Figure 1.
(A) Schematic representation of the arterial bifurcation. The yellow arrow indicates bifurcation between the superficial femoral artery and deep femoral artery. (B) An angiographic image of femoral artery bifurcations.
Figure 1.
(A) Schematic representation of the arterial bifurcation. The yellow arrow indicates bifurcation between the superficial femoral artery and deep femoral artery. (B) An angiographic image of femoral artery bifurcations.
Figure 2.
Flow hemodynamics of the artery bifurcation. (A) Development of the low wall shear stress (WSS) regions on the bottom wall of the main vessel in the opposite of the side branch, as well as along the lateral wall of the branch itself; (B) Flow bifurcation induces local vortices both in the distal main vessel and side branch and also creates a stagnation region with a long residence time for circulating particles. Flow deceleration and recirculation promote longer residence times, increased collision rates, and increased platelet aggregation. Low shear rates observed in these regions also favor the adhesion of platelets at the vascular wall. Platelets potentially activated by exposure to high shear and subsequently entrapped in vortices could potentially lead to the formation of free emboli.
Figure 2.
Flow hemodynamics of the artery bifurcation. (A) Development of the low wall shear stress (WSS) regions on the bottom wall of the main vessel in the opposite of the side branch, as well as along the lateral wall of the branch itself; (B) Flow bifurcation induces local vortices both in the distal main vessel and side branch and also creates a stagnation region with a long residence time for circulating particles. Flow deceleration and recirculation promote longer residence times, increased collision rates, and increased platelet aggregation. Low shear rates observed in these regions also favor the adhesion of platelets at the vascular wall. Platelets potentially activated by exposure to high shear and subsequently entrapped in vortices could potentially lead to the formation of free emboli.
Figure 3.
The experimental setup used for artery bifurcation investigations. The block diagram of the main recirculating flow loop contained a flowmeter, particle injection mechanism—syringe pump and test section—bifurcation model, valve, particle filter, reservoir, and centrifugal pump.
Figure 3.
The experimental setup used for artery bifurcation investigations. The block diagram of the main recirculating flow loop contained a flowmeter, particle injection mechanism—syringe pump and test section—bifurcation model, valve, particle filter, reservoir, and centrifugal pump.
Figure 4.
Experimental arterial bifurcation model. (A) General view of the model fashioned with a constant internal diameter of 8 mm. (B) Detail regarding model bifurcation angle. Notations used in this figure: PMV (proximal main vessel), DMV (distal main vessel), SB (side branch), α (bifurcation angle).
Figure 4.
Experimental arterial bifurcation model. (A) General view of the model fashioned with a constant internal diameter of 8 mm. (B) Detail regarding model bifurcation angle. Notations used in this figure: PMV (proximal main vessel), DMV (distal main vessel), SB (side branch), α (bifurcation angle).
Figure 5.
Comparison between the viscosity curves of the blood analog carrier fluid (glycerol–water fluid), the model suspension fluid (CF + 0.16% ferromagnetic particles), and blood. Blood viscosity curves were compared with values from the literature [
41] and values measured from two healthy volunteers (Sample no_1 and Sample no_2).
Figure 5.
Comparison between the viscosity curves of the blood analog carrier fluid (glycerol–water fluid), the model suspension fluid (CF + 0.16% ferromagnetic particles), and blood. Blood viscosity curves were compared with values from the literature [
41] and values measured from two healthy volunteers (Sample no_1 and Sample no_2).
Figure 6.
Ferromagnetic particle (FMP) separation in the presence of the magnetic field; (A) suspension in the absence of the magnetic field; (B) Fe particle separation in the presence of the magnetic field; (C) Fe particles contained in the model suspension forming chain structures aligning along the direction of the applied magnetic field. (D) Detail of the magnetic field orientation and and the ferromagnetic particle deposition along the magnetic lines.
Figure 6.
Ferromagnetic particle (FMP) separation in the presence of the magnetic field; (A) suspension in the absence of the magnetic field; (B) Fe particle separation in the presence of the magnetic field; (C) Fe particles contained in the model suspension forming chain structures aligning along the direction of the applied magnetic field. (D) Detail of the magnetic field orientation and and the ferromagnetic particle deposition along the magnetic lines.
Figure 7.
Microscopic image of the 4–6 μm Fe powder’s morphology. The image shows particle size distribution variation from the indicated mean size and the presence of the particle cluster.
Figure 7.
Microscopic image of the 4–6 μm Fe powder’s morphology. The image shows particle size distribution variation from the indicated mean size and the presence of the particle cluster.
Figure 8.
Magnetization curve and hysteresis loops measuring micro-sized (4–6 μm, Carl Roth GmbH, Karlsruhe, Germany) Fe particles in a powdered state. The hysteresis loops presented in the figure are smooth with no hysteresis, which indicates a soft magnetic material with coercive force, and the residual magnetization approaches zero.
Figure 8.
Magnetization curve and hysteresis loops measuring micro-sized (4–6 μm, Carl Roth GmbH, Karlsruhe, Germany) Fe particles in a powdered state. The hysteresis loops presented in the figure are smooth with no hysteresis, which indicates a soft magnetic material with coercive force, and the residual magnetization approaches zero.
Figure 9.
A magnetic field generated by the permanent ferrite magnet used in the experimental investigation. The ferrite magnet dimension and axis association: The used magnet has an axial polarization indicated in the figures; a comparison between the calculated and experimentally measured magnetic flux density produced by the ferrite type permanent magnet against the distance from the magnet surface (along axis Z). Experimental measurement was done using an F.W. Bell Gaussmeter, model 5080, and the magnetic field was obtained from numerical simulations using FEMM 4.2 software. The plot shows that the numerical solution of the magnetic field agrees well with the experimentally measured values. The differences are probably due to the precise position of the gaussmeter hole.
Figure 9.
A magnetic field generated by the permanent ferrite magnet used in the experimental investigation. The ferrite magnet dimension and axis association: The used magnet has an axial polarization indicated in the figures; a comparison between the calculated and experimentally measured magnetic flux density produced by the ferrite type permanent magnet against the distance from the magnet surface (along axis Z). Experimental measurement was done using an F.W. Bell Gaussmeter, model 5080, and the magnetic field was obtained from numerical simulations using FEMM 4.2 software. The plot shows that the numerical solution of the magnetic field agrees well with the experimentally measured values. The differences are probably due to the precise position of the gaussmeter hole.
Figure 10.
Numerical simulation of the magnetic field used during the experimental investigation (via the free Finite Element Methods Magnetics (FEMM) software). This figure shows the magnitude of the magnetic field produced by the Y8T permanent magnet in the longitudinal section, along with the bottom wall of the bypass graft at a distance of 7 mm from the magnet’s surface.
Figure 10.
Numerical simulation of the magnetic field used during the experimental investigation (via the free Finite Element Methods Magnetics (FEMM) software). This figure shows the magnitude of the magnetic field produced by the Y8T permanent magnet in the longitudinal section, along with the bottom wall of the bypass graft at a distance of 7 mm from the magnet’s surface.
Figure 11.
(A) The abnormal flow field is characterized by the flow division, strong flow impact around the apex, and flow oscillation on the host artery floor. The complex vortex structures created in the bifurcation area depend on the incoming flow structure; (B) detail of the flow bifurcation. Identification of the flow characteristic in the apex region: (1) impingement region, (2) acceleration region, (3) recovery region, and in the host artery floor: (2) acceleration zone and (3) deceleration (recovery) zone.
Figure 11.
(A) The abnormal flow field is characterized by the flow division, strong flow impact around the apex, and flow oscillation on the host artery floor. The complex vortex structures created in the bifurcation area depend on the incoming flow structure; (B) detail of the flow bifurcation. Identification of the flow characteristic in the apex region: (1) impingement region, (2) acceleration region, (3) recovery region, and in the host artery floor: (2) acceleration zone and (3) deceleration (recovery) zone.
Figure 12.
(
A) Flow dynamics in the bifurcation region. (
B) Particle deposition at the end of the injection time of 30 s. The distance between the permanent magnet and the bifurcation wall are 7 mm. (
C) Magnetic and drag force distribution in the bifurcation region. The average intensity of the magnetic field along the bypass bottom wall was B = 0.05 T, according to
Figure 9. In the case of comparable values of magnetic force and flow drag force, flow perturbation influences the FMP depositions, especially in the peripheral region.
Figure 12.
(
A) Flow dynamics in the bifurcation region. (
B) Particle deposition at the end of the injection time of 30 s. The distance between the permanent magnet and the bifurcation wall are 7 mm. (
C) Magnetic and drag force distribution in the bifurcation region. The average intensity of the magnetic field along the bypass bottom wall was B = 0.05 T, according to
Figure 9. In the case of comparable values of magnetic force and flow drag force, flow perturbation influences the FMP depositions, especially in the peripheral region.
Figure 13.
Particle retention in the artery bifurcation during an injection time of 30 s. The distance between the permanent magnet and the bifurcation wall are 7 mm. The average intensity of the magnetic field along the bypass bottom wall was B = 0.05 T, according to
Figure 9. Particle deposition at different time steps: (
A) T = 10 s, (
B) T = 15 s, (
C) T = 20 s, (
D) T = 30 s (end injection). Different thicknesses of the particle deposition in the flow acceleration (red arrow) and deceleration regions (white arrow).
Figure 13.
Particle retention in the artery bifurcation during an injection time of 30 s. The distance between the permanent magnet and the bifurcation wall are 7 mm. The average intensity of the magnetic field along the bypass bottom wall was B = 0.05 T, according to
Figure 9. Particle deposition at different time steps: (
A) T = 10 s, (
B) T = 15 s, (
C) T = 20 s, (
D) T = 30 s (end injection). Different thicknesses of the particle deposition in the flow acceleration (red arrow) and deceleration regions (white arrow).
Figure 14.
Particle accumulations in the bifurcation region for the different vertical positions of the magnet. (A) a magnet distance of 2 mm; (B) a magnet distance of 5 mm; (C) a magnet distance of 7 mm; (D) the magnetic field induction function of the distance to the magnet’s surface along the z-axis. The same working condition was applied for all magnet positions: an inlet velocity of 0.12 m/s, and an injection time of 30 s. (E) Flow evolution in the bifurcation section.
Figure 14.
Particle accumulations in the bifurcation region for the different vertical positions of the magnet. (A) a magnet distance of 2 mm; (B) a magnet distance of 5 mm; (C) a magnet distance of 7 mm; (D) the magnetic field induction function of the distance to the magnet’s surface along the z-axis. The same working condition was applied for all magnet positions: an inlet velocity of 0.12 m/s, and an injection time of 30 s. (E) Flow evolution in the bifurcation section.
Figure 15.
Particle accumulation efficiency in the targeted regions. Deposition trendlines are also represented.
Figure 15.
Particle accumulation efficiency in the targeted regions. Deposition trendlines are also represented.
Figure 16.
(A) Magnetic field induction function of the distance to the permanent magnet surface along the z axis for different types of magnets: the N35...52 Neodymium type magnet and the Y8T...Y32 ferrite type magnet. (B) Suspensions of the magnetic carrier containing PEG-coated nanoparticles.
Figure 16.
(A) Magnetic field induction function of the distance to the permanent magnet surface along the z axis for different types of magnets: the N35...52 Neodymium type magnet and the Y8T...Y32 ferrite type magnet. (B) Suspensions of the magnetic carrier containing PEG-coated nanoparticles.
Table 1.
Particle trajectory visualization parameters.
Table 1.
Particle trajectory visualization parameters.
Parameters | Values |
---|
Simulated artery bifurcation vessel inner diameter | 8 mm |
Blood velocity in the axial direction (Vmax) | 0.12 m/s |
Ferromagnetic particle diameters | 4–6 μm |
Magnetic field intensity (max) | 0.15 T |
Blood analog fluid viscosity | 0.0036 mPa·s |
The mass density of the ferromagnetic particles (Fe) | 7680 kg/m3 |
Table 2.
Rheological characterization of the carrier fluid and Fe particle suspensions.
Table 2.
Rheological characterization of the carrier fluid and Fe particle suspensions.
Fluid | T [°C] | B [T] | | | C [s] | p [–] | r2 |
---|
Carrier fluid - CF | 25 | 0 | 0.0015 | 0.193 | 244.48 | 0.421 | 0.997 |
CF + 0.16% Fe | 25 | 0 | 0.00154 | 0.095 | 18.08 | 0.664 | 0.999 |
Table 3.
Fe particle characteristics.
Table 3.
Fe particle characteristics.
Characteristics | Value |
---|
particle diameter | 4–6 μm |
density | 7.86 g/cm3 |
molar mass | 55.8 g/mol |
chemical composition | in mass concentration percentage: Fe ≥ 99.5%; C ≤ 0.03%; O2 ≤ 0.2%; N2 ≤ 0.01%; Al ≤ 0.001%, As ≤ 0.0002%; Pb ≤ 0.0001%; Cu ≤ 0.001%; Mn ≤ 0.001%; Ca ≤ 0.001%; Cr ≤ 0.002%; Co ≤ 0.001%; Mg ≤ 0.001%. |
Table 4.
Fe particle magnetic properties (particles size of 4–6 μm).
Table 4.
Fe particle magnetic properties (particles size of 4–6 μm).
Saturation Magnetization | Saturation Field | Coercive Field | Remanent Magnetization |
---|
Ms [A·m2/kg]: 177 | Hs [kA/m]: 575 | Hc [kA/m]: 1.32 | Mr [A·m2/kg]: 0.891 |
Table 5.
Particle deposition parameter setup.
Table 5.
Particle deposition parameter setup.
Parameters | Particle Diameter | Mean Flow Velocity | Reynolds (Re) | Fluid Viscosity | Magnetic Field Induction |
---|
Value | 4–6 μm | 0.12 m/s | 283 | 0.0036 Pa.s | 0.07 to 0.15 T |
Table 6.
Characteristics of the particle accumulation shape during the injection time along the host’s arterial wall.
Table 6.
Characteristics of the particle accumulation shape during the injection time along the host’s arterial wall.
Time Step [s] | Accumulation Length [mm] | Average Thickness Corresponding to the Acceleration Zone [mm] | Average Thickness Corresponding to the Deceleration Zone [mm] | Magnetic Field Magnitude [T] |
---|
10 | 29 | 1 | 2.4 | 0.05 |
15 | 32 | 1.5 | 2.6 | 0.05 |
20 | 33 | 2 | 3.1 | 0.05 |
30 | 33 | 2.2 | 3 | 0.05 |
Table 7.
Characteristics of the particle accumulation for different magnet distances.
Table 7.
Characteristics of the particle accumulation for different magnet distances.
Magnet Distance [mm] | Magnetic Field Magnitude [T] | Accumulation Length [mm] | Particle Quantity [g] |
---|
2 | 0.068 | 36 | 0.289 |
5 | 0.058 | 35 | 0.195 |
7 | 0.048 | 33 | 0.163 |
Table 8.
Targeting efficiency (TE) in the artery bifurcation model for different magnet distances.
Table 8.
Targeting efficiency (TE) in the artery bifurcation model for different magnet distances.
Magnet Distance [mm] | Accumulated Quantity mFMP [g] | TE [%] |
---|
7 | 0.163 ± 0.058 | 16.3 |
5 | 0.195 ± 0.085 | 19.5 |
3 | 0.251 ± 0.061 | 25.1 |
2 | 0.289 ± 0.072 | 28.9 |