SUPPLEMENTARY INFORMATION - Nature Research · Supplementary Information: Conformal phased surfaces...

In the format provided by the authors and unedited.

Supplementary Information: Conformal phased surfaces

for wireless powering of bioelectronic microdevices

Devansh R. Agrawal1, Yuji Tanabe2, Desen Weng1, Andrew Ma2, Stephanie

Hsu2, Song-Yan Liao3, Zhe Zhen3, Zi-Yi Zhu3, Chuanbowen Sun5, Zhenya

Dong5, Fengyuan Yang5, Hung Fat Tse3,4, Ada S. Y. Poon2, and John S. Ho1,5

1Singapore Institute for Neurotechnology,

National University of Singapore, Singapore

2Department of Electrical Engineering,

Stanford University, CA 94305, USA

3Cardiology Division, Department of Medicine,

University of Hong Kong, Hong Kong, China

4Hong Kong-Guangdong Joint Laboratory

on Stem Cell and Regenerative Medicine,

the University of Hong Kong, Hong Kong, China and

5Department of Electrical and Computer Engineering,


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1

















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© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONVOLUME: 1 | ARTICLE NUMBER: 0043

NATURE BIOMEDICAL ENGINEERING | DOI: 10.1038/s41551-017-0043 | www.nature.com/natbiomedeng 1

http://dx.doi.org/10.1038/s41551-017-0043

CONTENTS

List of Figures 3

Additional Methods 4

Phased Surface Design 4

Theory 4

Passive Loading 5

Microdevice Construction 7

Power Measurement Apparatus 7

Construction 7

Calibration 8

Usage 8

Field Mapping 9

Numerical Methods 9

Thermal Monitoring Calculation 10

Imaging 10

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SUPPLEMENTARY INFORMATION

http://dx.doi.org/10.1038/s41551-017-0043

LIST OF FIGURES

S1 Structure of the phased surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

S2 Surface current distribution on the phased surface . . . . . . . . . . . . . . . . 12

S3 Circuit and layout schematic of the microdevice . . . . . . . . . . . . . . . . . 13

S4 Wireless powering measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . 14

S5 Field shaping in air and homogenous tissue . . . . . . . . . . . . . . . . . . . . . 15

S6 Effect of curvature on the field shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

S7 Performance during physiological motion . . . . . . . . . . . . . . . . . . . . . . . 17

S8 Printed Ag ink trace under mechanical deformation . . . . . . . . . . . . . . 18

S9 Effect of substrate thickness on performance . . . . . . . . . . . . . . . . . . . . 19

S10 Dependence of transferred power on orientation . . . . . . . . . . . . . . . . . . 20

S11 Specific absorption rates (SAR) distribution on neck and arm. . . . . . 21

S12 Surface thermal effects during wireless powering operation . . . . . . . . 22

S13 Wireless powering performance with bone structures . . . . . . . . . . . . . 23

S14 Spectral characteristics of the phased surface . . . . . . . . . . . . . . . . . . . . 24

S15 Wireless pacing in the right atrium at different power levels . . . . . . . 25

S16 Portable integration of the phased surface on rigid substrates . . . . . . 26

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ADDITIONAL METHODS

Phased Surface Design

Theory

The system is described by the scattering matrix formalism

b = Sa (1)

where a are the forward wave amplitudes and b the backward amplitudes. We

seek to maximize the fraction of power transferred to the last port labelled by

subscript L. The S matrix is symmetric as a consequence of reciprocity and can

be partitioned as bS

bL

=

ΣS κ

κT σL

aS

aL

. (2)

where κ is the coupling vector, σL the scalar reflection coefficient of the last port,

and ΣS the remaining submatrix in the partition. The load on the last port is

selected so that all power is absorbed aL = 0. We then have

bL = κTaS (3)

and

bS = ΣSaS. (4)

The power transferred to the last port is given by

PR = |bL|2 = |κTaS|2 (5)

The total power dissipated within the system is then

PT = |aS|2 − |bS|2 − |bL|2 = aHS (I − Σ†SΣS − κκH)aS (6)

The efficiency is given by

η =PR

PT

=|κTaS|2

aHS (I − ΣHS ΣS − κκH)aS

(7)

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Maximizing η with respect to aS is a matched filtering problem. The solution is

given by

aS,opt = (I − ΣHS ΣS − κκH)−1κ∗. (8)

The corresponding currents in the ports are given by

i =a−b√

Z0

=(I − S)a√

Z0

(9)

where Z0 is the characteristic impedance of the port.

Passive Loading

The components that realize the optimal currents are determined by first solv-

ing for the corresponding unconstrained impedances, which may include active

ports, then using coordinate descent to optimize over the space of passive (strictly

reactive) elements.

The unconstrained impedances are solved by considering the impedance matrix

for the N -port structure. For simplicity, the receiver is neglected as it is weakly

coupled to the structure. The impedance matrix is given by

v = Zi. (10)

The source port is isolated by partitioning the impedance matrix asv0

vP

=

z0 ζT

ζ ZP

i0

iP

. (11)

Each remaining port, labeled 1 through N − 1, is terminated by a passive compo-

nent with impedance zL,n. This yields an additional set of equations vP = −ZLiP

where ZL is the diagonal matrix with entries zL,n. Incorporating this into Eq. (12),

we obtain the set of balance equationsv0

0

=

z0 ζT

ζ ZP + ZL

i0

iP

. (12)

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The lower row yields the expression

i0ζ + (ZP + ZL)iP = 0 (13)

from which the load impedances can be solved

zL,n = − i0iP,n

ζn +∑m

ZP,nm

iP,miP,n

. (14)

These impedances are unconstrained such that the real parts may be positive

(passive) or negative (active). Note that the input impedance of the structure can

be computed by taking the Schur complement of Eq. (12)

zin =v0i0

= z0 − ζT (ZP + ZL)−1ζ. (15)

Coordinate descent is used to select a locally optimal set of strictly reactive

(imaginary) impedances. We form the diagonal matrix

ZL =

ix1

. . .

ixN−1

(16)

consisting of only the imaginary part of the unconstrained solution Eq. (14). The

efficiency η corresponding to this choice of reactances can be found by solving for

the currents flowing through each source port

iP/i0 = −(ZP + ZL)−1ζ (17)

and substituting into Eq. (7) and (9). We define the following cost function

C(x1, . . . , xN−1) = η(x1, . . . , xN−1) + λL|z0 − zin(x1, . . . , xN−1)|2 (18)

where λL is a Lagrangian multiplier. The cost function is then minimized by

sequential coordinate descent using the reactances of the unconstrained solution

as the initial vector. The reactances were found to be all capacitive and are realized

using the closest available commercial components (Table S1).

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Microdevice Construction

The microdevice circuit consists of a two-stage voltage doubler with the helical

coil across the input terminals and a LED across the output terminals (Supplemen-

tary Fig. 3). The input capacitance of the circuit was designed to resonate with

the inductance of the coil (Advanced Design Systems, Keysight). The circuit was

implemented using commercial Schottky diodes and capacitors on a commercially-

produced printed circuit board (PCB; Interhorizon Corporation).

Construction of the implants requires the following components: (1) the PCB,

(2) 10 nF capacitor (Murata Electronics, GRM033R61A103KA01D), (3) 10 pF ca-

pacitor (Johanson Technology, 250R05L100GV4T), (4) Schottky diode (Skyworks

Solutions, SMS7630-061), (5) 36-gauge enameled wire (Belden, 8058), (6) solder

paste (Chip Quik, SMD291SNL10). Furthermore, it requires the following tools:

(1) microscope, (2) soldering iron and cartridge (JBC, C105-101), (3) tweezers, (4)

wire cutters. Ample solder is applied on the solder pads using the soldering iron

with a soldering tip. Surface mount components are then placed onto the PCB.

The solder is heated to 270 C to attach the components.

The device is encapsulated by pouring polydimethylsiloxane (PDMS) over a 3D-

printed mould (ABS filament). PDMS is prepared by mixing an elastomer base

(Sylgard, 3097366-1004) with a silicone elastomer curing agent (Sylgard, 3097358-

1004) at a 10:1 ratio for 15 minutes. The mixture is degassed in a vacuum chamber,

and then cured in an oven at 70 C overnight.

Power Measurement Apparatus

Construction

Construction of the measurement probe requires the following components:

(1) optical fiber (Thorlabs, M74L01), (2) photodetector/transimpedance ampli-

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fier (Thor Labs, PDA36A-EC), (3) 30-gauge Kynar wire (Pro-Power, 100-30-far;

100-30BK-far), (4) LED (Vishay, VLMB1500-GS08), and (5) the microdevice prior

to encapsulation (see Microdevice Construction).

The optical fiber is cut so that one end is bare fiber and the other is a FC/PC

connector. The bare end is passed partially into a clear thin plastic tube. The LED,

terminals attached to two 30-gauge wires, is inserted into the tube and secured

with a drop of transparent glue. The stability of the optical link between the LED

and the photodetector was tested for each probe by shaking the fiber as the LED

was powered by a DC power supply. The wires are cut to a minimal (< 2 mm)

length and soldered to the output terminal of the microdevice. Heat shrink tubing

is further applied around the LED to secure the junction. The FC/PC end of the

optical fiber is attached to a photodetector (Thorlabs, PDA36A-EC). The gain of

the transimpedance amplifier is set to 70 dB and is connected to an oscilloscope

(Tektronix, MDO3012) using a coaxial cable with BNC connectors.

Calibration

Prior to attachment of the helical coil, the input terminals of the microdevice

rectifier are connected to a network analyzer (Keysight, N9915A Field Fox). The

forward power of the analyzer is varied from −10 dBm to 5 dBm as the return

loss (calibrated for cable losses) and the voltage output of the photodetector is

recorded. The optical output, measured by the photodetector, as a function of the

power injected into the rectifier is then computed. This process is repeated for

each probe and at each operating frequency.

Usage

Following calibration, the input terminals of the microdevice rectifier are at-

tached to the helical coil. The entire device is encapsulated in silicone elastomer.

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The probe is inserted into a tissue volume and wirelessly powered in pulsed (50 ms

width, 50% duty cycle) by the phased surface in the configuration shown in Sup-

plementary Fig. 5. The amplitude of the optical pulse is recorded by the photode-

tector, enabling the received power to be inferred from the calibration curve.

Field Mapping

Field mapping experiments used a RF magnetic field probe (Detectus AB, RF-

R 0,3-3) mounted on a 3D positioning system (Detectus AB, RSE644). The signal

from the probe is monitored by a network analyzer (Rohde & Schwarz, ZVL Net-

work Analyzer) at each position by a computerized system. Step sizes of 2-mm

were used. Fields were generated in a tissue-mimicking cylindrical volume (vary-

ing diameters, constructed from 0.15-mm thick PVC sheets) filled with water by

a phased surface conformally attached to the cylinder wall at a 8-cm height above

the floor.

Numerical Methods

Field simulations used the finite-difference time-domain method (CST Mi-

crowave Studio). A computational human body model was used for SAR cal-

culations (adult male, ‘Gustav’, CST Microwave Studio). SAR is defined using

10-g averaging mass (IEEE/IEC 62704-1 method), consistent with the most re-

cent safety standards (IEEE C95.1-2005). Dielectric permittivity of tissues were

with modeled using ColeCole dispersion with values for different tissue types as

in Ref. [31]. A table of the relative permittivities used in this paper at 1.5 GHz is

given below.

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TABLE I. Dielectric properties of biological tissues at 1.5 GHz

Tissue type Relative permittivity Loss tangent Conductivity (S/m)

Air 1.0 0.0 0.0

Muscle 53.9 0.26 1.19

Heart 57.2 0.33 1.57

Skin 44.4 0.29 1.09

Bone (Cancellous) 19.76 0.30 0.5

Bone (Cortical) 11.98 0.23 0.23

Thermal Monitoring Calculation

For thermal experiments, the rise in temperature attributed to RF heating is

calculated as ∆T = (TPS,P−TSS,P )−(TPS,0−TSS,0), where TPS,P is the temperature

under the phased surface with output power of P watts and TSS,P is the average

surface temperature of a reference skin area not in contact with the phased surface.

TPS,0 and TSS,0 are the corresponding average temperatures when the output power

is set to P = 0, controlling for temperature change due to skin contact with room

temperature silicone.

Imaging

Computed tomography (256 Flash CT scanner, Siemens) was performed on pig

carcass (male, 70 kg) in the National Large Animals Research Facility (NLARF).

The scan parameters for the lower abdomen, upper abdomen, and neck configu-

rations were: (i) 120 kVp , 133 mAs, helical; (ii) 120 kVp, 174 mAs, helical; and

(iii) 120 kVp, 120 mAs, helical. The slice thickness was 0.5 mm in all scans.

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C4 C3 C2 C1 C4C3C2C1

MMCX

FIG. S1. Structure of the phased surface. All dimensions are to scale. Components

are listed in Table II. Scale bar, 1 cm.

TABLE II. Phased surface components

Component Description Company Part No

MMCX Connector Amphenol RF 908-22/01T

SMA-MMCX Cable Amphenol RF 245106-02-03.00

C1 Capacitor, 0.7 pF Venkel C0402HQN500-0R7BNP



C4 Capacitor, 0.7pF Venkel C0402HQN500-0R7BNP

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0 11

Surface Current (A/m)

a

b

FIG. S2. Surface current distribution on the phased surface. (a) Schematic of

phased surface over a non-planar tissue volume with radius-of-curvature R = 10 cm. (b)

Top-down projection of the instantaneous surface current vector distribution at 0.5 W

input. Scale bar, 1 cm.

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Top

Bo

tto

m

X1 X2

C2 C3

C1 C4

D1

D2

D3

D4

LED

X1

X2

C2

C3

C1

C4

D1

D2

LED

D3

D4a

b

c

3mm

1.5

mm

FIG. S3. Circuit and layout schematic of the microdevice. (a) Circuit diagram

of the microdevice consisting of a two-stage voltage doubler. (b) Top and (c) bottom

view of the component layout on the printed circuit board (PCB). X1 and X2 indicate

terminals of helical coil. The dimensions of the PCB are 3.0 mm × 1.5 mm. Components

are listed in Table III.

TABLE III. Microdevice components

Component Description Company Part No

C1, 2, 3 Capacitor, 10 pF Johanson Technology 250R05L100GV4T

C4 Capacitor, 10 nF Murata Electronics GRM033R61A103KA01D

D1, 2, 3, 4 Schottky Diode Skyworks Solutions SMS7630-060

LED Blue LED, 475 nm Vishay VLMB1500-GS08

X1-X2 Magnet Wire Belden 8058

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Signal

generatorPower

amplifier

Receiver

coil

Phased

surface

Rectifier

Photodetector/

transimpedance

amplifier

Optical fiber Oscilloscope

Coaxial

cable

LED

Microdevice

Cable

Coaxial

cable

Optical pow

er

density (

mW

/mm

2)

0

0.5

1

1.5

2

2.5

Received power (mW)

0 1 2 3

a b

FIG. S4. Wireless powering measurement setup. (a) A pulsed 1.6 GHz signal is

produced by a RF signal generator and a power amplifier. The signal is injected into

the phased surface at a 50 Ω port. The field in the body is shaped by the phased surface

and transfers energy to an implanted receiver coil. Radio-frequency power is converted

to an optical signal by the rectifier circuit, which is guided outside of the body by an

optical fiber. The optical signal is monitored by the photodetector on an oscilloscope.

(b) Optical output intensity as a function of the RF power received by the microdevice.

The power transferred to the microdevice can be inferred from the pulse amplitude.

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75

-25

-40 -400-30 0

60

0

Measurement Simulation

0

75

-25

-40 -400-30 060

0

0

Body

a

b

Free-space

yx

z

x (mm)

x (mm)

z (

mm

)z (

mm

)

Air Air

Saline Tissue

Lo

g m

ag

ne

tic f

ield

inte

nsity (

a.

u.)

z (

mm

)z (

mm

)

Min

Max

FIG. S5. Field shaping in air and homogenous tissue. (a) Measured and simulated

magnetic field intensity in air. (b) Measured and simulated magnetic field intensity

in saline and in homogenous muscle tissue, respectively. The radius of curvature is

R = 10 cm.

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SimulationMeasurement

0

1

-30 300-30

30

0

x (mm)

y (

mm

)

Flat R=10 cm R=8 cm R=5.75 cm

Sim

ula

tio

n

-50 500

x (mm)

1 1.5

Frequency (GHz)

c

d

|S

|1

1 (

dB

)M

ag

ne

tic f

ield

inte

nsity (

a.

u.)

0

1

0.5

Ma

gn

etic f

ield

am

plit

ud

e (

a.

u.)

2

-30

0

-10

-20

e

Me

asu

rem

en

t

Phased surfaceRigid

Conformal

Radius of

curvature R

d=4 cm

a

Curvature

Focal plane

Radius of curvature R (cm)

68101214161820

Pre

c/P

max

0

0.2

0.4

0.6

0.8

1

b

Rigid

Conformal

FIG. S6. Effect of curvature on the field shape. (a) Illustration of a conformal and

rigid phased surface on an interface with radius-of-curvature R. (b) Normalized received

power as a function of R. (c) Simulated and measured magnetic field amplitudes at the

z = 4 cm focal plane at varying curvatures. Measurements were performed in saline in

cylindrical polyethylene containers (150 µm thickness). (d) Intensity profile along the

along dashed line in (c). (e) Simulated and measured reflection coefficient (S11) at the

curved interfaces.

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On leg

On chest

Ch

an

ge

in

po

we

r (%

)

Sit Stand Sit Stand Sitd

0

0.01

0.02

-0.02

-0.01

Ch

an

ge

in

po

we

r (%

)

0

-20

-40

-10

-30

|S11| (d

B)

c

Stand Walk Stand Walk Stand

Stand Walk Stand Walk Stand

Stationary Motion Stationary Motion Stationary

a

Tegaderm

RF cable

0

0.01

0.02

-0.02

-0.01

Sit Stand

Stand Walk Stand

Sit

Subject 1

Subject 2

Subject 3

b

-8

-6

-4

-2

0

On body

Above body

> 4 cmCh

an

ge

in

po

we

r (%

)

e

Control

FIG. S7. Performance during physiological motion. (a) Photograph of phased

surface attached to body surface. (b) Physiological motions. (c) Reflection coefficient

S11 during stand-walk motion for three subjects. The phased surface is attached to the

leg while the control consists of the phased surface in air. (d) Change in power coupled

into the body during physiological motions for phased surface attached to the chest and

to the leg. (e) Change in power when the phased surface is removed from the body by

distance greater than 4 cm. Scale bars, 10 seconds.

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Crease

D

Trace

D (mm)

0102030405060708090100

Resis

tance (Ω

)

0

0.5

1

1.5

2

2.5

3

3.5

4

Flat Crease

FIG. S8. Printed Ag ink trace under mechanical deformation. Resistance of the

trace shown by the white line as the curvature is increased by reducing distance D. At

D = 0, the resistance is measured after sufficient force is applied to crease the substrate.

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0 2 4 6 8 10

Substrate thickness t (mm)

0

0.2

0.4

0.6

0.8

1

Pre

c/P

ma

x

Phased surface

Microdevice

t

Design

FIG. S9. Effect of substrate thickness on performance. Normalized received power

as a function of substrate thickness for the phased surface design. The thickness modu-

lates the proximity of the metal layer from tissue and can alter the coupling between the

rings. The phased surface was optimized for a thickness of 3 mm, such that the coupling

is inductive and the passive elements used to resonate the rings are all capacitive.

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Azimuth angle

Altitude angle

0

π/2

π

3π/2

θ

0

π/2

π

3π/2

φ

1

0.5

0N

orm

aliz

ed r

eceiv

ed p

ow

er

0.5

1

a

b

θ

x

y

k^

E^

Local Incident field

φ

x

z

E^

k^

Local Incident field

1

0.5

0

0.5

1

Sim

Fit

Sim

Fit

Norm

aliz

ed r

eceiv

ed p

ow

er

FIG. S10. Dependence of transferred power on orientation. Received power as

the helical coil receiver is rotated in (a) azimuthal (xy) and (b) altitudinal (xz) plane in

the focal spot on the z = 50 mm plane (homogenous muscle tissue), normalized to peak

received power of fit function. Fit function: r(θ) = a sin2(θ + c) + b cos2(θ + c).

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SA

R 1

0-g

(W

/kg)

10

0

Neck Arma

b

d

eTransmitter

Transmitter

10

00 70

5

SA

R 1

0-g

(W

/kg)

Position (mm)

10 20 30 40 50 60-100

5

10

Max. 10-g

SA

R (

W/k

g)

Arm Neck

c f

Safety Threshold

1

2

3

4

6

7

8

9

Arm

Neck

Abdomen

Abdomen

FIG. S11. Specific absorption rates (SAR) distribution on neck and arm.

(a, b) Neck and (d, e) arm SAR distribution in a computational human body model.

The phase surface is slightly removed from skin (<1 cm) to prevent intersection with

the computational domain. (c) SAR profile along white dashed line in (b) and (e).

Scale bars, 2 cm. Position of 0 mm is defined as skin surface. (f) Maximum SAR for

arm, neck, and abdomen (Fig. 3a) positions. The simulated output power is 0.8 W.

SAR is defined using 10-g averaging mass (IEEE/IEC 62704-1 method).

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0 m

ins

1 m

in2

min

s3

min

s4

min

s

Arm

30 40

Temperature (oC)

2W

Neck

1.25W 0.8W

32 42

Temperature (oC)

2W 1.25W 0.8W No PowerNo Power

0

3

2W

1.25W

0.8W

0 4

ΔT

(oC

)

Time (mins)

a d

b c e f

0

3

0 4

2W

1.25W

0.8W

ΔT

(oC

)

Time (mins)

FIG. S12. Surface thermal effects during wireless powering operation. Infrared

images of skin surface at varying times and power levels on (a) neck and (d) forearm. (b,

e) Photograph of placement position. (c, f) Change in surface temperature from t = 0.

Error bars indicate standard deviation in temperature in the target circular region (black

circle) in (a) and (d). The diameter of the black circle is 4 cm. Scale bars, 1 cm.

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1

1.1

0.9

No

rma

lize

d r

ece

ive

d p

ow

er

40-40 0

Δx (mm)

Phased surface width

-20 20

1

1.2

0.87010 4020 30 6050

Devic

e

Tis

sue S

urf

ace

-20

80

0

40

500-50

z (

mm

)

x (mm)

Late

ral

Bone

Device

Magnetic fie

ld a

mpltid

ue (

dB

A/m

)

15

-22

a

b

c

1

1.5

0.971 42 3 65 8 9 100

Vert

ical

Layere

d

Phased surface

Phased surface

Phased surface

Bone

Bone

Device

Device

d e f

Δz (mm) T (mm)

No occlusion

Δz

Δx

T

Lateral Vertical Layered

-20

80

0

40z (

mm

)

-20

80

0

40z (

mm

)

FIG. S13. Wireless powering performance with bone structures. (a, b) Magnetic

field amplitude as the position of a bone structure is varied along (a) the lateral direction

(x direction, at z = 25 mm depth) and (b) the vertical direction (z-axis at x = 0 mm).

The bone structure is an elliptical cylinder (10-mm major axis, 6-mm minor axis) in

otherwise homogenous muscle. (c) Magnetic field amplitude with curved layered bone

of varying thickness. (d–f) Received power as a function of bone position and thickness.

Supplementary Videos 1 and 2 show (a) and (b) animated. Since the dielectric contrast

between bone and muscle is one of the largest in the human body, other potential

obstructions (such as scar tissue) are expected to have less effect on wireless powering.

23




http://dx.doi.org/10.1038/s41551-017-0043

a

-40

-10

0

-30

-20

Frequency (GHz)

1.5 1.6 1.7

In air

On body

|S11| (d

B)

Bandwidth

60 MHz

50 μs 100 μs30 μs 200 μsb

FIG. S14. Spectral characteristics of the phased surface. (a) S11 of the phased

surface in air and on the surface of the body. The 10-dB bandwidth of the phased surface

over the body is 60 MHz. (b) Optical output of the microdevice during pulsed operation

of the wireless powering system with pulse widths 30 µs, 50 µs, 100 µs, and 200 µs. No

pulse distortion is observed above 200 µs. The bandwidth is limited by the microdevice

rather than the phased surface.

24




http://dx.doi.org/10.1038/s41551-017-0043

Heart

Rate

(bpm

)

60

80

100

120

140

Heart

Rate

(bpm

)

60

80

100

120

140

RA, 142 mW

RA, 108 mW

100 bps

120 bps

a

b

10 s 10 s

10 s 10 s

FIG. S15. Wireless pacing in the right atrium at different power levels. (a,b)

ECG recording and heart rate during 10-s stimulation and rest intervals with (a) pulse

width 10 ms and period 500 ms; and (b) pulse width 10 ms, period 600 ms, and peak

input power 1.5 times higher than (a).

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http://dx.doi.org/10.1038/s41551-017-0043

y (

mm

)

-20

-10

0

10

20

0 10 20-10-20

x (mm)

Magnetic fie

ld inte

nsity (

a. u.)

0

1

0 10 20-10-20

x (mm)

30-30

0.2

0.4

0.6

0.8

Backa b

c d

Battery

Signal source

Magnetic field (A/m)

10

In contact with skin

FIG. S16. Portable integration of the phased surface on rigid substrates. (a)

Image of the front of the phased surface which should be in contact with the skin.

(b) Image of the back of the phased surface showing the battery and signal source

(Crystek). (c) Magnetic field amplitude at the z = 50 mm focal plane in saline. The

air-liquid interface is flat. (d) Magnetic field intensity profile (normalized to peak) along

the dotted line in (c). Full width at half maximum is 2.2 cm. The substrate material

is FR4. The maximum output power is 1 W and the operating frequency range is

1.623–1.678 GHz.

26




http://dx.doi.org/10.1038/s41551-017-0043

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