Abstract
Purpose: Our aim was to compare different magnet arrangements for magnetic cell delivery to human lower leg arteries and investigate the theoretical targeting efficiency under realistic flow conditions as a possible treatment after angioplasty. Additionally the potential of scaling down or translating the magnetic actuation device for preclinical studies was explored.Methods: Using finite element methods, the magnetic field distribution was calculated in 3D for the optimization of magnet arrangements. Computational fluid dynamics simulations were performed for the human posterior tibial artery with the geometry and boundary condition data derived from magnetic resonance imaging (MRI) studies. These simulations were used to trace the trajectories of cells for an optimized magnet arrangement. Additionally the behavior of cells close to the vessel wall was investigated using a fluid-structure interaction model.Results: The optimal magnet for the lower leg arteries was a Halbach cylinder k3 variety (12 elements with 90° rotation steps for the magnetization orientation). With this magnet, numerical simulations predict a targeting efficiency of 6.25% could be achieved in the posterior tibial artery for cells containing 150 pg iron. Similar simulations, which were scaled down to rabbit dimensions while keeping the forces acting on a cell constant, lead to similar predicted targeting efficiencies. Fluid dynamic and fluid-structure interaction simulations predict that magnetically labeled cells within a 0.5% radii distance to the vessel wall would be attracted and remain at the wall under physiological flow conditions.Conclusions: First pass capture of magnetically labeled cells under pulsatile flow conditions in human lower leg arteries leads to low targeting efficiencies. However, this can be increased to almost 100% by stopping the blood flow for 5 min. A magnetic actuation device can be designed for animal models that generate magnetic forces achievable for cells in human leg arteries.
Original language | English |
---|---|
Pages (from-to) | 3932-3943 |
Number of pages | 12 |
Journal | Medical Physics |
Volume | 38 |
Issue number | 7 |
DOIs | |
Publication status | Published - Jul 2011 |
Externally published | Yes |
Keywords
- computational fluid dynamics
- fluid-structure interaction
- Halbach cylinder
- magnetic cell delivery
- magnetic resonance imaging
- peripheral arterial disease
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In: Medical Physics, Vol. 38, No. 7, 07.2011, p. 3932-3943.
Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Magnetic cell delivery for peripheral arterial disease
T2 - A theoretical framework
AU - Riegler, Johannes
AU - Lau, Kevin D.
AU - Garcia-Prieto, Ana
AU - Price, Anthony N.
AU - Richards, Toby
AU - Pankhurst, Quentin A.
AU - Lythgoe, Mark F.
N1 - Funding Information: We would like to thank the endovascular team from the University College London Hospital and Kathryn Broadhouse from the Robert Steiner MRI Unit, Hammersmith Hospital for their assistance. Paul Southern from The Royal Institution of Great Britain for magnetic susceptibility measurements using SQUID. Additionally, we would also like to thank the British Heart Foundation and the Engineering and Physical Sciences Research Council for funding this work. TABLE I. Physical parameters used for this manuscript. Parameter Symbol Value Units Length for magnets and vessel section L 200 (200–300) a , 40 b mm Halbach cylinder inner radius r 1 80 (54–98) a , 25 b mm Halbach cylinder outer radius r 2 140 (82–240) a , 29 b mm Magnetic rod radius r 3 115 (18–226) a mm Linear Halbach array height a 259 (6–1005) a mm Linear Halbach array width b 160 (40–160) a mm Equilateral triangle side length c 309 (75–609) a mm Outer radius endplate r 4 130 (100–140) a mm Endplate angle α 45 (30–90) a ° Endplate hight h 25 (5–50) a mm Residual flux density NdFeB c B r 1.36 T Coercivity NdFeB c H c 1051 kA m −1 Relative permeability NdFeB c μ r 1.04 — Residual flux density sintered ferrite B r 0.37 b T Coercivity sintered ferrite H c 240 b kA m-1 Relative permeability sintered ferrite μ r 1.21 b — SPION d crystal size D 8.8 nm Saturation magnetization iron oxide M s 354 kA m −1 Temperature T 300 K Magnetic permeability free space μ 0 4 × π × 10 −7 H m −1 Boltzmann constant k b 1.38 × 10 −23 J K −1 Cell radius R c 10 μm Cell density φ c 1100 kg m −3 Cells Young’s modulus — 10 kPa Cells Poisson ratio — 0.45 — Dynamic viscosity, fluid η 0.0039 kg m s −1 Fluid density φ f 1080 kg m −3 a The first number indicates dimensions which were used for the comparison of magnet arrangements with the same volume, while numbers in brackets indicate the range used for simulations. b Numbers indicate values used for the rabbit scale model. c NdFeB Neodymium Iron Boron. d SPION superparamagnetic iron oxide nanoparticles. TABLE II. Leg dimensions for a small group of patients with peripheral arterial disease. n = 40 Radius below knee Maximum radius Radius above ankle Radius ankle mean ± SD (mm) 59 ± 10 60 ± 11 38 ± 7 43 ± 5 minimum (mm) 37 46 25 35 maximum (mm) 91 99 59 59 FIG. 1. Geometrical arrangement of different magnet shapes around a human leg. A magnetic resonance image is shown in the center of the Halbach cylinder to indicate the three major blood vessels of the lower leg. Open arrows indicated the magnetization orientation of different elements. Note that only one of the basic geometries was used at one time for finite element simulations. FIG. 2. Average forces acting on magnetically labeled cells in the three major arteries of the human leg for different magnet arrangements with increasing magnet volume. All Halbach cylinders consisted of 12 elements while one magnetic rod and triangular magnetic rod were used. The linear Halbach array consisted of five elements. FIG. 3. Average magnetic force produced by an increasing number of the basic geometrical magnet arrangements arranged symmetrically around the leg. The magnet volume is constant (6600 cm 3 ) for all of these arrangements. Note that for the Halbach cylinder/magnetic cylinder, the cylinder was not modified; only the number of elements it was divided into was changed. As outlined in Sec. II D , the magnetization orientation of the Halbach cylinder follows k3 for more than six elements. FIG. 4. Example force profiles for different magnets using the same volume of magnetic material (6600 cm 3 ) All Halbach cylinders consist of 12 elements while the linear Halbach array consists of five elements. The radial position of the major lower leg arteries have been plotted to indicate their position within the magnet. FIG. 5. Linearity of the magnetic force along the z -axis of k3 Halbach cylinders with different lengths and endplates. The definition of the endplate height and the circumferential angle α are shown in Fig. 6 . FIG. 6. Geometrical arrangement of endplates on a Halbach cylinder k3. Endplates are made of the same magnetic material as the Halbach cylinder. Open arrows have been used to indicated the magnetization orientation of the four endplates. FIG. 7. Average magnetic forces produced by Halbach cylinders k3 with different inner diameters illustrating the scalability for different human leg diameters. A constant ratio between inner and outer diameter of 0.62 was used for all Halbach cylinders. The black horizontal line indicates an inner radius of 80 mm corresponding to the sixth circle on the Halbach cylinder k3 line of figure 2 . FIG. 8. Force profile for a Halbach cylinder k3 and a scaled down version for a rabbit injury model. The radial position of the right common carotid artery has been plotted to indicate the force cells would experience along the centerline of the artery. FIG. 9. Close up of the meshed artery channel with the different cell seeding points indicated by full circles at the start of the dashed lines. The size of this section with respect to the whole artery channel is indicated by the box at the bottom of the figure. FIG. 10. Trajectories for cells labeled with 60 pg iron per cell at the time of maximum forward flow (A) (toward the foot) and maximum backflow (C) are shown. (B) and (D) show the trajectories for cells labeled with 150 pg iron per cell. The magnetic force is orientated up for all plots, as indicated by the arrow in the lower left corner. Other arrow heads indicate the velocity of the fluid, which are scaled in magnitude. The two plots in the middle show the inflow and outflow profile for a 200 mm anterior tibial artery section over three cardiac cycles, the current time point of the simulations indicated by the difference in shading. Plots A-B show the flow field 1 s after the first heart beat, while C-D show the flow field 1.3 s after the first heart beat. FIG. 11. Finite element mesh of the cell (structure) and fluid used for fluid-structure interaction simulations. A constant fluid velocity is applied on the right side. Here the magnetic force is orientated downwards. FIG. 12. Fully develop fluid velocity field around the cell (0.4 s after simulation start). The cell has been attracted to the wall and flattened by the magnetic force acting on the cell. The fluid forces result in the slow rolling of the cell during the simulation as the wall of the artery has been modelled as frictionless (see supplementary movie 1).
PY - 2011/7
Y1 - 2011/7
N2 - Purpose: Our aim was to compare different magnet arrangements for magnetic cell delivery to human lower leg arteries and investigate the theoretical targeting efficiency under realistic flow conditions as a possible treatment after angioplasty. Additionally the potential of scaling down or translating the magnetic actuation device for preclinical studies was explored.Methods: Using finite element methods, the magnetic field distribution was calculated in 3D for the optimization of magnet arrangements. Computational fluid dynamics simulations were performed for the human posterior tibial artery with the geometry and boundary condition data derived from magnetic resonance imaging (MRI) studies. These simulations were used to trace the trajectories of cells for an optimized magnet arrangement. Additionally the behavior of cells close to the vessel wall was investigated using a fluid-structure interaction model.Results: The optimal magnet for the lower leg arteries was a Halbach cylinder k3 variety (12 elements with 90° rotation steps for the magnetization orientation). With this magnet, numerical simulations predict a targeting efficiency of 6.25% could be achieved in the posterior tibial artery for cells containing 150 pg iron. Similar simulations, which were scaled down to rabbit dimensions while keeping the forces acting on a cell constant, lead to similar predicted targeting efficiencies. Fluid dynamic and fluid-structure interaction simulations predict that magnetically labeled cells within a 0.5% radii distance to the vessel wall would be attracted and remain at the wall under physiological flow conditions.Conclusions: First pass capture of magnetically labeled cells under pulsatile flow conditions in human lower leg arteries leads to low targeting efficiencies. However, this can be increased to almost 100% by stopping the blood flow for 5 min. A magnetic actuation device can be designed for animal models that generate magnetic forces achievable for cells in human leg arteries.
AB - Purpose: Our aim was to compare different magnet arrangements for magnetic cell delivery to human lower leg arteries and investigate the theoretical targeting efficiency under realistic flow conditions as a possible treatment after angioplasty. Additionally the potential of scaling down or translating the magnetic actuation device for preclinical studies was explored.Methods: Using finite element methods, the magnetic field distribution was calculated in 3D for the optimization of magnet arrangements. Computational fluid dynamics simulations were performed for the human posterior tibial artery with the geometry and boundary condition data derived from magnetic resonance imaging (MRI) studies. These simulations were used to trace the trajectories of cells for an optimized magnet arrangement. Additionally the behavior of cells close to the vessel wall was investigated using a fluid-structure interaction model.Results: The optimal magnet for the lower leg arteries was a Halbach cylinder k3 variety (12 elements with 90° rotation steps for the magnetization orientation). With this magnet, numerical simulations predict a targeting efficiency of 6.25% could be achieved in the posterior tibial artery for cells containing 150 pg iron. Similar simulations, which were scaled down to rabbit dimensions while keeping the forces acting on a cell constant, lead to similar predicted targeting efficiencies. Fluid dynamic and fluid-structure interaction simulations predict that magnetically labeled cells within a 0.5% radii distance to the vessel wall would be attracted and remain at the wall under physiological flow conditions.Conclusions: First pass capture of magnetically labeled cells under pulsatile flow conditions in human lower leg arteries leads to low targeting efficiencies. However, this can be increased to almost 100% by stopping the blood flow for 5 min. A magnetic actuation device can be designed for animal models that generate magnetic forces achievable for cells in human leg arteries.
KW - computational fluid dynamics
KW - fluid-structure interaction
KW - Halbach cylinder
KW - magnetic cell delivery
KW - magnetic resonance imaging
KW - peripheral arterial disease
UR - http://www.scopus.com/inward/record.url?scp=79960215284&partnerID=8YFLogxK
U2 - 10.1118/1.3593363
DO - 10.1118/1.3593363
M3 - Article
AN - SCOPUS:79960215284
SN - 0094-2405
VL - 38
SP - 3932
EP - 3943
JO - Medical Physics
JF - Medical Physics
IS - 7
ER -