Flow driven robotic navigation of microengineered endovascular probes

Minimally invasive medical procedures, such as endovascular catheterization, have considerably reduced procedure time and associated complications. However, many regions inside the body, such as in the brain vasculature, still remain inaccessible due to the lack of appropriate guidance technologies. Here, experimentally and through numerical simulations, we show that tethered ultra-flexible endovascular microscopic probes can be transported through tortuous vascular networks with minimal external intervention by harnessing hydrokinetic energy. Dynamic steering at bifurcations is performed by deformation of the probe head using magnetic actuation. We developed an endovascular microrobotic toolkit with a cross-sectional area that is orders of magnitude smaller than the smallest catheter currently available. Our technology has the potential to improve state-of-the-art practices as it enhances the reachability, reduces the risk of iatrogenic damage, significantly increases the speed of robot-assisted interventions, and enables the deployment of multiple leads simultaneously through a standard needle injection and saline perfusion.


Supplementary Figures
Supplementary Figure 1. Illustration showing the insertion system. The µ-probe is proximally coupled to a rigid rod and its position controlled by the movement of the rod. The main purpose of the rigid rod is to provide a rigid coupling across the gasket between the linear positioner and the flexible µprobe, and to control the release rate of the µ-probe that is being pulled by the flow. The µ-probes used in this study were longer than 70 mm. Drawings are not to scale. Supplementary Figure 11. Characterization of the flow sensor. a Pictures of the experimental channel where flow measurements were taken. The mother vessel bifurcates into two daughter vessels with different cross-sectional area. Thus, the fluid velocities are expected to be different. Scale bar, 10 mm. b The repeatability of the measurements was verified in a 2 mm x 2 mm channel using three different µ-probes and by performing three independent trials with each µ-probe (n = 9). Mean value is marked with black dots. Figure 12. 2D projection of proposed 3D navigation control strategies. a Large view of a vascular tree example presenting three bifurcation (I, II, III) leading to the target region (black circle). Fluoroscope views are boxed with black dotted lines. b Perpendicular actuation control: the magnetic head is rotated with minimal magnetic field by orienting it perpendicular to the incident vessel (assumed parallel to magnetic head). c Target vessel direction control: magnetic field is oriented towards the target vessel and the magnetic field increased until the head is properly oriented. Dark grey dashed lines indicate the target trajectory. Drawings are not to scale. Figure 13. Imaging of µ-probes using two different fluoroscopes in realistic environments. a,b Optical images of the samples under test. The composite consists of PDMS:NdFeB microparticles that was mixed at a 1:1 volume ratio. The diameter of the magnetic samples varied between 150 µm and 350 µm. c Fluoroscope images (Canon Alphenix Sky+, 200 µm resolution) of the magnetic structures (top) placed in an ex vivo rabbit head (bottom). d Fluoroscope images (Canon Alphenix Core+, 76 µm resolution) of the magnetic structures (top) inside an anthropomorphic head phantom (bottom). Scale bars, 5 mm. Figure 14. Flow-driven deployment using off-the-shelf equipment. a A standard cannula was connected to the insertion device that is perfused by a standard pressurized IV-bag. b Snapshots of a cannulation process of a PDMS phantom. Scale bars, 30 mm and 5 mm (inset). Figure 15. Flow-driven deployment using commercially available endovascular catheter. a A 3 F catheter is connected to a perfusion syringe and a pressurized IV-bag. The µ-probe (∅150 µm x 2 mm magnetic head) is glued to the guidewire and pulled into the catheter. Upon introduction of perfusion, pushing the guidewire allows the µ-probe to exit the catheter (right). b Demonstration of the hybrid catheter/µ-probe device. Once the catheter reach places that it cannot advance (e.g. a high curvature turn), it can deploy the µ-probe that can effortlessly advance with the flow and reach the target location. Scale bars, 5 mm. Figure 16. Blood compatibility assay performed on fresh human blood under high shear stress condition. Three different samples were tested, kapton film (K: 0.004 x 0.2 x 10 mm 3 ), magnetic head with silica-coated magnetic particles (H: ∅0.3 mm x 1 mm), and whole µ-probe (P: K + H). Negative and positive control are platelet rich plasma (PRP -non-activated platelets) and PRP exposed to collagen type-I (PRP+Col-I -activated platelets). a ATP release from platelets was measured using luciferin-luciferase reaction. b Platelet aggregation was measured using absorbance (595 nm). The aggregation % was defined by the transmission of light through non-activated PRP, represented as 0 % aggregation, and through platelet-poor plasma (PPP) as 100 % aggregation. Both techniques have been vastly used in the platelet field to investigate the thrombogenicity of different materials and devices. Values were compared with the non-activated platelet, (***P < 0.001, PRP) by one-way ANOVA followed by Dunnett's post hoc test (SEM, duplicate average from four independent experiments). Figure 17. Experimental platform. a Digital to Analog Converter (DAC) card allows real-time communication between the computer and the hardware. The servo drives adjust the current provided by the power supplies to the coils. The linear positioner allows controllable release of the µprobe through the rigid rod of the insertion system. Windkessel system is placed between the peristaltic pump and the perfusion-based insertion system to dampen the flow oscillations from the pump. Visual feedback for teleoperation is provided by a CMOS camera. Drawings are not to scale. b Picture of the experimental platform. Figure 18. Illumination system for biomimetic phantoms. Backlight system provides optimal contrast for visualizing the µ-probe inside transparent channels. Grey arrows indicate the position of the µ-probe head. Figure 19. Fabrication of biomimetic phantoms. The 3D printed open channel is sandwiched between two glass slides and laminated using UV glue as shown in the (a) oblique and (b) side views. c Refractive index-matching UV glue provides optical transparency for visualization. Difference in transparency of a 3D printed phantom prior (left) and after (right) the addition of UV glue is shown. Scale bar, 1 cm d Process flow for manufacturing the elastomer phantoms. Commercially available 1.75 mm-diameter polyvinyl alcohol (PVA) filament is thermoplastically shaped and bonded. Sonication in a heated bath dissolves the PVA inside the casted elastomer, which was removed with extensive washing. e Pictures of representative devices. Channels are made visible with a blue ink. Figure 20. Fabrication of µ-catheters a Elastomer tubes are fabricated through controlled Joule heating of a tungsten wire. The magnetic tubular head is glued to the tube. Drawings are not to scale. b Close-up picture of a microfluidic µ-catheter with an inner diameter of 40 µm and outer diameter of 120 µm. Scale bar, 100 µm. c Calibration curve between the obtained outer diameter of the µ-catheter with respect to the curing time at a current density of 320 A×mm -2 through a 40 µmdiameter tungsten wire.

Supplementary Tables
Supplementary Table 1. Flow velocity and shear stress measurements. Comparison between the analytical and empirical values of flow velocity and wall shear stress under different conditions. Flow velocity and shear stress were calculated from the input flow velocity and measured using the microfabricated flow sensor. Number in parenthesis corresponds to the incremental factor with respect to the levels in the pre-stenosis or vessel 1.

Supplementary Notes
Supplementary Note 1. Computational modelling of µ-probe dynamics.
In our platform, the filament dynamics is driven by the interplay of four physical effects -elastic bending forces, contact forces, magnetic torques, and viscous stresses. We assume external forces, such as gravity, to be negligible with respect to viscous forces. The primary output is The filament is discretized and the fluid velocity at each node is known and can be projected onto a local coordinate system (see Fig. 3a). It is then possible to obtain the local velocities at the node from the velocity vector : -. and ∥ . . The forces in this local coordinate system become: (1) where h is one of the body lengths (2R for the cylinder and a for the ribbon 20 The calculated forces were compared with the force values obtained using CFD. Filaments where modelled in COMSOL Multiphysics using the laminar flow module. The flow was considered planar in a (X, Y) plane purely along the X direction. The angle theta was considered to be 0° when perpendicular to the flow. These results were used to perform a weighted fit (equal weight for each node) of theand ∥ coefficients: Table 3 Fitting parameters used for calculating the drag coefficient .
The amplitude of the parameters λ shows that the default model is capable of accurately estimating the normal fluid forces but tends to overestimate tangential fluid forces. By using these fitting parameters, we developed a model that can accurately calculate the fluid forces. The proximal tip of the µ-probe was considered to be clamped and the distal tip of the µ-probe was considered as free. With these hypotheses, it is possible to model the two-dimensional µprobe using a geometrically non-linear approach to the pure bending theory of beams. The local strain is considered to be small and thus linear elasticity can be considered for the beam.
Forces have to be transformed in torques, for 0 ≤ ≤ − 1 the forces at each node are: Finally, the relative angle at each node becomes: For small deformations, it is possible to analytically solve the Euler-Bernoulli equation and consequently solve the lumped model in one iteration. However, for large deformations, the loading is position dependent (geometrical non-linearities). An iterative method was implemented 2 to solve the lumped model for large deformation scenario. A relaxation factor was used: where values of the relaxation factor were chosen between 0.8 and 0.99 depending on the convergence rate of the problem. This algorithm was validated using COMSOL Solid Mechanics on a largely deformed beam.
The magnetic moment . at each node of the magnetic head was obtained by estimating the magnetization of the heat. The magnetic powder used has a residual induction £ = 850 mT that was considered to be constant in magnetic fields ≤ 50 mT. The magnetization is then defined as ( e = 4 • 10 M¬ N • A M3 ): The magnetic torque can be expressed as: For a 1 mm long and 0.35 mm in diameter magnetic head the total volume is 0.0952 mm 2 of which between 5% and 20% of the volume is magnetic material. The obtained head has a magnetization between 3 µA·m -2 and 13 µA·m -2 and the maximum torque at 30 mT is between 0.09 µN·m and 0.39 µN·m.
A simple penalty algorithm was also implemented in order to account for contact between the walls of the channel and the µ-probe. A force normal to the channel is applied on each node of the µ-probe that violates the non-penetration condition. This contact force depends quadratically on the penetration distance as follows: Where the multiplication factor , which is between 10 • 10 M¼ and 200 • 10 M¼ was tuned depending on the amount of reaction force needed. These reaction forces can directly be used in the lumped model as an additional set of forces acting on the system.

Supplementary Note 2. µ-Probe navigation under limited flow velocity
Accessing geometrically unfavourable daughter vessels poses a major problem for conventional endovascular devices. We showed so far that the advancement is governed by the viscous stresses, which in turn facilitate the steering into difficult bifurcations, for instance 90° diverting daughter vessels (T-shape). However, in scenarios with unfavourable hydrodynamic conditions, i.e. poor or absent flow, the µ-probe may experience insufficient drag force and, therefore, has difficulty to advance further. In some cases, the proximal filament may even be suctioned in the wrong daughter vessel given a prohibitive ratio "1/"2 as shown with red arrows (Supplementary Fig. 23a). To overcome this limitation, the magnetic head can be controllably actuated to boost the drag force or exploit the vessel walls as anchor points. In the event that 0 < "1/"2 < 0.1, i.e. fluid is predominant in vessel 2 but still present in vessel 1, the magnetic head can be orientated at a specific offset with respect to the fluid direction in order to increase drag force ( Supplementary Fig. 23b). The sudden increase in drag force is sufficient to regain tensile regime in the filament and to advance the µ-probe. After successfully transporting the µ-probe in the target daughter vessel using the drag-boosting protocol, the total drag force acting on the filament becomes sufficient to sustain advancement without external help.
In total absence of flow the µ-probe can advance by crawling inside the vessel. Crawling requires synchronisation between the release of the µ-probe and the rotation of the magnetic field ( Supplementary Fig. 23c). To visualize the navigation success in the T-shape bifurcation, we created a phase diagram illustrating the navigation score at different "1/"2 ratio and for two different head geometries channel ( Supplementary Fig. 24). "1 is the average velocity in the 90°-diverting vessel and "2 the average velocity in the straight channel. We iteratively navigated the µ-probe into the target daughter artery and recorded the navigation of three different µ-probes. Each dot, dash or bar corresponds to the score result of 10 navigation runs for each µ-probe (n = 10). The results show a wide regime in which the µ-probe can efficiently navigate into the target vessel (dotted green area) regardless the total input flow. Intuitively, increasing the flow going into the target vessel facilitates the navigation. At lower "1/"2 ratio, and low input flow, the µ-probe can be steered into the T-vessel but requires time-varying actuation of the head to reach the target (dashed light green area). Increasing the total input flow, completely precludes the navigation because of dominant suctioning effects transporting the proximal filament into the straight channel (crossed sky-blue area). These adverse effects became even more significant at higher input flow.

Supplementary Figure 24. Evaluation of steering success in an asymmetric T-shaped bifurcation.
Phase diagram illustrating the navigation success (green area) under uneven flow distributions between the two daughter vessels. Upon hydrodynamically unfavourable conditions, the µ-probe can exploit kite effect or crawling locomotion (light green area) or be unable to continue the navigation (sky-blue area). Each symbol represents the result of 10 trials. A total of three µ-probes were tested (n = 30). Two different head diameters were tested: 350 µm (top) and 150 µm (bottom).

Supplementary Note 3. Flow profile in a square duct
The flow profile was calculated using the Fourier sum representing the general formula for flow velocity in rectangular ducts 3  where " âÛãäå is the velocity of the fluid and ÚåaeÚç·jèjçé is the rate at which the µ-probe is released. The value of k depends on the Reynolds number as described in Equations (3) and (5). The tension on the µ-probe and the normal forces on the inward wall of the turns is maximized when ÚåaeÚç·jèjçé = 0 and " âÛãäå is larger than 0. Here, we assume ÚåaeÚç·jèjçé = 0 to take into consideration the highest normal forces that may act on the µ-probe.
To calculate the normal forces acting on the vessel walls, we had to quantify the drag forces as a function of μ-probe length. To this end, we developed an experimental platform that consists of a straight channel where the µ-probe was inserted and exposed to flow with constant velocity (Supplementary Fig. 27a). The μ-probe was clamped to an external force sensor (SI-KG7, WPI) that is sensitive enough to report the sub-mN tension on the μ-probe, which is solely determined by the fluid forces as the μ-probe does not contact the channel walls. The plot shown in Supplementary Figure 27b reports the total drag force per µ-probe length for the following parameters: " = 10 cm·s -1 , μ-probe width h = 200 µm, dynamic viscosity = 1 mPa·s, density = 1000 kg·m -3 . We provided an analytical model in the Supporting Information (Supplementary Note 1) that is based on resistive force theory. Assuming Re larger than 20, the drag force can be calculated using the following formula: b Experimental data and simulation of the total drag force acting on a µ-probe subjected to an average flow rate of " = 0.1 m×s -1 at Re > 20. The µ-probe length is the part of the µ-probe subjected to viscous stresses. Each experimental measurement was repeated at least three times.
The experimental results are in good agreement with the calculated values and the observed offset between simulations and experimental data (on average 30 µN) is due to the fact that we ignored the magnetic head in our calculations. After validating the analytical model, we calculated the drag force exerted on a 12 cm-long μ-probe by the blood flow ( = 3.5 mPa·s, " = 10 cm·s -1 , density = 1060 kg·m -3 ). The total drag force is ß = 0.28 mN, which is orders of magnitudes lower that push forces involved in the advancement of conventional guidewires 4,5 . In addition, we assumed that all the forces applied by the fluid will be transmitted to the vessel wall, which is very unlikely due to mechanical instabilities.
We next studied the normal forces generated by the μ-probe that is being pulled by the flow on the inward wall of a turn. In this configuration, the highest normal forces are recorded in a single turn channel. As an extreme example, in a 180° turn, the total force acting on the inward wall is equal to the total drag force acting on the part of the µ-probe distal to the turn.
In general, the normal force can be written as ß = Þ sin Supplementary Figure 29. Calculation of tension on a fixed capstan system. a Filament is assumed to slide on a circular object of radius R forming a contact arc region with angle (left). The dynamic friction coefficient decreases the tension forces across the turn from to 2 . Infinitesimal representation of the filament with d as the contact angle, dN the normal force, d the dynamic friction and dT as the difference between the tension forces across the turn (right). The reference frame is the normal n and the tangential t directions. b Series of turns with contact angle . between the filament and the object.
The force balance along the tangential (t) and normal (n) axis leads to where FN is the normal force, T is the tension on the rope, is the dynamic friction, and is the total angle between the inward wall of the artery and the µ-probe. Equations (27) and (28) can be combined as: The solution of the integral leads to the Euler-Eytelwein formula 6 or Capstan equation, that expresses the tension drop across each turn: For a series of n turns, the cumulative tension ñÇé (i.e. force required to retract the µ-probe) is given by: In our experimental setup, the tension 2 corresponds to the drag force acting on the µ-probe before entering the first turn, Þ,ôÚÈjÛäçj . Thus, As described above, the highest normal forces are recorded in the first turn of the channels.
The total normal force exerted to the wall on the first turn is calculated by integrating the total pressure (p) acting on the contact arc: To validate the model, we devised a setup where the µ-probe was connected to a force sensor and pulled inside a 3D printed phantom with a well-defined geometry ( Supplementary   Fig. 30a). The channel has 6 turns each with 90° turn angle and is made of cured 3D printed resin ( Supplementary Fig. 30b). The retraction forces were recorded while the µ-probe was pulled at 2 mm·s -1 under different flow rates. We then normalized the data with respect to the baseline drag force, Þ,ôÚÈjÛäçj . The normalized data essentially follow the same curve ( Supplementary Fig. 32). Thus, the total force required to retract the µ-probe can be estimated for a given number of turns and the measured or calculated value of the drag force acting on the µ-probe just before the first turn. We next extracted the dynamic friction coefficient from the experimental data using the analytical formula. As the turn angle is kept constant at each turn, the total retraction force is calculated as: We used an exponential fit to the data recorded at " = 20 cm·s -1 to quantify the exponent of the exponential, which was found as 0.152. The dynamic friction coefficient is then found as: After this verification step, we can conclude that the total retraction force required to pull back a µ-probe that passes through n number of 90° turns, with dynamic friction coefficient 3e = 0.13, can be calculated using the following simple formula: In our phantoms filled with water, the baseline drag force is calculated as Þ,ôÚÈjÛäçj = 0.021 mN (see Supplementary Fig. 27b). For a μ-probe l = 5 cm, " = 5 cm·s -1 , and 20 turns, the total retraction force is The total retraction force and the normal forces on the inward walls remain in the µN-range, assuring that no damage would occur during retraction, perforation, dissection, or otherwise.

Supplementary Note 5.3 During steering.
We analytically calculated the forces that are applied by the magnetic head due to application of magnetic fields using an experimentally validated model. We do not apply push or pull forces to the magnetic head because we use homogeneous magnetic fields for steering. The only force exerted by the magnetic head on vessel wall arise from the magnetic torque and the rotation of the head (Supplementary Fig. 33). These forces are transmitted at the longitudinal extremes of the head and are maximized with the application of a perpendicular magnetic field.
We assumed the worst-case scenario in the following analysis to report the highest possible forces. The total force acting at the tip can be computed from the torque -force relation assuming perpendicular actuation (i.e. magnetic field is perpendicular to the longitudinal axis of the µprobe head):

Supplementary
where M is the torque applied by the magnetic field and L the distance between the centre of rotation and the tip. The magnetic torque is computed from: where m is the magnetic dipole moment and B the applied magnetic field. The vector product imposes maximal torque at 90° between applied magnetic field and magnetization direction of the magnetic head (B ^ m). The magnetic dipole moment can be computed as: where e is the permeability of vacuum (= 4 • 10 M¬ H×m -1 ), Br is the factory-measured residual flux density of the neodymium iron boron (NdFeB) magnetic particles (0.8 T) and V is the volume of the magnetic head (20% volumetric ratio between NdFeB particles and PDMS).
Next, we calculated the maximal force that the magnetic head would exert on the vessel wall if we accidentally applied the magnetic field in the most misdirected way. The analytical results are shown in Supplementary Figure 34. The maximum field strength that we used for steering is 30 mT and the largest magnetic head has a diameter of 350 µm. For these parameters, the maximal force was calculated to be around 0.4 mN.
Supplementary Figure 34. Contact force generated due to magnetic actuation. Calculation of the magnitude of the contact force applied by the tip of the magnetic head on the vessel wall. The data is plotted as a function of the head diameter. Magnetic field is assumed to be perpendicular to the long axis of the head, at a constant magnitude of 30 mT.
We experimentally validated the analytical model by measuring the change in the weight of an actuated magnetic head ( Supplementary Fig. 35). To avoid magnetic interaction between the Helmholtz coils and the scale, a light plastic bar was vertically positioned on the scale to transmit the forces applied from the fiber. We applied uniform magnetic field of 20 mT strength to a horizontally placed 5 mm long and 700 µm-thick magnetic fiber that was clamped at one end. For these parameters, the calculated force is 0.98 mN. The increase in mass that was measured by the scale was 0.09 g, which corresponds to 0.88 mN.
Supplementary Figure 35. Schematics of the setup used to measure the force applied by the tip of the actuated magnetic head. The setup consists of a pair of electromagnetic coils (Helmholtz configuration) placed above a sensitive scale. A lightweight bar serves as an adapter to transmit the forces generated by the clamped magnetic head that is kept in position by a fixed holder (top inset). Upon application of homogeneous magnetic field perpendicular to the long axis of the head, the structure rotates and presses on the vertical bar (bottom inset). Drawings are not to scale.

Supplementary Note 6. Fabrication of electronic µ-probes
The flow sensor has been fabricated by standard microfabrication techniques ( Supplementary   Fig. 36a). A silicon (Si) wafer, 4-inch, has been primed by oxygen (O2) plasma for 5 min. A thin layer of polyimide (PI, PI2611 Hitachi Chemical DuPont MicroSystems GmbH, 3 μm) has been spin-coated at 4000 RPM for 30s. Curing of the polymer required an initial soft bake at 75 °C and at 115 °C for 3 min for each temperature, followed by a gradual hard bake. ( Patterning of the traces has been performed by spin-coating of positive photoresist (AZ9260,