*4.2. Wireless Pressure Sensor*

One of the main symptoms of shunt failure is headache [4,5]. As this is a non-specific symptom with many causes, it can be difficult to determine whether this, or any symptom, is due to uncontrolled hydrocephalus. In the worst case, shunt patients will need exploratory surgery to determine whether their device is working appropriately. The most straightforward way to check the valve functionality is to observe the CSF pressure in the brain, the intracranial pressure (ICP), because ICP is the most related factor for showing HCP symptoms. If the HCP treatment device is not working properly, the ICP will be out of the normal range—usually elevated. Through ICP measurement, we can confirm that the symptoms must be due to issues with the device.

To this end, we need to observe the status of the device when the HCP patients show any related symptoms of device failure in a more patient-friendly way. Therefore, we developed a fully-passive wireless pressure sensor to measure ICP non-invasively. The sensor was designed using a resistive pressure sensor and RF backscattering to transmit the ICP measurement transcranially.

The RF components of the device use the varactor and antenna to encode information about the sensor voltage onto the second harmonic of a backscattered RF signal [26]. Additionally, the present design uses a secondary input from an external LED powering an internal photodiode. The LED and photodiode operate at infrared (IR) wavelength in order

to pass through tissue. The LED is pulsed at two different frequencies in order to encode information from the pressure sensor in a manner which is resilient to natural variations in the RF and IR attenuation.

## 4.2.1. Pressure Value Calculation

Wireless intracranial pressure (ICP) monitoring through a fully-passive method is shown in Figure 5. External pressure affects the resistance of the pressure-sensitive resistor. Increasing the pressure decreases the resistance. To read out the resistance change, *R*3, *C*1, and the resistive sensor form a voltage divider circuit, which divides the output voltage of the photodiode based on the impedance ratio between *R*3k*C*<sup>1</sup> and the resistance of the pressure-sensitive resistor. For simplicity, suppose the photodiode generates a sine wave to the voltage divider circuits. The sine wave has a frequency of f1 and an amplitude of *Ai*1. The resistance of the pressure sensor is *Rx*. Then the amplitude of the output signal, *Ao*1, can be written as:

$$A\_{o1} = \frac{R\_{\chi}}{Z\_{t1}} \times A\_{i1} \tag{1}$$

where *Zt*<sup>1</sup> represents the impedance of *R*3k*C*<sup>1</sup> (the impedance of *R*<sup>3</sup> in parallel with *C*1). For simplicity, suppose *R*<sup>3</sup> is 100 kΩ and *C*<sup>1</sup> is 1 nF, then *Zt*<sup>1</sup> can be expressed as:

$$Z\_{l1} = \sqrt{10^{10} \left[ I m(\frac{1}{1 + i \frac{\pi f\_1}{5000}}) \right]^2 + \left[ R\_x + 10^5 Re(\frac{1}{1 + i \frac{\pi f\_1}{5000}}) \right]^2} \tag{2}$$

where *Re*(*f*) and *Im*(*f*) denote the real and imaginary parts of *f*. The amplitude of the voltage divider output signal *Ao*<sup>1</sup> is a function of the pressure-sensitive resistor (*Rx*), photodiode output voltage *Ai*1, and the modulation frequency *f* <sup>1</sup>. The diode output voltage *Ai*<sup>1</sup> is greatly affected by the external environment, making the output *Ao*<sup>1</sup> unstable. To overcome such an effect, a second modulation frequency, *f* <sup>2</sup>, is introduced. Under *f* <sup>2</sup>, the output signal amplitude can be written as:

$$A\_{o2} = \frac{R\_X}{Z\_{t2}} \times A\_{i2} \tag{3}$$

where *Zt*<sup>2</sup> is the impedance of *R*3k*C*<sup>1</sup> at *f* <sup>2</sup>, which can be expressed as:

$$Z\_{I2} = \sqrt{10^{10} \left[ I m (\frac{1}{1 + i \frac{\pi f\_2}{5000}}) \right]^2 + \left[ R\_x + 10^5 Re \frac{1}{1 + i \frac{\pi f\_2}{5000}} \right]^2} \tag{4}$$

The ratio between *Ao*<sup>1</sup> and *Ao*<sup>2</sup> is:

$$\text{Ratio} = \frac{A\_{o1}}{A\_{o2}} = \frac{A\_{i1} Z\_{t2}}{A\_{i2} Z\_{t1}} \tag{5}$$

Since the voltage output of the diode detector is not affected by the frequency, *Ai*<sup>1</sup> = *Ai*2. Therefore, the ratio is:

$$\text{Ratio} = \frac{Z\_{t2}}{Z\_{t1}} \tag{6}$$

The above equation shows that the ratio is only a function of *R<sup>x</sup>* (resistance of the pressure-sensitive resistor), whose value is only related to the external pressure. Therefore, the pressure value can be obtained by calculating the ratio between *Ao*<sup>1</sup> and *Ao*2.

The two frequencies (*f* <sup>1</sup> and *f* <sup>2</sup>) are chosen to be 500 Hz and 2000 Hz, respectively. It should be noted that the actual signal outputted by the photodiode is a pulse wave instead of a sinewave; therefore, additional digital filters need to be applied during the post-processing steps. During testing, the DAQ output alternates between two frequencies

(*f* <sup>1</sup> and *f* <sup>2</sup>) of the square wave to modulate the emission of IR light. The ratio of the two signal amplitudes is measured to calculate the real-time pressure value.

#### 4.2.2. The External Interrogator

Figure 5e shows the structure of the external interrogator. The RF source (RF function generator E4432B, Agilent, Santa Clara, CA, USA) produces a 2.33 GHz RF carrier (*f* <sup>0</sup>) signal, which is equally divided into two paths through a power splitter [26]. The first path doubles the frequency to be 4.66 GHz (2*f* <sup>0</sup>) via a frequency multiplexer for the local oscillator (LO) of the down-converter. The second path amplifies and filters the RF carrier and radiates the signal through a dual-band (2.4 GHz/5 GHz) ceramic chip antenna (A10,194, Antenova, Cambridgeshire, UK). Concurrently, the antenna picks up 4.66 GHz (2*f* <sup>0</sup> ± *f* <sup>m</sup>) backscattered third-order mixing products which carry target pressure information. The circulator isolates the backscattered signal from the RF carrier. After amplifying and filtering, the third-order mixing products (2*f* <sup>0</sup> ± *f* <sup>m</sup>) mix with the LO (2*f* <sup>0</sup>) to down-convert the output to be *f* <sup>m</sup>. The demodulated signal (*f* <sup>m</sup>) goes through filtering and amplifying (SR560, Stanford Research System, Sunnyvale, CA, USA) and is sampled at 40,000 bit/s using a Data Acquisition Card (DAQ, NI-6361, National Instrument, Austin, TX, USA). The Labview (National Instrument, Austin, TX, USA) program is developed to post-process the signal and calculate the pressure value.

**Author Contributions:** S.L. (Seunghyun Lee) performed the overall research investigation, including experiments and data analysis, and prepared the main manuscript text and all figures. S.L. (Shiyi Liu), R.E.B. and M.C.P. assisted with preparing the experiments and edited the manuscript. J.B.C. oversaw the project and assisted with the writing of the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Army Medical Research Acquisition Activity (USAMRAA), grant number W81XWH2010805.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no competing interest.

#### **References**

