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where T denotes the temperature of the sensor and T
0
the ambient temperature.
The relation between resistance and temperature overheat ratios is expressed as
a
R
¼
ð
R
R
0
Þ
R
¼ að
T
T
0
Þ;
ð
16
:
6
Þ
where
a
is temperature coefficient of resistivity or TCR. For shear stress
measurement, we applied a high overheat ratio by passing higher current and
by generating a ''hot'' sensing element to stabilize the sensor. Calibration was
conducted for individual sensors to establish a relationship between heat exchange
(from the heated sensing element to the flow field) and shear stress over a range of
steady flow rates (Q
n
) in the presence of rabbit blood flow at 37.8
C. The
theoretical shear stress value corresponding to each flow rate was calculated using
Equation 16.7.
1
6Q
n
m
h
2
w
;
t
w
¼
ð
16
:
7
Þ
where
t
w
is the wall shear stress,
m
is the blood viscosity, and h and w are the
dimensions of the flow channel. The viscosity of the blood as a function of flow
rate was measured using a viscometer. The individual calibrated sensors were then
deployed into the NZW rabbit's aorta for real-time shear stress assessment.
16.4.3.1. Fabrication.
Yu et al. have recently developed biocompatible,
polymer-based MEMS sensors for real time measurements of shear stress and
velocity with excellent spatial and temporal resolution. The micron-size and
flexibility of the sensors allow the sensors to be inserted and/or attached into
various anatomic structures of biological systems. The sensor is currently targeted
to assess the physical parameters in the circulatory system of New Zealand White
(NZW) rabbits (Fig. 16.14).
The newly developed micro polymer-based vascular sensors are composed of
resistive heating and sensing elements that are encapsulated in the biocompatible
polymer (parylene C). The sensor is fabricated by surface micromachining
technique utilizing parylene C as microelectronic insulation. The sensor detects
small temperature perturbation as fluid passed the sensing elements leading to
changes in the resistance, from which shear stress is inferred. Novel biocompatible
materials such as Titanium (Ti) and Platinum (Pt) are used as the heating and
sensing elements which are exposed to blood flow. The Ti/Pt sensing element
offers low resistance drift, large range of thermal stability, low 1/f noise without
piezoresistive effect, and biocompatibility and resistance to corrosion/oxidation.
Moreover, Ti/Pt is deposited at room temperature, allowing for integration with
flexible parylene fabrication process. A hundred of the sensors are fabricated on a
3-inch silicon substrate. Given that parylene offers the structural stiffness and
sturdiness to encapsulate the electrodes, the sensor has excellent mechanical
strength and can be easily conformed to various anatomic curvatures. The
resistance of the sensing element is about 1.7 k
O
, and the temperature coefficient
of resistance (TCR) is at 0.11%/
1
C, compatible for blood rheology.
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