A Continuous, Drift-Compensated Impedimetric
Thermal Flow Sensor for In Vivo Applications
Trevor Hudson, Alex Baldwin, and Ellis Meng
Department of Biomedical Engineering, University of Southern California, USAABSTRACT
We report a liquid flow sensor developed forbiomedical applications based on electrochemical
impedance (EI) measurements across a constantly-biased
heating element. Prior EI-based flow transduction methods
were limited to periodic measurements; this novel sensing
approach is amenable to real time flow monitoring anddoes not require curve analysis or cooling between
measurements to extract EI response to flow. The use ofisolated reference electrodes in the sensor layout reduces
sensitivity to environmental drift in ionic concentration andtemperature by over 5×. Our sensor achieved a 2σ
resolution of 35 μm/sec between 0-200 μm/sec in a
flexible, biocompatible form factor.

INTRODUCTION
Liquid flow sensing is important for various industrial
and medical applications. Of the many flow sensing
technologies that have been developed, thermal flow
sensing remains popular for its ease of implementation,
simple structure, and minimal electronics overhead.
Thermal flow sensors include some combination of heaterand temperature sensor and are commonly categorized as:
hot-film or anemometric, calorimetric, or time-of-flight[1]. Traditional thermal flow sensors are typicallythermoresistive,
in which resistive
metal orsemiconducting elements are used for both heating andtemperature sensing. Sensors are typically constructedfrom hard materials such as silicon and metals due to theirease of fabrication and familiarity, as well as the linear
temperature coefficient of resistance (TCR) of metals overa wide temperature range. However, the use of suchmaterials in vivo requires additional packaging to prevent
liquid and salt intrusion, which can decrease sensitivity;
corrosion and formation of spurious conductive paths may
occur with packaging failure [2].
Alternatively, sensors constructed using soft,
biocompatible materials show promise for successful longterm implanted use. Our group previously presented anelectrochemical-impedance (EI) based temperature sensor
using exposed platinum electrodes on a Parylene substrate[3]. This method uses a high frequency signal to bypass
the electrical double-layer to measure fluid resistance,
which possesses an order-of-magnitude higher TCR thancommon metal sensing materials (human cerebrospinal
fluid: -2%/°C vs platinum: 0.39%/°C [4], [5]). Using EI
temperature sensors, we previously demonstrated time-offlight and calorimetric thermal flow sensing which use
thermal pulses to minimize the effect of drift on long-term
measurements [6], [7]. While effective in measuring steadyflow rates under laboratory conditions, these designs
require long warm-up and cooldown periods to capture themeasurement signal, resulting in a maximum demonstrated
flow sensing rate of one measurement each 30 seconds.
They also suffered from drift due to stochastic changes insolution conductivity. Older examples of EI nonthermal

flow sensors using alternate tracer techniques also exist[8]–[10], but showed poor sensing resolution.

Figure 1: Schematic of device layout with two flow cells.
The upstream cell contains reference electrodes only, while
the downstream cell is actively heated. Each flow cell isenclosed by a thermoplastic module with luer connectors
to facilitate integration. Flow cells are connected with a 3
cm length of silicone tubing, which isolates the referencecell from the heat signal.
Traditional thermal flow sensors often use anadditional temperature sensing element as a reference.
When fully isolated from the heater, the reference can becompared against the hot-film temperature signal toproduce a differential signal, which eliminates common
mode temperature fluctuations [11].
This strategy
improves sensor response to any temperature drift which
may occur. In this paper, we extend this concept byemploying a reference EI cell to mitigate sensor drift fromnot only temperature variation, but also from changes insolution concentration and composition. We also introduce
a novel sensing method in which the EI of fluid above aheated element is used to transduce flow rate in an
impedimetric hot-film analog.

CONCEPT AND FABRICATION
The flow sensor consists of two EI-measurement cells
in series. The reference cell is upstream and contains onlya temperature sensor. The downstream active cell contains
a heater and temperature sensor. As flow rate increases,
more heat is removed by forced convection, resulting in alower temperature. Both cells are fabricated as part of thesame die and are connected by ~3 cm of silicone tubing.
When a potential is applied across two electrodes
exposed to an ionic solution, current flows via movementof ions through solution; this relation is approximated by
Ohm’s law. The equivalent circuit is described by thesolution resistance and two electrode-fluid interfaces andcan be represented by the simplified Randles circuit. The
equivalent impedance is:2𝜔𝐶𝑑𝑙
𝑍𝑒𝑞 = 𝑅𝑆 +(1)𝑅𝑐𝑡 𝜔𝐶𝑑𝑙 + 1
where 𝑅𝑆 is the solution resistance, 𝑅𝑐𝑡 is the electrode’s
charge transfer resistance, and 𝐶𝑑𝑙 is the double-layer
capacitance.

The temperature coefficient of solution resistance foran ionic solution is high relative to typical sensing
materials, which allows EI cells to be effective temperaturedetectors. This sensitivity, however, is impacted by the rateof change of the TCR with temperature. For example, theTCR of phosphate-buffered saline (PBS), a common
analog for physiological fluid, decreases approximately
40% from 20 to 40°C [3]. Solution resistance is also afunction of various other parameters such as soluteconcentration, solute identity (due to differences inelectrical mobility), and presence of suspended solid
particles [12]. The double-layer capacitance and chargetransfer resistance are primarily determined by the surface
area and material properties of the electrode, which areideally stable, but can drift over time from degradative
processes such as substrate layer delamination andbiological deposition on electrode surfaces.

connections. Devices were packaged into a thermoplasticmodule (ID 3.25 mm). Silicone tubing (ID 1.58 mm)
connected the reference and flow transduction cells.

Figure 3: Microscope image of measurement cell. Central
resistive trace acts as heater. Electrochemical impedanceof fluid above heater is measured using exposed electrodes.

Drift = 1.4 Ω/min

Figure 2: Phosphate-buffered saline (PBS) is pumped
through the flow sensor to simulate physiological flows.
Impedance is measured at 100 kHz using a LCR meter fromboth cells while the heater is biased with constant power.
To correct for these potential confounding factors, weacquire a differential impedance signal between the active
and reference cells to eliminate common mode
disturbances. The temperature sensors are separated into
two cells to thermally isolate the reference sensor
completely from the active heater, even at zero flow. Eachcell is identical apart from the presence or absence of theresistive heater.
The fabrication process was previously described in[13]. First, 15 μm of Parylene C was deposited on a siliconcarrier wafer. 2000 Å thick layer of Pt was then deposited
via electron-beam evaporation and patterned by lift-off(AZ5214 photoresist). A second 15 μm Parylene insulating
layer was deposited, after which electrodes (180×20 μm2area) and contact pads were exposed via a deep reactive ion
etch in oxygen plasma using patterned AZ 4620 as an etchmask. Individual device dies were removed from thecarrier and annealed under vacuum at 200°C for 48 hours
to improve adhesion between Parylene layers. A thinpolyetheretherketone spacer was added to support thecontact pads and the assembly was inserted into a zeroinsertion force connector to establish external electricalFigure 4: Two measurement cells in the same fluid patheach detect the drift signal in environmental
electrochemical impedance at zero flow, caused bystochastic changes.

EXPERIMENTAL METHOD
Flow sensing performance was characterized using 1×
PBS flow set by a calibrated syringe pump connected to thesensor pair. Heating current to the active cell was supplied
by a Keithley 2400 SourceMeter. A constant power of 20mW (4°C overheat temperature) was delivered to the heater
during flow transduction in order to dissipate constant heat
flux into the fluid according to the Joule-Lenz law [14];power regulation was achieved using proportional-integralderivative feedback implemented in LabVIEW. Given that
our flow sensor functions via temperature detection acrossthe heater, constant temperature mode would not be
expected to show any sensitivity to flow – this wasconfirmed experimentally (results not shown). Impedanceacross EI electrodes was measured using an Agilent
E4980A precision LCR meter (100 kHz, 0.3 VP-P). Thissignal was alternated between each device at 10 Hz using amultiplexer.

Flow rates were calibrated to the differential
impedance signal between the active and reference cells.
This signal was normalized to its initial value and to thereference impedance to minimize the effect of drift.

we observed a similar negative drift. Clearly, the active
cell alone is incapable of resolving flow rates due to thismonotonic instability. Using the differential signal in blue,
we observed more stable flow rate tracking (Figure 5b).

(a)

Drift = 7.2 Ω/min(b)Figure 5: (a) Active cell impedance measurements alone
cannot transduce flow rate due to environmental drift. (b)Monitoring the difference between the impedances of thereference and active electrodes resulted in sensitive
tracking of flow rate.

Figure 6: Comparing impedance between electrodes in two
flow cells allows for flow rate transduction without waiting
for a baseline measurement or cooling time betweenmeasurements.
Figure 6 shows the differential impedance acquired
through the sensor and outputted flow rate simultaneously.
A significant difference in sensitivity clearly was observed
at different flow rates, as would be expected in a typicalanemometer. For example, the difference in response
between 1000 and 200 μL/min was -0.023%, while thedifference between 200 and 50 μL/min was -0.103%, a 24fold change in sensitivity. The sensor’s time constant,defined as the time required for the sensor response to reach
63.2% of its final value, also varied significantly with flowrate and with initial sensor value – from 0 to 1000 μL/min,the calculated time constant is 4.12 seconds, versus 60.93
seconds when changing from 50 to 100 μL/min. These
preliminary results will require further investigation.

RESULTS AND DISCUSSION
Prior to flow velocity measurement, it was necessary
to demonstrate that adjacent reference and active
measurement cells were able to detect congruent drift
signals. In Figure 4, the impedance from each cell wasmeasured with no flow or heater activation. These
measurements in red and black were observed to bequalitatively similar over 45 minutes of measurement. The
differential signal in blue varied only ~50 Ω after a 5
minute warmup period, resulting in a net drift of 1.4
Ω/minute.
Figure 5a shows impedance signals from each cellwith the heater and pump active. The reference impedance
signal in black shows a noticeable downward slope of ~7.2
Ω/min over the timespan of the experiment. This drift was
not induced; we suspect it is the result of a temperature orconcentration gradient occurring in our test setup. We
exploit this drift as a basic model for drift that one might
encounter during in vivo use. From the active signal in red,

Figure 7: The normalized difference between reference andactive impedance linearly transduces flow velocity at a 2σ
resolution of 35 μm/s up to 200 μm/s.
Similarly, warm-up times for this sensor depend
heavily on flow rate. At zero flow, the sensor requires
205.6 seconds to reach 10% of its final stable value. At 50

μL/min, this value is 170.0 seconds. The above warm-up
times and time constants are longer than traditional thermal
anemometers, which are typically in the millisecond range[15], and represent a weakness of this method. To more
effectively use this flow sensor, we aim to improve thesevalues by reducing the thermal inertia of the measurement
system, which is a lumped value dependent upon specificheat, thermal conductivity, dimensions, and geometry of
the system. Methods to decrease thermal inertia could
include decreasing the inner diameter of the thermoplastic
module, decreasing output power through the heater, orreducing the surface area of the heater. The thermal
conductivity of our substrate material, Parylene C, is 0.084
W/(m*K) at 298K, which compares favorably with silicon
dioxide at 1.3 W/(m*K) [16], [17], a common substrate in
MEMS sensor fabrication. Thus, we suspect that minimalheat loss occurs through our substrate. This and otherassumptions will be tested via finite element modeling in
future publications.
Continuous flow transduction was tested over therange of 0-400 μm/sec in Figure 7. A 2σ resolution of 35μm/sec was achieved within the linear range of 0-200μm/sec, which was taken as the flow range. Using a moresophisticated calibration method would allow an extensionof this range. Our sensor operates with a sensitivity of 3.00E-4 %/(μm/sec). We demonstrate a comparable
resolution to other EI sensors in the literature while gaining
the advantage of continuous sensing (Table 1).
Table 1: Comparing this work with other single-phase EI
sensors [6, 8-10], we demonstrate comparable resolution
as recent discrete sensors, while achieving continuoussensing.
Sensing
Resolution Measurement
PaperMethod(μm/s)
ModeToF,
Wu
dissolved
Discrete
2002
O2 tracer
Ionic
Ayliffepathway
4.60E5
Continuous2003
changesToF,
Yu
microbubble896
Discrete2015
tracer
BaldwinCalorimetric
19.1Discrete
2018
This
"Hot-film"
35.3
ContinuousWork
analogPrevious versions of EI sensors used heat pulses toreduce the effect of drift on measurements. This requires
heater timing control to implement, as well as some curve
analysis of the resultant impedance vs time curve. In thispaper, only arithmetic operations are required for sensor
operation, which could reduce electronics complexity.
Additionally, no cooldown period is required between flow
measurements, which limited previous designs.

ACKNOWLEDGEMENTS
This work was funded in part under NSF EFRI1332394 and by the Provost PhD Fellowship (TH). Theauthors would like to thank Priya Lee for fabrication
assistance, Dr. Kee Scholten for experimental input, and all
the remaining members of the BML for help and support.

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CONTACT*E. Meng, tel: +1-213-740-6952; ellis.meng@usc.edu