Implantable, Bioresorbable Radio Frequency Resonant Circuits for Magnetic Resonance Imaging

Abstract Magnetic resonance imaging (MRI) is widely used in clinical care and medical research. The signal‐to‐noise ratio (SNR) in the measurement affects parameters that determine the diagnostic value of the image, such as the spatial resolution, contrast, and scan time. Surgically implanted radiofrequency coils can increase SNR of subsequent MRI studies of adjacent tissues. The resulting benefits in SNR are, however, balanced by significant risks associated with surgically removing these coils or with leaving them in place permanently. As an alternative, here the authors report classes of implantable inductor–capacitor circuits made entirely of bioresorbable organic and inorganic materials. Engineering choices for the designs of an inductor and a capacitor provide the ability to select the resonant frequency of the devices to meet MRI specifications (e.g., 200 MHz at 4.7 T MRI). Such devices enhance the SNR and improve the associated imaging capabilities. These simple, small bioelectronic systems function over clinically relevant time frames (up to 1 month) at physiological conditions and then disappear completely by natural mechanisms of bioresorption, thereby eliminating the need for surgical extraction. Imaging demonstrations in a nerve phantom and a human cadaver suggest that this technology has broad potential for post‐surgical monitoring/evaluation of recovery processes.


Note S1. | Reactive diffusion model for PA-and OPA-encapsulated Mg.
A 1D model can be used to analytically solve the governing reaction and diffusion process in the polymer substrate (PA), water-barrier (oil), and encapsulated conductive elements (Mg), while immersed in an aqueous solution (1×PBS, pH 7.4) at body temperature.The model, adopted from the encapsulation strategy for transient electronics described by Li et al. [1] and modified in Choi.et al [2] for polyanhydrides, is used since the PA/oil/Mg specimen thickness (hMg + hOil + hPA), where hMg, hOil, and hPA are the initial thicknesses of the Mg, the oil, and PA layers, respectively, are much smaller as compared to the lateral dimensions.The effect of the water-barrier was captured by calculating the change in electrical resistance for different encapsulation labeled as PA (hPA, 135 µm thick) and OPA (hOil + hPA, 350/135 µm thick).The electrical resistance of Mg layer is given by  =  0 ℎ 0 ℎ , where  0 is the initial resistance.The analytical equation for normalized Mg thickness as a function of time is given by: where,  0 is the initial water concentration,   is the diffusivity,  is reaction constant of water in Mg and DOPA is the diffusivity of double encapsulation of oil and PA.  and   2  are the molecular mass of Mg and water, respectively, and  = 2 means the two water molecules that react with each Mg atom in the process and  Mg is the density of Mg.   is a coefficient obtained from the initial boundary conditions and   are eigenvalues in the water concentration function.The complete details of the analytical model derivation are presented in Li. et al. [1] The critical time   (i.e., functional lifetime) can be determined when the value of the resistance reaches a critical value (i.e.,  = 500 Ω) and by using  0 ≈ 45 Ω, measured from experiments, and setting ℎ(  ) ℎ 0 = 0.1.The material parameters used in the analytical model are  Mg = 24 g mol -1 ,   2  = 18 g mol -1 ,  Mg = 1.738 g cm -3 ,  0 = 1 g cm -3 ,  = 1.2×10 -3 s - 1 ,  = 6.0×10 -16 m 2 s -1 , and   = 2.55×10 -15 m 2 s -1 .

Note S2. | Electromagnetic simulation: B1 and SNR
The commercial software ANSYS HFSS was used to perform 3D electromagnetic finite element analysis of two RF birdcage coil geometries at 4.7 T (Larmor Frequency, 200 MHz) to produce a homogeneous and circular polarized magnetic field B1, perpendicular to B0, and quantify the SNR in different implantable scenarios.The birdcage coils include two circular loops (i.e., end rings), evenly spaced for an (1) 8-element (210 mm long, 144 mm diameter) and a (2) 16-element conductive (80 mm long, 63 mm diameter) paths (legs), modeled as 2D finite conductive elements, joined by matching capacitors in a low-pass configuration to tune the coils to a the Larmor frequency of 200 MHz. [3]A lumped circuit model was used to determine the value of the matching capacitors C at the end rings by considering the selfinductance of the conductive leg paths and end rings, and the corresponding mutual inductances between the legs.The matching capacitors are 23 pF and 104 pF for the 8-element and 16element legs birdcage coils, respectively.A cylindrical shield with finite conductivity was included in the modeling.Adaptive meshing is used to refine the mesh and ensure convergence of the simulation.The total number of elements in the FEA model is ~400,000.A schematic of the geometrical dimensions of the birdcage is shown in Figure S11.To produce the rotational magnetic field B1, a four-port excitation was adopted through lumped ports placed 90 o degrees apart with the phase excitations of 0 o , -90 o , 180 o and 90 o in the end rings resulting in a sinusoidal current distribution in the birdcage legs.B1 + is the vector component that rotates in the same direction as nuclei inducing a flip angle with respect to the stationary magnetic field B0 and B1 -is the vector component that rotates in the opposite direction defined as [4]  1 + = (  +   ) 2 (1) where   and   are complex in-plane magnetic fields magnitudes in the birdcage,  is the imaginary unit and the asterisk indicates the complex conjugate.The flip angle is defined as   =  1 +  where  1 + is the value of  1 + in a mesh element in the region of interest,  is the gyromagnetic ratio of 1 H and  is the duration of the RF pulses.
The SNR in the regions of interest is calculated as [4] SNR ∝  2 where,  is the Larmor frequency,   is the number of mesh elements in the region of interest,   is the water content (by percent mass) in the tissues, and  1 − is the value of  1 − in a mesh element in the region of interest.  is the total power absorbed in the tissue model and is calculated from the magnitudes of the electric field  intensity as, [5] where  is the electrical conductivity of the tissue and ∆  , ∆  , ∆  are the dimensions of the meshed elements in the three principal directions.The values of the relative permittivity, electrical conductivity, and density used in the simulation for the tissue equivalent models with nerve bundles, wrist model, and the bioresorbable implant are shown in Table S1. [4,6]aterial and tissue Relative permittivity (  depending on the thicknesses of dielectric layers with the inside layout of device.A red asterisk corresponds to optimized thickness for desired f0 in inside layout (electrode area, 36 mm 2 ; loop diameter, 7 mm).Two LC-resonant circuits used same dimension, but only different layouts.
Electrode area, 36 mm 2 ; thickness in dielectric layer, 35 μm; loop diameter, 7 mm.Stabilization process for devices with a f0 of ≈220 MHz, immersed in 1×PBS (pH 7.4 at 37 o C) before implantation.From day 3, the devices used for testing stabilize at a f0 of ≈200 MHz.

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Figure S1.| Mechanical flexibility of wax and OPA layer.

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Figure S11.| Evaluation of recovery in f0 of the hydrated BICs by drying.a,b) Retention of the f0 of the resonators after drying.As the soaking time of the devices increases, the drying time also increases to return to the original value of f0.Long-term immersion may alter the metal features (e.g., oxidation or hydrolysis), resulting in irreversible drift of f0.Independent samples, n=8.

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Figure S15.| Specifications of the MRI system used for imaging of a cadaver arm.