centreline of the vein supporting section and the centreline of the artery supporting section), p1 = [xp1 , yp1 , zp1] is the location of a mid-point of the centreline of the vein-supporting section, and p2 = [xp2, yp2, zp2] = [-10D, 5D cos (ξ), 5D sin (ξ)] is the location of the distal point of the centreline of the vein-supporting section (which is required to lie on the circumference of a circle in a plane parallel to the y-z plane, having a centre [-10D, 0, 0] and a radius 5D) wherein D is a diameter of the vein supporting section.

Tangents mO, ml and m2 are also illustrated and are tangents at points p1 , p2 and p3 respectively. For these tangents, mO = [xmO, ymO, zmO] = [10Dcos (Θ) sin (Φ), 10Dsin (Θ) sin (Φ), l ODcos (Φ)], m2 = [xm2, ym2, zm2] = [-10D, 0, 0] and ml = [xm1 , ym1 , zm1 ] = ¾(p2 - pO) - 1/4(m2 + mO) (defined to ensure C2 continuity at p1 ).

Within these constraints, 6 parameters define the geometry of the system. These are Θ, Φ, xp1 , yp1 , zp1 and ξ.

In a preferred embodiment, these parameters are as follows:

Figure imgf000010_0002
Figure imgf000011_0001

More generally, preferred outcomes were identified for ranges of each parameter value. Preferred ranges for each parameter are as follows:

• xp1 is preferably in the range -6D to 4D, more preferably -6D to 2D, more preferably -5.5D to 0.5D

• yp1 is preferably in the range -4D to 5D, more preferably -2D to 5D, more preferably -0.5D to 3.5D

• zp1 is preferably less than 5D, more preferably in the range -5D to 5D, more preferably in the range -5D to 3D

· Θ is preferably in the range 200 to 300 degrees, more preferably 215 degrees to 300 degrees, more preferably 215 degrees to 270 degrees

• Φ is preferably in the range 225 degrees to 270 degrees, more preferably in the range 250 degrees to 270 degrees. The geometry of the device 10 may be further constrained such that the radius of curvature of the centreline of the vein-supporting section is greater than 1 D/1.8, the length of the centreline of the vein supporting section is less than 20D and the vein-supporting section has to lie within a cylinder having radius 7.5D around the x axis. Mirror images of the above geometry reflected in the x-y plane are equally effective (e.g. with all z values of positions and tangents negated). That is to say, modifying coordinates [x, y, z] to [x, y, -z] for all tangents and positions.

The benefits of the geometry will now be demonstrated with reference to the accompanying figures. An optimization loop was implemented using a Kriging framework to identify optimum values for the six parameters identified above: θ, Φ, xp1 , yp1 , zp1 and ξ. A computational fluid dynamics (CFD) approach was adopted to calculate an objective function F to be optimised. The CFD simulations were undertaken using STAR-CCM+. During the process, the parameter Θ was constrained within the range 180 to 360 degrees while the parameter Φ was constrained within the range 90 degrees to 270 degrees. Thus solutions on only one side of the x-y plane were analysed, and the skilled person will understand that geometries reflected to form a mirror image around that plane would obtain the same results. The geometry of the artery supporting section was as described above, with ra = 20D and further constraints on the geometry of the vein-supporting section were also as outlined above. In addition, self-intersecting solutions were considered to be impossible and were therefore discarded.

The Kriging method, sometimes referred to as Gaussian process regression, provides interpolation for which the interpolated values are modelled by a Gaussian process governed by prior covariances. Kriging predictors depend on stochastic processes, which mean they are probabilistic predictors with a standard error which quantifies the uncertainty of the predicted value.

In order to establish an appropriate model of the AVF, the present disclosure adopts the Kriging predictor implemented in the MATLAB DACE (design and analysis for computer experiments) package described in S0ren N Lophaven, Jacob S0ndergaard, and Hans Bruun Nielsen. DACE: A Matlab Kriging Toolbox. Informatics and Mathematical Modelling, Technical University of Denmark, DTU, pages 1-28, 2002, the contents of which are incorporated herein in their entirety. Alternative approaches may be adopted as appropriate. Furthermore, boundary conditions are set as follows. Steady-state parabolic boundary- normal flow profiles were applied at the Proximal Artery Inlet (PAI) and the Distal Venous Outlet (DVO). The flow conditions correspond to a Reynolds number of 800 at the PAI (based on the spatially averaged velocity at the PAI and the diameter of the PAI). This is an appropriate Reynolds number for a patient with an AVF. Also, the aforementioned conditions enforce an 80:20 flow split between the DVO and the Distal Arterial Outlet (DAO). A constant (and arbitrary) pressure was applied at the DAO, and a zero-velocity no-slip condition was applied at the arterial and venous walls, which were assumed to be rigid. The Kriging Method is designed to minimise an objective function F given parameters x. In the present case, the parameters are those outlined above. The objective function adopted represents unsteadiness within the system.

The particular objective function representing unsteadiness used in these calculations can be understood as follows. For evaluating the unsteadiness inside the vessel, it was assumed that, if the flow is steady, the results given by a steady solver and an un-steady one should be the same. The objective function for the Kriging model was calculated by evaluating the Wall Shear Stress WSSSt from a steady solution, and comparing it with the evolving Wall Shear Stress WSS(t) calculated after restarting from the aforementioned steady solution with an unsteady solver, and running for a period of time. Therefore, the objective function F was defined as:

Therefore, the objective function F was defined as:

Figure imgf000013_0001
where S is the surface of the configuration, tmin = 5D/V, and tmax = 10D/V, with V the spatially averaged inflow speed at the PAI, and both tmin and tmax measured from the point at which the unsteady solver was started. The optimization process is divided in two main parts:

1. Initialization: in which Latin Hypercube Sampling (LHS) is used to calculate a number of valid parameter sets N for N CFD simulations (in this case N is 91 ). This first set of simulations is used to construct the Kriging surrogate the first time. LHS guarantees a well distributed sets of initial points in the parameter space.

2. A mesh adaptive direct search (MADS) method is used together with a Kriging- based surrogate model of the function F to find the set of parameters so tim such that:

Figure imgf000014_0001
The mesh adaptive direct search (MADS) adopted in this disclosure is a derivative free optimisation algorithm as described in Charles Audet and J. E. Dennis, Mesh Adaptive Direct Search Algorithms for Constrained Optimization, SIAM Journal on Optimization, 17(1 ): 188-217, 2006 (referred to hereinafter as "Audet and Dennis"). It is an iterative algorithm and each iteration has two main steps, the SEARCH step and the POLL step.

At each iteration k, the parameter space Ω is divided in a parameter space mesh, defined as:

Mk = (J s + A Dz : z c N"

With Sk the set of points where the objective function F has already been evaluated, Amk defines the mesh size, D is a nxnD positive spanning matrix, in which each column represents a direction dj, and z is a vector of integers. The steps in each iteration (SEARCH and POLL), can be summarised as follows:

During the SEARCH step, a Kriging-Based surrogate model of F is used to predict values of F at points in Mk. More precisely, if Mk has less than 1 x104 points the surrogate model of F is evaluated on all points that do not already have a value of F assigned. However, if Mk has more than 1 x104 points, then the surrogate model of F is evaluated on a LHS of Mk. The 3 trial points having the smallest predicted value of F are tested via CFD simulations, and added to Sk, together with a fourth trial point which has the biggest uncertainty on the predicted value.

The parameter set sk represents the point where the objective function assumes the current minimum value. If F assumes a smaller value than the current optimum on one of the newly tested set, sk is updated, Amk+1 = 4Amk, k=k+ 1 , and the SEARCH step is repeated, otherwise, if no trial point improves the objective function, the iteration goes to the POLL step. During the POLL step the real value of objective function F (calculated through CFD simulation) is evaluated on a frame Pk, with Pk={sk+ Amkd:d <≡ Dk}cMk where Dk is a positive spanning set of n+1 dimensions, with AmkHdH^Apk, and where Apk is the poll size parameter. The relationship Apk=npAmk was used in the following calculations. In fact, in the MADS algorithm, when Apk and Amk go to zero, the number of candidate sites for POLL increase.

The generation of the positive basis Dk follows the rules described in Audet and Dennis. If during the POLL step an improved mesh point is found, sk is updated, Amk+1 = 4Amk, k=k+1 , otherwise sk+1 =sk, Amk+1 = Amk/4, k=k+ 1. The algorithm is repeated until the new Amk<Amkmin.

In the calculations presented below, each CFD simulation employed a mesh with approximately 1 million cells, and the average element size close to the anastomosis was the 3% of the arterial diameter.

The optimisation framework was fully automated, and the automation was achieved through MATLAB and JAVA scripts which worked with the CFD modelling. The construction of the model was performed by first generating 600 initial configurations via LHS that satisfied the parameter range constraints. Of these 600 configurations, 509 were rejected because they were self-intersecting, or violated the other constraints on maximum venous curvature, venous length, and overall AVF size. F was evaluated on the remaining 91 valid configurations.. The optimisation process was then launched, and a total of 39 further parameter sets were identified, 29 of which led to feasible geometries. The 22nd of the further feasible parameter sets was found to be the optimal configuration.

Figure 3 illustrates the value of the objective function against the simulation number. Vertical line 31 divides simulations selected via LHS (to the left of the line) from those run during the optimisation phase (to the right of the line). To the right of the line, only simulations that the Kriging surrogate model predicted had a low value of F are illustrated plus the simulations run during the POLL step (i.e. the value of F for the simulations with the worst uncertainty are not plotted). Marker 33 shows the optimum of F achieved. Figure 4 shows similar plots, this time including both the value of the objective function F against simulation number and the values of the six parameters for each simulation. Again, simulations during the LHS phase are illustrated to the left of vertical lines 41 and to the right are simulations during the optimisation phase. Markers 42 show the simulation with the optimum value of F. From Figure 4, it can be seen that there is greater variation in some parameters than in others during the optimisation process. This indicates a greater dependence of the objective function F on certain parameters, particularly Θ and Φ. Figure 5 further explores the optimum values of the parameters. Specifically, it illustrates the median values, upper and lower quartile ranges and full ranges of each parameter associated with a corresponding F<0.1. The median values are represented by horizontal lines within the bars illustrating the upper and lower quartile ranges, while the total range for parameter sets meeting the F<0.1 criteria is represented by the total extend of the vertical lines. Also shown are markers 51 indicating the parameter values associated with the optimum simulation.

Figure 5 illustrates that Θ and Φ are the most influential parameters with greater influence on the outcome of the objective function F than the others. This is further demonstrated in Figure 6, which plots the values of the objective function F predicted by the surrogate model when a single parameter is varied at a time keeping the other values constant. The initial parameter sets are based on the five best parameter sets identified using the Kriging method, with a single parameter then varied in order to calculate its effect on the objective function F.

As can be seen from Figure 6, the greatest effect on the objective function in these scenarios comes from variation of Θ and Φ. Again, this suggests these parameters are particularly important in optimising the geometry of the AVF. Nevertheless, other parameters also play a role as demonstrated by Figure 6.

The results illustrated in Figure 6 can be understood to illustrate that the angle of a connection between vein and artery is important in optimising the geometry of the AVF. Furthermore, the optimal results are achieved with similar medial points p1 . However, the position of the final point p2 appears far less influential, allowing a range of geometries to provide outcomes with low values of the objective function F. Figures 7 and 8 show the 1 to 5 and 6 to 10 best identified geometries in terms of obtaining a minimum objective function F respectively. Each geometry is illustrated from three principle views, ZXY, XYZ and YZX. On the left hand side of each of Figures 7 and 8 are shown the calculated values of the objective function F for each geometry.

A high-resolution unsteady simulation of flow within the optimal AVF configuration was carried out to demonstrate that high-frequency unsteadiness remains suppressed when the inflow is pulsatile.

Blood flow was modelled with μ (blood viscosity) = 3.5 χ 10-3Pa s and p (blood density) = 1060kg m-3. A space-time varying velocity boundary condition was imposed at the PAI . The inflow waveform, which had a period of 1 s, was obtained from "Vascular remodelling in autogeneous arterio-venous fistulas by MRI and CFD" by M Sigovan et al (Annals of Biomedical Engineering, 41 (4):657-68, 2013). Specifically the first 15 Fourier modes were extracted, and the signal was scaled such that the peak Reynolds number at the PAI was 1300. The resulting time-averaged Reynolds number at the PAI was ~ 750, similar to the time-constant PAI Reynolds number of 800 used during the optimisation process. The resulting Womersley number was 6.9. All flow was prescribed normal to the PAI inflow plane, and in line with previous studies, a Womersley profile was imposed in space. The PAI inflow rate QPAI as a function of time is shown in Fig. 9.

An RCR Windkessel model was applied at the DAO and DVO. Specifically:

PDAO— QDAO(RIDAO + R2DA0) ~

Figure imgf000018_0001
~ RIDAOQDAO)

And

d

PDVO— QDVO(RIDVO + R2DV0) ~ RIDVOCDVO ^ (PDVO ~ RIDVOQDVO) where PDAo and PDVo are the spatially averaged pressures at the artery outlet (DAO) and venous outlet (DVO) respectively, QDAO and QDvo are the outflow rates at the DAO and DVO respectively, and RIDAO,

Figure imgf000019_0001
CDAO> RIDVO, CDVO are relevant Windkessel parameters.

These were selected such that PDAo had a physiological range 80-130mmHg, and the average flow split between the DVO and DAO of ~66:34, and a flow split at peak inflow between the DVO and DAO of ~45:55. Specifically, values of R-IDAO = 0.78mmHgmr1s, R2DA0 = 27.0mmHgmr1s, CDAo = 0.018mlmmHg"1 , RiDvo = 7.33mmHgmr1s, R2DVO = 8.46mmHgmr1s, CDvo = 3.48mlmmHg~1 were used. The resulting outflow waveforms QDAO and QDVO at the DAO and DVO respectively are shown in Figure 9. Finally, a no-slip boundary condition was applied at the AVF wall.

Star-CCM+ v9.06.9 (CD-Adapco, Melville, NY USA) was used to solve in the optimal AVF configuration. The simulation was initialised with zero velocity, a reference pressure of 80mmHg, and run with the coupled steady-state solver until every momentum and mass continuity residual was below 10~10. The resulting steady-state solution was then used as the initial condition for the coupled implicit unsteady solver. This solver was run for 1 s (one pulse period) with a timestep of 1 χ 10~4s in order to allow transient 'start-up' phenomena to pass, and then a further 1 s (one pulse period) with a time-step of 1 x 10~4s, during which time data was exported for analysis.

A polyhedral unstructured volume mesh, with a prismatic boundary layer mesh adjacent to the wall, was used for the simulation. The mesh was refined near the anastomosis. Specifically, elements near the anastomosis had an average size of 7 χ 10-5m, expanding progressively to 1 .35* 10-4m beyond a distance of ~ 2.5x 10-2m from the anastomosis. The prismatic boundary layer meshes were 25 elements thick, with the first element having a thickness of 2.5 x 10-6m. The mesh had ~ 12 χ 106 elements in total.

Figure 10 shows snapshots of velocity magnitude u(x) on the arterial symmetry plane, and on a three-dimensional surface that tracks the venous centreline, at four points in the pulse cycle. Figure 1 1 shows snapshots of plane-normal vorticity ω(χ) on the arterial symmetry plane, and on a three-dimensional surface that tracks the venous centreline, at four points in the pulse cycle. Figure 12 shows streamlines, originating from the PAI, shaded by velocity magnitude, at four points in the pulse cycle. It is clear that the majority of arterial flow is shifted to the outside of the arterial curvature throughout the pulse cycle. It is also apparent that the majority of venous flow is shifted to the outside of the venous curvature throughout the pulse cycle. Finally, it can be observed that a region of recirculating flow is present adjacent to the inside of the venous curvature, proximal to the anastomosis. The nature of this re-circulating region changes through the pulse cycle. However, finescale separated vortical structures, associated with high-frequency flow unsteadiness in previous studies, are absent.

A quantitative assessment of unsteadiness was made via snapshot Proper Orthogonal Decomposition (POD) of WSS fluctuations of(x, t) = o(x, t) - σ(χ), where o(x, t) is the WSS field, and σ (x) is the time-averaged WSS field. Specifically, snapshot POD of of(x, t) was undertaken in a window from 1 .0 - 2.0s, spanning a full pulse period, using 1000 temporal snapshots with a uniform spacing of 0.001 s.

Figure 13 shows the Power Spectral Density (PSD) of a-i(t) and a5(t), the first and fifth temporal POD modes respectively. The second through fourth modes exhibited similar behaviour and are hence omitted for brevity. All significant energy is below 10Hz, and on comparison with Figure 14, which shows the PSD of QPAi, it is reasonable to attribute the majority of this low-frequency content to the pulse waveform. There is no significant energy content around 60Hz, nor above 100Hz, both of which have been observed in previous studies. Consequently, the results demonstrate that the optimal configuration can suppress potentially pathological high-frequency flow unsteadiness even when the inflow is pulsatile.

Furthermore, an experiment has been carried out in a porcine model to demonstrate the efficacy of the chosen model. Figure 15 illustrates devices used for this experiment, the devices being fabricated in Object TangoBlackPlus FLX980 using a Connex 350 3D printer. In particular, left-sided and right-sided devices were formed (illustrated in Figures 15(a) and 15(b) respectively) as mirror images around the plane of the arterial curve. The internal diameter D of the devices was 5 * 10"3mm. The experiment was carried out in accordance with all necessary conditions and licenses on a 60kg Large White/Landrace swine under terminal anaesthesia.

A mid-line incision was made in the neck and the jugular and carotid vessels dissected out on both the left and right sides of the neck (with left-right laterality defined in respect of the animal). Bilaterally, the jugular vein was then cut distally and mobilised, with all visible tributaries ligated, and a slit arteriotomy was made in the common carotid artery before a microsurgical anastomosis (10/0 nylon) was made between the mobilised jugular vein and the common carotid artery to create an end-to-side AVF. Following creation of the AVF, the right-handed and left-handed devices were implanted to shape the left-side and right- side AVF, respectively. Due to anatomical limitations of the surgical field a short (~5 x 10"3 m) portion of the device in the region of the DVO had to be trimmed on both sides to permit implantation.

To obtain an indication of unsteadiness, digital stethoscope recordings were made directly over the anastomosis both before (left-side AVF only) and after (left-side and right-side AVF) device implantation. Specifically, recordings were made for approximately 20s with a sample rate of 4000 Hz, and three independent recordings were made at each location.

Figures 16, 17 and 18 show the left-side AVF before implanting the device, the left-side AVF after implanting the device, and the right-side AVF after implanting the device respectively. In both cases where the device was implanted it held itself in place via the guttering, and visually formed the AVF into the desired configuration.

Figures 19, 20 and 21 show PSD computed with a Burg Autoregressive model of the stethoscope recordings from the left-side AVF before implanting the device, the left-side AVF after implanting the device, and the right-side AVF after implanting the device respectively. All three recordings for the left-side configuration without the device exhibit a clear peak at ~ 600Hz, which is eliminated from all three subsequent recordings after the device is implanted. This indicates that the device is acting to suppress high frequency unsteady flow in the AVF. Moreover, the PSD spectra for the right-side AVF after implanting a device look visually similar to their left-side counterparts; without a significant peak at ~ 600Hz. However, right-side AVF PSD spectra before implanting a device were not available for direct comparison. It can be clearly seen from Figures 19 to 21 that the device can suppress high-frequency unsteady flow in an AVF.

Variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known and which may be used instead of, or in addition to, features described herein. Features that are described in the context of separate embodiments may be provided in combination in a single embodiment. Conversely, features which are described in the context of a single embodiment may also be provided separately or in any suitable sub-combination.

It should be noted that the term "comprising" does not exclude other elements or steps, the term "a" or "an" does not exclude a plurality, a single feature may fulfil the functions of several features recited in the claims and reference signs in the claims shall not be construed as limiting the scope of the claims. It should also be noted that the Figures are not necessarily to scale; emphasis instead generally being placed upon illustrating the principles of the present invention. Where ranges are disclosed, they should be considered to include their endpoints.

Claims

Claims
1. A device for maintaining a vascular connection comprising a vein-supporting section and an artery-supporting section, wherein
a centreline of the vein-supporting section and a centreline of the artery-supporting section meet at an intersection point which defines the origin of a right-handed Cartesian coordinate system;
the centreline of the artery-supporting section is arcuate and lies in the region y<=0 and has a tangent parallel to the x axis at the origin and wherein the artery- supporting section is configured to carry blood flow in a direction from negative x towards positive x; and
a tangent of the centreline of the vein-supporting section at the origin has direction
[cos (Θ) sin (Φ), sin (Θ) sin (Φ), ± cos (Φ)], where Φ is in the range 225 to 270 degrees and Θ is in the range 200 to 300 degrees.
2. A device according to claim 1 , wherein the centreline of the artery-supporting section is an arc within the x-y plane.
3. A device according to claim 1 or claim 2, wherein the vein-supporting section has a diameter D and passes through an intermediate point having coordinates (xp1 , yp1 , ±zp1 ), wherein:
xp1 lies in the range -6D to 4D, preferably -5.5D to 0.5D; and/or
yp1 lies in the range -4D to 5D, preferably -0.5D to 3.5D; and/or
zp1 is less than 5D, preferably in the range -5D to 5D.
4. A device according to any one of the preceding claims, wherein a distal point of the centreline of the vein-supporting section is parallel to the x axis at a distal point.
5. A device according to claim 4, wherein the distal point of centreline of the vein- supporting section has coordinates (-Xd, Kd cos (ξ), ± Kd sin (ξ)).
6. A device according to claim 4, wherein Xd is twice Kd.
7. A device according to claim 5, wherein Xd equals 10D and Kd equals 5D, where D is a diameter of the vein-supporting section.
8. A device according to any one of claims 4 to 7, wherein the length of the vein- supporting section from the intersection point to the distal point is less than 25D, preferably less than 20D, where D is a diameter of the vein-supporting section.
9. A device according to any one of the preceding claims, wherein the centreline of the vein-supporting section is a two-piece cubic hermitian spline.
10. A device according to any one of the preceding claims, wherein the minimum radius of curvature of the vein-supporting section is 1 .8D, where D is a diameter of the vein-supporting section.
1 1 . A device according to any one of the preceding claims, wherein the vein- supporting section is constrained within a cylinder of radius 7.5D centred on the x axis, where D is a diameter of the vein-supporting section.
12. A device according to any one of the preceding claims, wherein the device comprises a biocompatible silicone.
13. A device according to any one of the preceding claims, wherein the device comprises a bioresorbable hydrogel.
PCT/EP2017/054420 2016-02-29 2017-02-24 A device for maintaining vascular connections WO2017148836A1 (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140194910A1 (en) * 2011-08-01 2014-07-10 Eyal Orion Vessel shaping devices and methods
US20150119908A1 (en) * 2013-10-25 2015-04-30 Abbott Cardiovascular Systems Inc. Extravascular devices supporting an arteriovenous fistula
US20150148825A1 (en) * 2012-08-01 2015-05-28 Laminate Medical Technologies Ltd. Apparatus for configuring an arteriovenous fistula
US20160000985A1 (en) * 2014-07-02 2016-01-07 Abbott Cardiovascular Systems Inc. Extravascular devices supporting an arteriovenous fistula

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140194910A1 (en) * 2011-08-01 2014-07-10 Eyal Orion Vessel shaping devices and methods
US20150148825A1 (en) * 2012-08-01 2015-05-28 Laminate Medical Technologies Ltd. Apparatus for configuring an arteriovenous fistula
US20150119908A1 (en) * 2013-10-25 2015-04-30 Abbott Cardiovascular Systems Inc. Extravascular devices supporting an arteriovenous fistula
US20160000985A1 (en) * 2014-07-02 2016-01-07 Abbott Cardiovascular Systems Inc. Extravascular devices supporting an arteriovenous fistula

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