curvature of the electronics scales as1/L, the bending energy scales [ 25 ]asDw/
L, withwis the width of the electronics. The surface membrane energy due to the
insertion of the electronics scales asncwd, withnis the number of cells on the
electronics anddis the size of cells. Considering in the long-term implantation, the
electronics will fully contact with tissue, thenndscales asL. Therefore, the ratio
of the bending energy and the surface energy gives the dimensionless numberD/cL^2 ,
which describes theflexibility of electronics compared to the membrane tension of
cells. Our mesh electronics have the properties ofD0.36 nN m^14 andL 300 –
500 μm, and typical cells havec1 mN/m^26 and neuron cells measured by AFM
havec0.01–0.4 mN/m [ 26 ]. We can calculateD/ctLis ca. 3.5–140. Given the
elastic modulus of Si, carbonfiber, gold and SU-8 are 130 GPa [ 24 ], 234 GPa [ 27 ],
79 and 2 GPa [ 8 ], respectively, we can calculate the bending stiffness of previous
reported Silicon microelectronic probe, carbonfiber probe and thinfilm electronics
is ca. 4.6 10 −^5 , 9.2 10 −^5 and 1.3 10 −^6 N m. The ratio of the bending energy
and the surface energy calculated for injectable electronics is orders magnitude
smaller than conventional silicon microelectronics (1.15 105 – 4.6 106 )[ 24 ],
carbonfiber probes (2.3 105 – 9.2 106 )[ 28 ] and reported thinfilm electronics
Fig. 5.4 Mechanics of mesh
during rolling.aSchematics
show that mesh roll up in
transverse direction in needle.
bSimulated highest strain
value as functions of 1 over
needle radius. Inset is a
representative simulation
shows the strain distribution
of unit cell in 200-lm inner
diameter needle. Red dashed
circle highlights the point
with highest strain. Black
dashed circle and black arrow
show the inner boundary and
diameter of the needle
5.2 Experimental 73