Electromagnetic Radiation Efficiency of Body-Implanted Devices

Autonomous wireless body-implanted devices for biotelemetry, telemedicine, and neural interfacing constitute an emerging technology providing powerful capabilities for medicine and clinical research. We study the through-tissue electromagnetic propagation mechanisms, derive the optimal frequency range, and obtain the maximum achievable efficiency for radiative energy transfer from inside a body to free space. We analyze how polarization affects the efficiency by exciting TM and TE modes using a magnetic dipole and a magnetic current source, respectively. Four problem formulations are considered with increasing complexity and realism of anatomy. The results indicate that the optimal operating frequency $f$ for deep implantation (with a depth $d\gtrsim 3\mathrm{cm}$) lies in the (${10}^8–{10}^9$)-Hz range and can be approximated as $f=2.2\times {10}^7/d$. For a subcutaneous case ($d\lesssim 3\mathrm{cm}$), the surface-wave-induced interference is significant: within the range of peak radiation efficiency (about $2\times {10}^8$ to $3\times {10}^9\mathrm{Hz}$), the max-to-min ratio can reach a value of 6.5. For the studied frequency range, 80%–99% of radiation efficiency is lost due to the tissue-air wave-impedance mismatch. Parallel polarization reduces the losses by a few percent; this effect is inversely proportional to the frequency and depth. Considering the implantation depth, the operating frequency, the polarization, and the directivity, we show that about an order-of-magnitude efficiency improvement is achievable compared to existing devices.

Figure 1

Mechanisms affecting the radiation efficiency $\eta$ of body-implanted devices. (a) Electromagnetic dispersion of tissues considered in this paper (illustrated by EM properties of muscle and fat) obtained using the four-region Cole-Cole model by Gabriel et al. [14, 15, 16]. (b) Penetration depths ${\delta }_p=1/\alpha$ of a plane wave propagating into dispersive muscle and fat tissues. (c) Maximum achievable radiation efficiencies ${\eta }_{\mathrm{ub}}$ of an antenna in a lossless dielectric, according to Eq. (3), for given fractional bandwidths ${\mathrm{FBW}}_2=f_0/\mathrm{BW}$ considering a $\mathrm{VSWR}=2$, $a=5\mathrm{mm}$, and the dispersive permittivity of muscle tissue. (d),(e) Reflection coefficients $|\mathrm{\Gamma }|$ of a plane wave incident upon an infinite planar dispersive-skin-to-air interface for (d) $s$ polarization and (e) $p$ polarization.

Figure 2

2D model formulations used in the paper (source regions are not to scale, and the $z$ axis is out of plane). EM properties are taken from Gabriel et al. [12]. (a) A planar interface between two semi-infinite homogeneous half-spaces. ${\mathrm{\Sigma }}_t(d<0)$ has dispersive muscle-equivalent EM properties. (b) A planar stratified heterogeneous model, as proposed by Poon et al. [9]. ${\mathrm{\Sigma }}_t(d<0)$ consists of muscle-, fat-, and skin-equivalent layers. (c) Circular heterogeneous phantom (not to scale) similar to the one used in Refs. [27, 28]. ${\mathrm{\Sigma }}_t(R<90)$, which includes dispersive layers with muscle-, fat-, and skin-equivalent EM properties. (d) Realistic model of a human abdominal region (nine dispersive tissues). (e) Magnetic dipole of a moment $\mathbf{m}$.

Figure 3

Radiation efficiencies ${\eta }_{\mathrm{idl}}$ and ${\eta }_{\mathrm{rad}}$ in infinite planar-bounded media. (a) Orientation of the magnetic dipole moment $\mathbf{m}$ strongly affects the efficiency (homogeneous half-space). (b) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode) compared to the out-of-plane magnetic current source (${\mathrm{TE}}_z$ mode) at $d=1\mathrm{cm}$ in the homogeneous half-space medium. (c) The homogeneous half-space medium at $d=1$ to 5 cm and (d) at $d=6$ to 10 cm implantation depths. (e) The layered (skin-fat-muscle) half-space medium at $d=1$ to 5 cm and (f) at $d=6$ to 10 cm implantation depths.

Figure 4

Normalized $\mathbf{E}$-field distributions at $d=1\mathrm{cm}$ in infinite planar-bounded homogeneous half-space media. (a) The magnetic current source (${\mathrm{TE}}_z$ mode) and (b)–(d) the 90°-oriented magnetic dipole (${\mathrm{TM}}_z$ mode). The radiation efficiency peaks at (a),(b) 2.1 GHz and (d) 480 MHz for both sources and drops at (c) 1.3 GHz due to the interference with the reflected wave.

Figure 5

Optimal frequency $f$ of a source in the infinite planar-bounded homogeneous half-space medium (dispersive muscle-equivalent EM properties).

Figure 6

Absolute reflection losses defined as the efficiency difference $\mathrm{\Delta }\eta$ [Eq. (11a)] for (a) magnetic dipole (${\mathrm{TM}}_z$ mode) and (b) magnetic current (${\mathrm{TE}}_z$ mode) sources in infinite half-space with muscle-equivalent EM properties.

Figure 7

Normalized $\mathbf{E}$-field distributions at 1-cm depth in the infinite planar-bounded layered half-space medium. The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode) at (a) 780 MHz (maximum efficiency) and (b) 2.1 GHz.

Figure 8

Normalized $\mathbf{E}$-field distributions at 110 MHz and 1-cm depth in the cylindrical stratified phantom. (a) The magnetic current source (${\mathrm{TE}}_z$ mode). (b) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode).

Figure 9

Radiation efficiencies ${\eta }_{\mathrm{idl}}$ and ${\eta }_{\mathrm{rad}}$ for the $R90$-mm cylindrical stratified phantom similar to the one used by Merli et al. [27] and Chrissoulidis and Laheurte [28]: a 4-mm skin-equivalent outer layer, a 4-mm fat-equivalent intermediate layer, and an $R82$ muscle-equivalent domain containing the source. The dispersive tissue EM properties of the layers are taken from Gabriel [12]. (a) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode) source at $d=1–4\mathrm{cm}$ and (b) $d=5–9\mathrm{cm}$ implantation depths. (c) The out-of-plane magnetic current source (${\mathrm{TE}}_z$ mode) at $d=1–4\mathrm{cm}$ and (d) $d=5–9\mathrm{cm}$ implantation depths. At $d=9\mathrm{cm}$, the source is in the middle of the phantom.

Figure 10

Radiation efficiencies ${\eta }_{\mathrm{rad}}$ in the anatomical phantom at $d=1–20\mathrm{cm}$ implantation depths. (a)–(c) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode). (d)–(f) The out-of-plane magnetic current source (${\mathrm{TE}}_z$ mode).

Figure 11

Normalized $\mathbf{E}$-field distributions of a source at 1-cm depth (subcutaneous) in an anatomical phantom. (a)–(d) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode). (e)–(h) The magnetic current source (${\mathrm{TE}}_z$ mode).

Figure 12

Normalized $\mathbf{E}$-field distributions of a source at 6-cm depth (stomach) in an anatomical torso phantom at 480 MHz. (a) The 90°-oriented magnetic dipole moment $\mathbf{m}$ (${\mathrm{TM}}_z$ mode). (b) The magnetic current source (${\mathrm{TE}}_z$ mode).

Figure 13

Absolute value of the relative residual power error for an infinite planar-bounded half-space homogeneous medium.