**1. Introduction**

56 Modern Telemetry

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Titanium or stainless steel rods are implanted to stabilize vertebrae movement during spinal fusion surgery, which allows bone grafts to fuse two or more vertebrae. Radiograph images (x-rays), computed tomography scans (CT) and magnetic resonance imaging (MRI) procedures are used to assess fusion progress and diagnose problems during patient recovery. However, the imaging techniques yield subjective results (Vamvanij et al.,1998) and as a consequence, result in unnecessary exploratory surgeries to ascertain the efficacy of the spinal fusion surgery. As the grafted bone fuses, the bending strain of the implanted rods decreases as the load is transferred to the fused vertebrae (Kanayama et al., 1997). Strain is measurable on the spinal fusion fixture, normally a stainless or titanium rod. In other words, the amount of strain is an indicator of the load applied to the rod. Therefore, it is proposed that the strain on the implant rods can be used as an alternative and non-invasive method to monitor the progress of spinal fusion (Hnat et al., 2008).

This chapter will demonstrate the realization of a telemetric strain measurement system for the spinal fusion detection as illustrated in Fig. 1. The system is composed of three major components: a sensitive strain sensor, a battery free transducer circuit that wirelessly interfaces the strain sensor, and an external interrogating reader that provides power to the implant as well as collects strain information from the transducer circuit. Research has shown that less power is consumed by a capacitive sensor than the resistive counterpart (Puers, 1993). In addition, the sensors require high sensitivity to eliminate the need for amplification that would require additional power. Therefore, the novel capacitive strain sensors are developed to meet both the power and sensitivity demand. Additional, in making the measurements a bodily-like situation, the sensor system, including the transducer circuit, is assembled on a housing (Aebersold et al., 2007) that is capable of transferring the strain from the rod to the sensor and accommodating for the size constrain. The testing loads on the rods will be provided by a material test system (MTS) with a corpectomy model fixture.

Although most strain sensors are capable of measuring axial strain due to tension and compression or their equivalents derived from bending, a sensitive bending strain sensor

Inductively Coupled Telemetry In Spinal Fusion Application Using Capacitive Strain Sensors 59

DeHennis et al. 2005 Suster et al. 2005

Backscttering, C-F, F-V converter

sensor

coils

Backscattering, C-F converter

sensor Capacitive sensor Capacitive strain

and temperature Strain

4.5mmx7.5mmx1mm 1000μm

relaxation oscillator Voltage output

Current source and

DeHennis et al. 2002

C-F converter

Capacitive

Range 4cm 1 inch

Frequency 40.68MHz 800KHz 3.18MHz 50MHz

2mmx2mm sensor on chip with circuit

Mounting ASIC chip On silicon On silicon

Testing method 3-point bending

channels 1 3 channels 3 channels 1 channel

range 1000 μ<sup>s</sup>

Dynamic/static Dynamic/static Dynamic/static Dynamic/static

range 5pF – 33pF 0.5pF-6pF 440fF

amplifier Class E amplifier

oscillator

Class E

Applications Pressure sensor Pressure Pressure, humidity

Secondary coil 4.5mmx7.5mm Co-axial 3 inches

Author, year

Overall sensor and circuit size

Number of

Strain/pressure

Capacitance

Reader type MC68HC705

Chatzandroulis et al. 2000

Method Backscattering Backscatterin,

pressure

450μm in diameter 2mm x 2mm

Circuit type C/F converter CMOS ring

micro-controller

Table 1. Some details of the inductively coupled detection systems

Sensor Capacitive

that only responds to bending strain is also desirable for spinal fusion purpose. The strain sensor is expected to measure 1000 με based on an adult of 200 pounds in a corpectomy model under bending with 2 stainless spinal fusion rods (6.4 mm in diameter and 50.8 mm long) implanted (Gibson, 2002).

Fig. 1. A strain gauge telemetry application in spinal fusion.

MEMS capacitive sensors using wireless data transmission have been evaluated in many applications such as humidity (DeHennis & Wise, 2005; Harpster et al., 2002;), temperature (DeHennis & Wise, 2005) and pressure sensing devices (Akar et al., 2001; Chatzandroulis et al., 2000; DeHennis & Wise, 2002, 2005; Strong et al., 2002). The telemetry approach to monitor strain uses inductively coupled battery-less technology similar to the technology used in Radio Frequency IDentification (RFID) devices (Finkenzeller, 1999). Some examples of the early applications are shown in Table 1. The inductively coupled wireless system with sensing capability needs not only the working passive telemetry circuitry, but also both the sensor interface circuitry and the sensor themselves. A fully integrated implanted sensor system was realized (Chatzandroulis et al., 2000) with a capacitive pressure sensor and an application-specific integrated circuit (ASIC) chip that controls RF modulation and converts capacitance variations into frequency variations. Suster et al. developed a wireless strain detection with the transducer coil size of 3-inch coaxial to the interrogating reader (Suster et al., 2005). However, this transducer coil size is not desirable for spinal fusion implant. Research using this technique coupled with MEMS sensors has become widespread in biomedical applications. It is a promising approach for orthopedic implant sensors and the key is a highly sensitive capacitive sensor (Benzel et al., 2002).

that only responds to bending strain is also desirable for spinal fusion purpose. The strain sensor is expected to measure 1000 με based on an adult of 200 pounds in a corpectomy model under bending with 2 stainless spinal fusion rods (6.4 mm in diameter and 50.8 mm

MEMS capacitive sensors using wireless data transmission have been evaluated in many applications such as humidity (DeHennis & Wise, 2005; Harpster et al., 2002;), temperature (DeHennis & Wise, 2005) and pressure sensing devices (Akar et al., 2001; Chatzandroulis et al., 2000; DeHennis & Wise, 2002, 2005; Strong et al., 2002). The telemetry approach to monitor strain uses inductively coupled battery-less technology similar to the technology used in Radio Frequency IDentification (RFID) devices (Finkenzeller, 1999). Some examples of the early applications are shown in Table 1. The inductively coupled wireless system with sensing capability needs not only the working passive telemetry circuitry, but also both the sensor interface circuitry and the sensor themselves. A fully integrated implanted sensor system was realized (Chatzandroulis et al., 2000) with a capacitive pressure sensor and an application-specific integrated circuit (ASIC) chip that controls RF modulation and converts capacitance variations into frequency variations. Suster et al. developed a wireless strain detection with the transducer coil size of 3-inch coaxial to the interrogating reader (Suster et al., 2005). However, this transducer coil size is not desirable for spinal fusion implant. Research using this technique coupled with MEMS sensors has become widespread in biomedical applications. It is a promising approach for orthopedic implant sensors and the key is a

long) implanted (Gibson, 2002).

Fig. 1. A strain gauge telemetry application in spinal fusion.

highly sensitive capacitive sensor (Benzel et al., 2002).


Table 1. Some details of the inductively coupled detection systems

Inductively Coupled Telemetry In Spinal Fusion Application Using Capacitive Strain Sensors 61

Fig. 2. The sensor on a substrate bar under bending. (b) The sensor's gap D0+D(x), zoomed in from above, varies as a function of position x. (c) shows the respect metal coordinates on

> *C <sup>r</sup>* ε ε

*<sup>r</sup>* is the dielectric constant of the material between the plates. In order to measure the strain magnitude, a cantilever test substrate is utilized. For strain and capacitance calculations, it is assumed that the dimensions of the cantilever test substrate very large compared to the sensor and that the sensor is firmly affixed to the substrate. For a cantilever beam, the

> 12 <sup>3</sup> *WT*

> > 2 6 *EWT Fd*

where, *W* is the beam width and *T* (or *R* as shown in Fig. 1) is the beam thickness. For a beam in uniaxial state of stress, the strain at any point on any surface under bending is given

> *EI Mc <sup>E</sup>* <sup>=</sup> <sup>=</sup> <sup>=</sup> σ

the bending moment, *c* is the distance from the neutral axis to the surface, *F* is the force

is the stress on the surface, *E* is the Young's modulus of the steel bar substrate, *M* is

ε

*D A*

= (1) <sup>0</sup>

ε

*I* = (2)

(3)

*<sup>0</sup>* is the permittivity and

The capacitance from two parallel electrode plates is given by

where *A* is the area, *D* is the distance between two parallel plates,

the cantilever substrate.

moment of inertia, *I,* is given by

by a textbook (Hibbleer, 1997),

ε

where σ

In the next sections, the highly sensitive MEMS bending strain sensor will be described in great detail followed by the system circuitry and the testing methods.

### **2. The MEMS strain sensors**

This section focuses on the development and fabrication of the custom bending strain capacitive sensing element needed for the spinal fusion measurement implant (SFMI) applications. This application requires a high bending strain sensitivity with enough nominal capacitance to avoid loss due to parasitic capacitance, compatibility with an inductively powered circuit, and suitable dimensions for system packaging. The sensitive bending strain sensor is expected to be packaged in a housing container that attaches to the diameter spinal fusion rod. The distance between two vertebrae is about 25.4 mm in the lumber region, making the maximum length of the housing limited to approximately 12 mm long. Therefore, it is desirable that the sensor length be less than 10 mm. The housing is installed between two pedicle screws and needs to transfer the bending strain from the rod to the sensor as described in (Aebersold et al. 2007). The curved surface of the rod is compensated with the 2 mm thick plastic housing which conforms to the rod and is trimmed 1 mm down to provide a flat area of 2 mm x 10 mm for the sensor to mount.

Certain characteristics were primarily considered when reviewing limited examples of previous parallel plate capacitive strain sensors in the literature. The basic concept of the capacitive strain sensor features a pair of metalized parallel plates with a dielectric gap. The sensing mechanism manifests itself in varying either the area of the plate, the gap between the plates, or the dielectric medium between the plates. A number of parallel plate sensor designs with a variable air gap were analyzed in the early 90's (Procter & Strong 1992). These sensors generally exhibited low nominal capacitance and sensitivity due to the large gap. In an attempt to increase the nominal capacitance in a non-air gap design, it was demonstrated by a sensor with a parallel plate structure and a thick-film dielectric material (Arshak et al., 1994). The dielectric film between the two plates was compressed during bending, thus expanding the film in area and decreasing the thickness from the perspective of the electrodes. These changes in the film geometry lead to a high gauge factor of 75-80 with a 15-25 μm gap based on a uniform model. The capacitive gauge factor is defined by the fractional change in capacitance with respect to strain. This thick-film dielectric produced both capacitive and resistive responses to strain making this approach electrically unique, but undesirable for the SFMI application due to power consumption. In another design, more effort was involved to invoke the change in permittivity of a dielectric material resulting in a gauge factor of 3.5 to 6, with a 150 μm gap (Arshak et al., 2000). This variable permittivity approach exhibits limited sensitivity that showed no dependency on its dimension (the gauge factor is constant and only depends on the "piezocapacitive" effect). This low gauge factor approach would require additional circuitry that is not desired for this implant design.

#### **2.1 The bending sensor theory**

The mechanism of sensing pure bending on a test substrate is described in two folds: the capacitance and the strain condition imposed on the sensor, as illustrated in Fig. 2. Assuming the bending sensor is attached to a steal cantilever with length L and thickness R in an elastic bending.

In the next sections, the highly sensitive MEMS bending strain sensor will be described in

This section focuses on the development and fabrication of the custom bending strain capacitive sensing element needed for the spinal fusion measurement implant (SFMI) applications. This application requires a high bending strain sensitivity with enough nominal capacitance to avoid loss due to parasitic capacitance, compatibility with an inductively powered circuit, and suitable dimensions for system packaging. The sensitive bending strain sensor is expected to be packaged in a housing container that attaches to the diameter spinal fusion rod. The distance between two vertebrae is about 25.4 mm in the lumber region, making the maximum length of the housing limited to approximately 12 mm long. Therefore, it is desirable that the sensor length be less than 10 mm. The housing is installed between two pedicle screws and needs to transfer the bending strain from the rod to the sensor as described in (Aebersold et al. 2007). The curved surface of the rod is compensated with the 2 mm thick plastic housing which conforms to the rod and is trimmed 1 mm down to provide a flat area of 2 mm x 10 mm for the sensor to

Certain characteristics were primarily considered when reviewing limited examples of previous parallel plate capacitive strain sensors in the literature. The basic concept of the capacitive strain sensor features a pair of metalized parallel plates with a dielectric gap. The sensing mechanism manifests itself in varying either the area of the plate, the gap between the plates, or the dielectric medium between the plates. A number of parallel plate sensor designs with a variable air gap were analyzed in the early 90's (Procter & Strong 1992). These sensors generally exhibited low nominal capacitance and sensitivity due to the large gap. In an attempt to increase the nominal capacitance in a non-air gap design, it was demonstrated by a sensor with a parallel plate structure and a thick-film dielectric material (Arshak et al., 1994). The dielectric film between the two plates was compressed during bending, thus expanding the film in area and decreasing the thickness from the perspective of the electrodes. These changes in the film geometry lead to a high gauge factor of 75-80 with a 15-25 μm gap based on a uniform model. The capacitive gauge factor is defined by the fractional change in capacitance with respect to strain. This thick-film dielectric produced both capacitive and resistive responses to strain making this approach electrically unique, but undesirable for the SFMI application due to power consumption. In another design, more effort was involved to invoke the change in permittivity of a dielectric material resulting in a gauge factor of 3.5 to 6, with a 150 μm gap (Arshak et al., 2000). This variable permittivity approach exhibits limited sensitivity that showed no dependency on its dimension (the gauge factor is constant and only depends on the "piezocapacitive" effect). This low gauge factor approach would require additional circuitry that is not desired for

The mechanism of sensing pure bending on a test substrate is described in two folds: the capacitance and the strain condition imposed on the sensor, as illustrated in Fig. 2. Assuming the bending sensor is attached to a steal cantilever with length L and thickness R

great detail followed by the system circuitry and the testing methods.

**2. The MEMS strain sensors** 

mount.

this implant design.

in an elastic bending.

**2.1 The bending sensor theory** 

Fig. 2. The sensor on a substrate bar under bending. (b) The sensor's gap D0+D(x), zoomed in from above, varies as a function of position x. (c) shows the respect metal coordinates on the cantilever substrate.

The capacitance from two parallel electrode plates is given by

$$C = \varepsilon\_0 \varepsilon\_r \frac{A}{D} \tag{1}$$

where *A* is the area, *D* is the distance between two parallel plates, ε*<sup>0</sup>* is the permittivity and ε*<sup>r</sup>* is the dielectric constant of the material between the plates. In order to measure the strain magnitude, a cantilever test substrate is utilized. For strain and capacitance calculations, it is assumed that the dimensions of the cantilever test substrate very large compared to the sensor and that the sensor is firmly affixed to the substrate. For a cantilever beam, the moment of inertia, *I,* is given by

$$I = \frac{WT^3}{12} \tag{2}$$

where, *W* is the beam width and *T* (or *R* as shown in Fig. 1) is the beam thickness. For a beam in uniaxial state of stress, the strain at any point on any surface under bending is given by a textbook (Hibbleer, 1997),

$$
\varepsilon = \frac{\sigma}{E} = \frac{Mc}{EI} = \frac{6Fd}{EWT} \tag{3}
$$

where σ is the stress on the surface, *E* is the Young's modulus of the steel bar substrate, *M* is the bending moment, *c* is the distance from the neutral axis to the surface, *F* is the force

Inductively Coupled Telemetry In Spinal Fusion Application Using Capacitive Strain Sensors 63

( ) <sup>3</sup> 3

*LL L*


<sup>3</sup> <sup>3</sup> 3 - 2 6

2 <sup>3</sup> 3 - 2

( ) ( ) ( ) <sup>3</sup>

The increased gap (see Fig. 2b) between the two electrode plates is a function in the x-

The capacitance change is determined by calculating the average distance between the two metal plates of the strain sensor. The average displacement, in addition to the initial gap,

2

1

2

<sup>1</sup> ( ( ) ( )) ( ) *M*

*t L D D v x v x dx M L*

*w M L*

+ ( ) <sup>+</sup>

0 2 2 1 1

1 1 3

2 1 3

1

*<sup>f</sup> <sup>r</sup> <sup>r</sup> Cp <sup>D</sup> <sup>D</sup>*

0

ε ε

*r p*


*dT L M L L M L M L L L L M L L L L M*

3 -

( ) ( ( ) ( )+( )( )+( )( ))

2 1

3 3

*w M L*

<sup>3</sup> - <sup>3</sup> - <sup>2</sup> - <sup>4</sup>

2 1 1

2 3

4 1 4 1

compared with the fabricated MEMS sensor in the following section.

*dT M L L M L M L L L L M L L L L M L*

3 -

Based on the equation above, the bending strain sensor is analytically formulated and to be

( ) ( ( ) ( )+( )( )+( )( ))

3 3

1 1


*w L M*

<sup>3</sup> - <sup>3</sup> - <sup>2</sup> - <sup>4</sup>

1 2 1


2 3

*C* +

where *M1* is where the sensing portion of metal starts and *L2* where it ends. The capacitance

<sup>1</sup> ( ( ) ( )) ( ) *L*

*t M D D v x v x dx L M*

2 1

1 1

where the metal stops at *L1*. Capacitance, due to beam deformation, *Cf*, is given by

*D D w L M*

+ ( ) <sup>=</sup>

0 1 1 2 1

4 1 4 2

2

The constant b from (7) is solved by combining (6), (8) and (9) at point *L3* and becomes

6

<sup>2</sup> - <sup>2</sup>

Therefore, the tangent line is expressed as

between main metal layers is expressed as

Combining (3), (13), (14) and (15), yields

*f r*

ε ε

0

*C*

*D*

0

+

ε

*D*

0

ε ε

0

+

ε

1 0

2 0

0

( ) <sup>=</sup>

3 1 3 2

<sup>1</sup> - -

ε ε

( ) <sup>+</sup>

3 1 3 1

<sup>1</sup> - -

due to the trace has an average displacement of *D2*, which is expressed as

direction and expressed as

*EI F*

*LL <sup>L</sup> <sup>x</sup> EI*

( ) = ( ) <sup>3</sup> *L*<sup>3</sup> *v L v <sup>t</sup>* (9)

*b* = (10)

3

*D*(*x*) = *v* (*x*) *v*(*x*) *<sup>t</sup>* - (12)

= + <sup>−</sup> <sup>−</sup> (13)

= + <sup>−</sup> <sup>−</sup> (14)

(15)

*C*

(16)

2 1 2 3 2

+

2 1 2

3 2


2


2 3

*<sup>F</sup> <sup>v</sup> <sup>x</sup> <sup>t</sup>* <sup>=</sup> + (11)

applied at the free end of the beam and *d* is the sensor location from the free end of the beam. The sensor location on the beam is given by

$$d = L \quad \frac{L\_4 + L\_2}{2} \tag{4}$$

where L is the length of the cantilever substrate, L4 and L2 are the longitudinal boundaries that define the bottom beam of the sensor. Fig. 2a shows the sensor location on the bent cantilever test substrate. Fig. 2b is the side view of a bending condition of the sensor design depicted in Fig. 2c, showing the sensor's metal layer coordinates and the widened gap, D0+D(x). Figs. 2c also shows the details of the top and bottom electrode while under bending for the designs of interest. The initial sensor capacitance is given by

$$C\_0 = \varepsilon\_0 \varepsilon\_r \frac{\varkappa\_1 (L\_2 \cdot M\_1)}{D\_0} + \varepsilon\_0 \varepsilon\_r \frac{\varkappa\_2 (M\_1 \cdot L\_1)}{D\_0} + C\_p \tag{5}$$

where L1 marks the beginning of the metal layer on the bottom electrode, L2 not only represents the boundary of the sensor but also the end of the metal layers on both the bottom and top electrode beams and therefore, L2-L1=L0 is the effective electrode length. With various designs, M1 is a variable that represents the start of the metal layer on the top electrode beam and also ends the trace that connects the electrode to the pad on the bottom beam. Therefore, w1(L2-M1) represents the area of the overlapping metal plates, w2(M1-L1) the area of the metal trace, and D0 the initial spacing between the plates (see Figs. 2b-2c). The first term represents the capacitance of the overlapping metal plates. The second term is the capacitance of the trace between the electrode and the pad. The third term, Cp, is the parasitic capacitance of the metal traces between L1 and L3 combined with the planar pads between L4 and L5. L3 is also the pivot point where the gap starts and L5 is the physical boundary of the top electrode beam. Capacitance calculations for planar pads indicate that the third term is 0.035 pF (Baxter, 1997). In order to estimate sensor sensitivity to strain, the capacitance change caused by an applied strain is calculated using standard beam equations. The sensor metal plate attached to the beam will follow the beam deflection while the initially parallel plate will remain straight under deformation. The deflection of a cantilever beam and the attached sensor metal plate is given by (Hibbleer, 1997),

$$\mathbf{v}(\mathbf{x}) = \frac{\mathbf{-}F}{6EI} (3L\mathbf{x}^2 \cdot \mathbf{x}^3) \tag{6}$$

where the *v(x)*, as seen in Fig. 2a, is the vertical displacement at position *x* on the beam. The initially parallel plate remains straight and its position is represented by a line tangent to the deformed beam at the pivot point of the sensor. The tangent line (see Fig. 2a) is given by

$$\mathbf{v}\_t(\mathbf{x}) = \theta(\mathbf{x})\mathbf{x} + b \tag{7}$$

where θ*(x)* is the slope at *x* and b is a constant determined by a boundary condition. The slope is determined from the first derivative of the deflection and given by

$$\theta(\mathbf{x}) = \frac{-F}{2EI} (2L\mathbf{x} \cdot \mathbf{x}^2) \tag{8}$$

At the sensor pivot point, *L3*, from Fig. 4b, the deflection of the two metal plates is equal, providing the boundary condition

$$\mathbf{v}\_t(L\_3) = \mathbf{v}(L\_3) \tag{9}$$

The constant b from (7) is solved by combining (6), (8) and (9) at point *L3* and becomes

$$b = \frac{F}{6EI} \left( 3LL\_3^2 \cdot 2L\_3^3 \right) \tag{10}$$

Therefore, the tangent line is expressed as

62 Modern Telemetry

applied at the free end of the beam and *d* is the sensor location from the free end of the

*<sup>L</sup>*<sup>4</sup> *<sup>L</sup>*<sup>2</sup> *<sup>d</sup> <sup>L</sup>*

where L is the length of the cantilever substrate, L4 and L2 are the longitudinal boundaries that define the bottom beam of the sensor. Fig. 2a shows the sensor location on the bent cantilever test substrate. Fig. 2b is the side view of a bending condition of the sensor design depicted in Fig. 2c, showing the sensor's metal layer coordinates and the widened gap, D0+D(x). Figs. 2c also shows the details of the top and bottom electrode while under

*<sup>C</sup>* <sup>+</sup> ( ) <sup>+</sup> ( ) <sup>=</sup>

bending for the designs of interest. The initial sensor capacitance is given by

*D w L M*

0 0

ε ε

0 1 2 1

cantilever beam and the attached sensor metal plate is given by (Hibbleer, 1997),

*vt*(*x*) = θ

slope is determined from the first derivative of the deflection and given by

θ

where θ

providing the boundary condition

( ) <sup>=</sup> ( ) <sup>2</sup> <sup>3</sup> <sup>3</sup> - <sup>6</sup> - *Lx <sup>x</sup> EI*

where the *v(x)*, as seen in Fig. 2a, is the vertical displacement at position *x* on the beam. The initially parallel plate remains straight and its position is represented by a line tangent to the deformed beam at the pivot point of the sensor. The tangent line (see Fig. 2a) is given by

> ( ) <sup>=</sup> ( ) <sup>2</sup> <sup>2</sup> - <sup>2</sup> - *Lx <sup>x</sup> EI F*

At the sensor pivot point, *L3*, from Fig. 4b, the deflection of the two metal plates is equal,

*(x)* is the slope at *x* and b is a constant determined by a boundary condition. The

2

*<sup>r</sup> <sup>r</sup> Cp <sup>D</sup>*


0

ε ε

where L1 marks the beginning of the metal layer on the bottom electrode, L2 not only represents the boundary of the sensor but also the end of the metal layers on both the bottom and top electrode beams and therefore, L2-L1=L0 is the effective electrode length. With various designs, M1 is a variable that represents the start of the metal layer on the top electrode beam and also ends the trace that connects the electrode to the pad on the bottom beam. Therefore, w1(L2-M1) represents the area of the overlapping metal plates, w2(M1-L1) the area of the metal trace, and D0 the initial spacing between the plates (see Figs. 2b-2c). The first term represents the capacitance of the overlapping metal plates. The second term is the capacitance of the trace between the electrode and the pad. The third term, Cp, is the parasitic capacitance of the metal traces between L1 and L3 combined with the planar pads between L4 and L5. L3 is also the pivot point where the gap starts and L5 is the physical boundary of the top electrode beam. Capacitance calculations for planar pads indicate that the third term is 0.035 pF (Baxter, 1997). In order to estimate sensor sensitivity to strain, the capacitance change caused by an applied strain is calculated using standard beam equations. The sensor metal plate attached to the beam will follow the beam deflection while the initially parallel plate will remain straight under deformation. The deflection of a

*w M L*

0 2 1 1

*<sup>F</sup> <sup>v</sup> <sup>x</sup>* (6)

*x* (8)

(*x*)*x* + *b* (7)

<sup>+</sup> = (4)

(5)

beam. The sensor location on the beam is given by

$$\mathbf{v}\_{l}(\mathbf{x}) = -\frac{\mathbf{-}F}{2EI} \Big\{ 2LL\_3 \cdot L\_3^2 \Big\} \mathbf{x} + \frac{F}{6EI} \Big\{ 3LL\_3^2 \cdot 2L\_3^3 \Big\} \tag{11}$$

The increased gap (see Fig. 2b) between the two electrode plates is a function in the xdirection and expressed as

$$D(\mathbf{x}) = \mathbf{v}\_l(\mathbf{x}) \cdot \mathbf{v}(\mathbf{x}) \tag{12}$$

The capacitance change is determined by calculating the average distance between the two metal plates of the strain sensor. The average displacement, in addition to the initial gap, between main metal layers is expressed as

$$D\_1 = D\_0 + \frac{1}{\left(L\_2 - M\_1\right)} \int\_{M\_1}^{L\_2} (v\_t(\mathbf{x}) - v(\mathbf{x})) d\mathbf{x} \tag{13}$$

where *M1* is where the sensing portion of metal starts and *L2* where it ends. The capacitance due to the trace has an average displacement of *D2*, which is expressed as

$$D\_2 = D\_0 + \frac{1}{\left(M\_1 - L\_1\right)} \int\_{L\_1}^{M\_2} (v\_t(\mathbf{x}) - v(\mathbf{x})) d\mathbf{x} \tag{14}$$

where the metal stops at *L1*. Capacitance, due to beam deformation, *Cf*, is given by

$$C\_f = \varepsilon\_0 \varepsilon\_r \frac{\varkappa\_1 (L\_2 \cdot M\_1)}{D\_0 + D\_1} + \varepsilon\_0 \varepsilon\_r \frac{\varkappa\_2 (M\_1 \cdot L\_1)}{D\_0 + D\_2} + C\_p \tag{15}$$

Combining (3), (13), (14) and (15), yields

$$C\_f = \varepsilon\_0 \varepsilon\_r \frac{\varkappa\_l (L\_2 \cdot M\_1)}{D\_0 + \frac{\varepsilon \{L (L\_2^3 \cdot M\_1^3) - \frac{1}{4} (L\_2^4 \cdot M\_1^4) + (3L\_3^2 L \cdot 2L\_3^3)(L\_2 \cdot M\_1) + \left(\frac{3}{2} L\_3^2 \cdot 3L\_3 L)(L\_2^2 \cdot M\_1^2)\}}} \tag{16}$$

$$+\begin{split} \star + \varepsilon\_0 \varepsilon\_r &\xrightarrow[\varepsilon\_0]{\mathfrak{w}\_2(M\_1 \cdot L\_1)} \frac{\mathfrak{w}\_2(M\_1 \cdot L\_1)}{4} + \frac{\mathfrak{w}\_2(M\_1 \cdot L\_1)}{4} \\ \times \frac{\varepsilon(L(M\_1^3 \cdot L\_1^3) \cdot \frac{1}{4}(M\_1^4 \cdot L\_1^4) + (3L\_3^2 L \cdot 2L\_3^3)(M\_1 \cdot L\_1) + \left(\frac{3}{2}L\_3^2 \cdot 3L\_3 L)(M1^2 \cdot L\_1^2))}{34T(M\_1 \cdot L\_1)} \end{split} \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{\*} C\_p \text{$$

Based on the equation above, the bending strain sensor is analytically formulated and to be compared with the fabricated MEMS sensor in the following section.

Inductively Coupled Telemetry In Spinal Fusion Application Using Capacitive Strain Sensors 65

silicon islands, which function as anchor platforms for the anodic bonding interface, as seen in Fig. 3e. An electrode and trace were then sputtered and patterned onto the silicon using the previously described metallization process. The small contact area on the raised anchor connected the pad on the glass plate with the electrode on the silicon plate via the traces, as

The glass and silicon wafers were stacked with the metal surfaces facing each other and visually aligned using a mask aligner. Methanol was used to temporarily maintain alignment. The substrates were anodically bonded at 450 oC on a grounded hotplate using a pointed probe to selectively place a -1000 V source on the glass, as shown in Fig. 3g. A gap is created between the electrodes on glass and silicon. This technique of selectively applying the electric field and bonding pressure prevented the recessed spaces from bonding to each other due to thermally induced warpage and electrostatic attraction. An automated dicing saw equipped with a 250 μm thick diamond blade was used to separate the individual sensor die from the bonded wafers. The silicon substrate was diced nearly through at the area above the contact pads. This was accomplished by limiting the depth of the cut and using the dicing alignment marks previously patterned on the silicon. Cuts to individually remove the sensors were similarly made from the silicon and glass substrate leaving approximately 30 μm of each substrate's depth (Fig. 3g). Care was taken to avoid chipping and prevent debris from filling the sensor gap. The sensors were separated from the wafer

Sensors with less than 3 μm gap have been fabricated, but with unreliable capacitance values and low yield. It is because of the collapsing of the two electrodes during the anodic bonding process. In an effort to maintain high nominal capacitance, preserve sensitivity and promote linearity, a sensor with an electrode area of 2 mm x 4 mm, and a gap of 3 μm was fabricated for final SFMI prototyping. This sensor was tested on a spinal fusion rod with a

Fig. 4. Comparison of the calculation and experimental results of a strain sensor glued to a

ε

*C dC*

*GF* = (2)

manually by flexing them to break the remaining thin substrate (Fig. 3h).

near-linear response, as shown in Fig. 4.

spinal fusion rod.

Gauge factor is defined as

seen in Fig. 3f.

#### **2.2 Strain sensor fabrication**

The sensor fabrication process is illustrated in Fig. 3. The materials include borosilicate glass (Pyrex Corning 7740, 500 μm thick) and silicon wafers (p-type, (100), 1-10 ohm-cm, double side polished, 310 μm thick). Fabrication began with clean glass and silicon substrates as shown in Figs. 3a and 3c. An electrode, traces, and a pair of contact pads were patterned onto the glass substrate by sputtering 0.02 μm chromium for adhesion layer followed by 0.2 μm of gold. The metal trace leading to the bonding area makes electrical contact with the silicon side electrode after anodic bonding. Wet etching was used to pattern the metal (Fig. 3b).The silicon wafer was wet oxidized (Fig. 3d), patterned using photolithography and etched with buffered oxide etch (BOE) solution to form an oxide mask for silicon surface machining. The wafer was etched using potassium hydroxide (KOH) at 85°C (approximately 0.7 μm / minute) to form recessed features and created the initial gap spacing. The etching mask was removed using BOE leaving two

Fig. 3. Cantilever bending strain sensor fabrication process. Illustrations on the left are the side views and on the right are the top views. (a) Pyrex (Coring 7400) glass, (b)sputter of Au/Cr on glass as one electrode, (c) silicon substrate, (d) oxidation of the silicon as the etching mask, (e) etching silicon with KOH to create platforms for anodic bonding with glass, (f) sputter Au/Cr on silicon as the other electrode, (g) side view of partial dicing (arrows marks) after glass and silicon are anodically bonded, (h) the individual sensor after final separation, noting the gap between the two electrodes.

silicon islands, which function as anchor platforms for the anodic bonding interface, as seen in Fig. 3e. An electrode and trace were then sputtered and patterned onto the silicon using the previously described metallization process. The small contact area on the raised anchor connected the pad on the glass plate with the electrode on the silicon plate via the traces, as seen in Fig. 3f.

The glass and silicon wafers were stacked with the metal surfaces facing each other and visually aligned using a mask aligner. Methanol was used to temporarily maintain alignment. The substrates were anodically bonded at 450 oC on a grounded hotplate using a pointed probe to selectively place a -1000 V source on the glass, as shown in Fig. 3g. A gap is created between the electrodes on glass and silicon. This technique of selectively applying the electric field and bonding pressure prevented the recessed spaces from bonding to each other due to thermally induced warpage and electrostatic attraction. An automated dicing saw equipped with a 250 μm thick diamond blade was used to separate the individual sensor die from the bonded wafers. The silicon substrate was diced nearly through at the area above the contact pads. This was accomplished by limiting the depth of the cut and using the dicing alignment marks previously patterned on the silicon. Cuts to individually remove the sensors were similarly made from the silicon and glass substrate leaving approximately 30 μm of each substrate's depth (Fig. 3g). Care was taken to avoid chipping and prevent debris from filling the sensor gap. The sensors were separated from the wafer manually by flexing them to break the remaining thin substrate (Fig. 3h).

Sensors with less than 3 μm gap have been fabricated, but with unreliable capacitance values and low yield. It is because of the collapsing of the two electrodes during the anodic bonding process. In an effort to maintain high nominal capacitance, preserve sensitivity and promote linearity, a sensor with an electrode area of 2 mm x 4 mm, and a gap of 3 μm was fabricated for final SFMI prototyping. This sensor was tested on a spinal fusion rod with a near-linear response, as shown in Fig. 4.

Fig. 4. Comparison of the calculation and experimental results of a strain sensor glued to a spinal fusion rod.

Gauge factor is defined as

64 Modern Telemetry

The sensor fabrication process is illustrated in Fig. 3. The materials include borosilicate glass (Pyrex Corning 7740, 500 μm thick) and silicon wafers (p-type, (100), 1-10 ohm-cm, double side polished, 310 μm thick). Fabrication began with clean glass and silicon substrates as shown in Figs. 3a and 3c. An electrode, traces, and a pair of contact pads were patterned onto the glass substrate by sputtering 0.02 μm chromium for adhesion layer followed by 0.2 μm of gold. The metal trace leading to the bonding area makes electrical contact with the silicon side electrode after anodic bonding. Wet etching was used to pattern the metal (Fig. 3b).The silicon wafer was wet oxidized (Fig. 3d), patterned using photolithography and etched with buffered oxide etch (BOE) solution to form an oxide mask for silicon surface machining. The wafer was etched using potassium hydroxide (KOH) at 85°C (approximately 0.7 μm / minute) to form recessed features and created the initial gap spacing. The etching mask was removed using BOE leaving two

Fig. 3. Cantilever bending strain sensor fabrication process. Illustrations on the left are the side views and on the right are the top views. (a) Pyrex (Coring 7400) glass, (b)sputter of Au/Cr on glass as one electrode, (c) silicon substrate, (d) oxidation of the silicon as the etching mask, (e) etching silicon with KOH to create platforms for anodic bonding with glass, (f) sputter Au/Cr on silicon as the other electrode, (g) side view of partial dicing (arrows marks) after glass and silicon are anodically bonded, (h) the individual sensor after

final separation, noting the gap between the two electrodes.

**2.2 Strain sensor fabrication** 

$$GF = \frac{dC}{\varepsilon} \tag{2}$$

Inductively Coupled Telemetry In Spinal Fusion Application Using Capacitive Strain Sensors 67

Fig. 6. The block diagram of the (a) transducer circuit and (b) oscillator circuit.

The interogating reader operating on 12 VDC, 175 mA provides the 125 kHz magnetic field for the implant, as illustrate in Fig. 7. The reader antenna is 24 cm in diameter and is tuned to 125 kHz. An EM Microelectronic (Marin, Switzerland), EM4095 IC contains an on-chip oscillator, antenna driver, and a demodulation circuit. The output of the demodulator is measured using an Agilent 53131A counter and logged with a computer based data

In the region of detection, see Fig. 8, the implant receives enough power to operate from the magnetic field sourced by the reader. There is no degradation of strain sensing performance

**4. The interrogating reader** 

Fig. 7. The block diagram of the power reader.

acquisition system.

**4.1 Detection region** 

where *d*C/C is the fractional change of capacitance and ε is the strain. Using a linear fit of the differential capacitance data graphed in Fig 5, the gauge factor was ploted and calculated to be 252 for 0 to 1000 με. This value is extremly high in comparison to the current literature (Arshak 1994, 2000; Proctor & Strong 1992). By comparison, piezoresistive gauges typically provide a gauge factor less than 200 (Fraden, 1995) even at the cost of high temperature sensitivity.

Fig. 5. Comparison of the calculation and experimental results of a strain sensor glued to a spinal fusion rod.
