Optimal Radiation of Body-Implanted Capsules

Autonomous implantable bioelectronics requires efficient radiating structures for data transfer and wireless powering. The radiation of body-implanted capsules is investigated to obtain the explicit radiation optima for $\mathbf{E}$- and $\mathbf{B}$-coupled sources of arbitrary dimensions and properties. The analysis uses the conservation-of-energy formulation within dispersive homogeneous and stratified canonical body models. The results reveal that the fundamental bounds exceed by far the efficiencies currently obtained by conventional designs. Finally, a practical realization of the optimal source based on a dielectric-loaded cylindrical-patch structure is presented. The radiation efficiency of the structure closely approaches the theoretical bounds and shows a fivefold improvement over existing systems.

Figure 1

Problem formulation (not to scale). (a) Stratified spherical model of body tissues (phantom) ${\mathrm{\Omega }}_P$ around the source ${\mathrm{\Omega }}_S$: 1 is the muscle $\{{ϵ}_{r,1}(\omega ),{\sigma }_1(\omega )\}$, 2 is the 5-mm layer of fat $\{{ϵ}_{r,2}(\omega ),{\sigma }_2(\omega )\}$, and 3 is the 2-mm layer of skin $\{{ϵ}_{r,3}(\omega ),{\sigma }_3(\omega )\}$. (b) Source region ${\mathrm{\Omega }}_S$ defined as a current density distribution on the cylindrical surface ${\mathrm{\Sigma }}_C$.

Figure 2

(a) ${\mathrm{TM}}_{10}$ and (b) ${\mathrm{TE}}_{10}$ sources are defined as current density ${\mathbf{J}}_s$ distributions on the surface ${\mathrm{\Sigma }}_C$; the contour lines depict the distribution of electric $\mathbf{E}$ and magnetic $\mathbf{B}$ fields, respectively (arb. units). (c)–(e) Implantation depth ($d\approx R_P-a$) significantly affects the optimal frequency $f_{\mathrm{opt}}$ and radiation efficiency $\eta$. (c) $\max (\eta )$ exponentially decays with implantation depth. (d)–(e) $\eta$ spectrum of (d) ${\mathrm{TM}}_{10}$ and (e) ${\mathrm{TE}}_{10}$. (f) Skin and fat layers [Fig. 1] increase $\eta$ (compared to a homogeneous $R_P=50\mathrm{mm}$ phantom) for both sources by improving wave-impedance matching with free space. The effect is observed for both the layers placed inside (inr, $R_P=50\mathrm{mm}$) and outside (otr, $R_P=57\mathrm{mm}$) of the homogeneous (hg) phantom.

Figure 3

(a),(b) Theoretical bounds on the radiation efficiency $\eta$ depend on the frequency and the source geometry: (a) ${\mathrm{TM}}_{10}$ mode and (b) ${\mathrm{TE}}_{10}$ mode sources centered inside of a spherical $R_P=50\mathrm{mm}$ phantom ${\mathrm{\Omega }}_P$ (dispersive muscle-equivalent EM properties, no stratification). (c)–(e) Normalized $\mathbf{E}$-field distributions of the ${\mathrm{TM}}_{10}$ mode source ($L=10$, $R_C=4$, and $T=0.5\mathrm{mm}$) in a $R_P=50\mathrm{mm}$ stratified ${\mathrm{\Omega }}_P$ at (c) 100 MHz (low $\eta$ due to an inefficient source), (d) 1.2 GHz (maximum $\eta$), and (e) 3.5 GHz (low $\eta$ due to attenuation).

Figure 4

(a) Cylindrical patch closely replicates surface current density of the ${\mathrm{TM}}_{10}$ source [Eq. (1a)]. Note the rise at $z>5\mathrm{mm}$ due to the feed. (b) The dielectric-loaded cylindrical patch efficiency ($\times$) exceeds the theoretical bounds of ${\mathrm{TE}}_{10}$ and closely approaches $\eta$ of ${\mathrm{TM}}_{10}$. (c) Synthesized cylindrical patch design (mm) and time snapshot of $\mathbf{E}$-field distribution.