Introduction

Implanted functional electrical stimulation (FES) devices provide beneficial therapies and functional assistance for patients with severe paralysis. These devices are powered by batteries implanted along with the device or by transcutaneous power sources. Replacement of depleted implanted batteries requires frequent, costly surgeries with increased risk of complications.5 Transcutaneous power sources have external equipment that can be damaged, burdensome to carry, cosmetically unappealing and cannot be used in a wet environment. Misalignment of the external and internal coils can cause power interruptions19,21 and the heat generated by the inherent resistance of the coils has the potential to cause tissue necrosis or an inflammatory reaction.21 The use of stimulated muscle power to drive a self-replenishable, totally implantable power source could augment the power systems that are currently used. It could extend the lifetime of implanted batteries, reducing or possibly eliminating the number of required replacement surgeries. Or, it could augment transcutaneous power sources by allowing periods of untethered FES device functionality during which a shower or other types of daily activities could be performed independently.

The fundamental concept of our implanted generator is to place a piezoelectric stack generator in series with a muscle-tendon unit as illustrated in Fig. 1. The generator is attached between the muscle-tendon unit and bone such that isometric muscle contractions result from stimulation of the nerve innervating the muscle. A mechanical device is used to hold the piezoelectric generator in place and to convert the tensile force produced by stimulated muscle contractions into a compressive force that is applied to the piezoelectric material. Repetitive stimulation of the motor nerve results in muscle contractions that exert a repetitive force on the piezoelectric material. Due to the electromechanical properties of the piezoelectric material, charge will develop when it is strained from the applied compressive forces. A portion of the resulting charge will be used to power the nerve stimulations and the remaining charge will be available to power the targeted application.

Figure 1.
figure 1

The Piezoelectric Generator Concept. A block diagram is used to illustrate the concept for an implanted, stimulated muscle powered piezoelectric generator. Piezoelectric material is attached in series with a muscle tendon unit. Electrically stimulated muscle contractions exert force on the piezoelectric material producing a charge across the material. The charge is collected in energy storage circuitry and used to power the stimulator and other loads.

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Others have evaluated the use of piezoelectric generators to harness the energy associated with various physiological processes. A variety of prototypes have been developed, using different types of piezoelectric material with different loading strategies, producing a range of power generation results. Elvin et al. used a single piece of polyvinylidene fluoride (PVDF) piezoelectric material mounted on a simply supported beam as a bone strain sensor and telemeter, which produced approximately 0.1 μW of power.6 Hausler et al. rolled PVDF piezoelectric material into a tube and connected it between two ribs in a canine. The rib displacement during breathing produced a strain on the piezoelectric material, which produced 17 μW of power.11 Ko placed a mass on the end of a single piezoelectric cantilever beam ceramic wafer (2 cm × 5 cm × 1 cm) and packaged it in a box for attachment to the heart. When 80 bpm mechanical pulses shook the box, the piezoelectric material was vibrated at 6.5 Hz, resulting in 160 μW of power.13, 14 When chronically driven by actual canine heart contractions, the efficiency of the generator was reduced to a sustained output power of 30 μW 14. The reduction in efficiency was due to the reaction of the tissue to wall-off the generator thus minimizing force transfer to the generator.

Our generator is less invasive than these previous designs, it has a more natural attachment in series with the muscle tendon unit and it operates with essentially with no moving parts. Attempts at chronically implanting power generating devices that require movement for operation have resulted in reductions in the efficiency of the generator due to fibrous growth. For example, after 12 weeks of operation a 65% reduction in output pressure was found with a device used to convert muscle power to pneumatic pressure for cardiac assist.17 Fibrous growth around our generator will be tolerable because the displacement of the piezoelectric stack is only in the micrometer range, a movement that should be undetectable by the surrounding tissue. This minimal excursion of the piezoelectric material dictates that isometric muscle contractions be used. While shortening contractions and long excursions of a power generating device might initially appear to be more advantageous, in the long term the efficiency of such a device will decrease. In contrast, the efficiency of our conversion device should not decrease due to our unique design features.

Our design incorporates the use of electrically-stimulated muscle contractions, which is a well established method for restoring function in spinal cord injury patients3. A portion of the power produced by the piezoelectric generator will be used to operate the electrical stimulator, which will produce the regular pulses that activate the muscle driving the piezoelectric generator. Theoretically, the output power of the generator will be greater than the power required to activate the driving stimulator since skeletal muscle is an autologous power source. The mechanical output power of a muscle is substantially greater than the electrical power necessary for artificial stimulation of the motor nerve. A conservative estimate of the sustained output power of stimulated, conditioned muscle producing isotonic tetanic contractions is 1 mW/g1, 9, 22. The human latissimus dorsi is approximately 150 g16, 20, corresponding to an output power of 150 mW. An estimate of the electrical power needed for stimulations to produce this amount of muscle output power is 0.5 μW, calculated from the stimulation parameters.9 Simply comparing the electrical stimulation input power to the muscle output power, muscle is a power conversion system with a multi-order gain (five orders of magnitude of gain in this simplified example). The gain is achieved through the chemical energy obtained from nutrients. In addition, as the size of the muscle increases the output power increases. However, the stimulus amplitude required to fully activate the nerve of different sized muscles is essentially the same relative to the differences in output power. Therefore, the gain available between the input power necessary to stimulate a muscle and the mechanical output power of the muscle increases as the size of the muscle increases. Three potential muscles are examined to represent the range of potential power sources allowing the muscle requirements for novel applications to be determined.

Electrically-stimulated power generation has some significant advantages over power scavenging schemes when considering a power source for neuroprosthetic applications. We hypothesize that more power can be obtained from a stimulated muscle than from scavenging power from intermittent processes such as the strain experienced by bone or by naturally occurring muscle contractions, even though the stimulation utilizes some of the power generated by the system. Since our targeted applications are for individuals with extensive paralysis, such as spinal cord injury, naturally occurring muscle contractions are significantly reduced. However, a paralyzed muscle could be used to run the generator to provide power for restoration of other functions. The system parameters dependent on frequency can be easily tuned for optimal performance if a consistent pattern of operation is used. For these reasons, we have incorporated into our design the use of stimulated-muscle contractions to drive our implanted generator.

This study was performed to determine the feasibility of a stimulated muscle powered piezoelectric generator. The theoretical output power of such a generator was compared to the power necessary for motor nerve stimulation. The output power of the generator was estimated with simulations of a software circuit model developed to represent the system. The model included the input force from the muscle, the piezoelectric material and the load circuit. The constraints of the system parameters were identified and simulations were performed to evaluate how changes to the system parameters within those constraints affect the output power. Force that mimics the force produced by muscles during contraction was applied mechanically to a non-optimized prototype system. Compressive force was applied directly to a piezoelectric generator and tensile force to a mechanical device built as a holder and connector for the piezoelectric generator. The results were used to determine the accuracy of the software model and to determine power losses due to mechanical coupling.

Methods

Software Model

Software Model Circuit Representation

The circuit representation of our system concept is shown in Fig. 2. The equations introduced in the following paragraphs describe the circuit components. The piezoelectric stack generator was electrically represented as a voltage source (V p ) in series with a capacitor (C p ). V p depends upon the applied input force, the piezoelectric constant and the shape and the dimensions of the material:

$$ V_p = \frac{{g_{33} t}} {A}F $$
(1)
Figure 2.
figure 2

Circuit Diagram of the generator system. The piezoelectric generator is electrically represented as a voltage source (V p ) in series with a capacitor (C p ). V p is proportional to the applied force. A diode bridge and filter capacitor were used to obtain a DC load voltage (V L ). V L was recorded across the load resistor (R L ) and used to calculate the system output power.

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The piezoelectric constant (g 33) is the electromechanical property of the material, t is the thickness of one layer of the stack, A is the cross-sectional area of the generator and F is input force, which results from muscle contractions for our application.4, 8 Triangle pulses with a pulse width of 250 msec were used to represent the force of a muscle contraction. In the software simulations a piece-wise linear data file of the force waveform was used.

The layers of stack generators are electrically connected in parallel, so the total capacitance of the stack is the capacitance of one layer multiplied by the number of layers in the stack. The dependence of the capacitance upon the shape and dimensions of the material and on the material’s dielectric constant is given by:

$$ C_p = \frac{{nE_r E_o A}} {t} $$
(2)

The number of layers equals n, E r is the relative dielectric constant and E o is the dielectric of free space (8.9 × 10−12 Fm−1).4, 8

A diode bridge and filter capacitor (C L ) were used to convert the piezoelectric voltage to an approximately DC voltage source across a load resistor (R L ). A small decrease in the steady state output voltage during each cycle (voltage ripple) is present due to the leakage current of the circuit. Increasing the size of C L reduces the ripple, however, it also increase the time it takes the generator to reach its steady state voltage. The amount of ripple that can be tolerated will depend on the load connected to the generator, dictating the size of C L and the charging time of the generator. For this study C L was chosen to be 100 times greater than C p .

The output power of the system (P out ) is the power dissipated through the load resistance. It can be calculated as:

$$ P_{out} = \frac{{V_{Lss} ^2 }} {{R_L }} $$
(3)

RL is the load resistor and V Lss is the steady state voltage across the load resistor. The maximum output power of the generator occurs when the load impedance matches the impedance of the piezoelectric generator 18:

$$ R_L = \frac{1} {{fC_p }} $$
(4)

The frequency of force application is f. When the impedances are matched, the steady state output voltage will equal one half of the peak piezoelectric voltage, neglecting the voltage drop in the diodes:

$$ V_{L\,ss} = \frac{{V_{p\,m} }} {2}{\hbox{ }} = {\hbox{ }}\frac{{{\hbox{g}}_{{\hbox{33}}} {\hbox{t}}}} {{{\hbox{2A}}}}F_m $$
(5)

F m is the peak amplitude of the input force pulse and V pm is the peak piezoelectric voltage. Substituting Eq. (2) into (4) and Eqs. (4) and (5) into (3) results in the following equation for the average optimal output power (P out opt ):

$$ P_{out\,opt} = \frac{{V_{p\,m} ^2 fC_p }} {4} = \frac{{g_{33} ^2 F_m ^2 tnE_r E_o f}} {{4A}} $$
(6)

Software Simulations within Parameter Constraints

Through inspection of Eq. (6) the relationship between the system parameters and output power can be determined. The output power increases as the piezoelectric and dielectric constants increase. However, these parameters are not independent. Piezoelectric material that has a high piezoelectric constant typically has a low dielectric constant. This results in stacks with either a high output voltage but low capacitance or a low output voltage but high capacitance. In Fig. 3, the relationship between the dielectric constant (E r ) versus the piezoelectric constant (g 33 ) is shown for several different commercially available piezoceramic materials, as specified in commercial data sheets. For these particular materials, a decaying exponential relationship was fitted between E r and g 33 with an r 2 value of 0.91:

$$ E_r = 11,572e^{ - 64.4g_{33} } $$
(7)
Figure 3.
figure 3

Relationship of piezoelectric and dielectric constants for commercially available piezoelectric materials. The piezoelectric (g33) and dielectric constants (E r ) for several commercially available piezoelectric materials are plotted to identify the relationship between the two constants. The data points were obtained from the manufacturer’s data sheets. The fitted relationship is \( E_r = 11,572e^{ - 64.4g_{33} } \), R2 = 0.91. The g33, Er pair that results in maximum power is g33 = 0.0325 VmN−1, Er = 1427 and was determined through software simulations.

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To increase the output power of the stack generator for this application, the length of the generator (the thickness of one layer times the number of layers) should be increased and the cross-sectional area should be decreased. Therefore, a long, slim stack is the best shape for the stack generator. This shape lends itself to a serial connection between tendon and bone, as proposed in our design. The limit on the overall length of the generator depends on the space available for implantation. Since the generator will essentially replace the tendon, the generator length can be designed to be approximately the length of the tendon. The generator length used in the simulations was chosen based on the tendon lengths. We assume that muscle length will not be significantly increased by the incorporation of the generator and artificial tendon connection into (or replacing) the natural tendon. The tendon lengths of skeletal muscles can range from 50 mm for the brachioradialis muscle in the forearm to 200 mm for the gastrocnemius in the leg.20 There is a lower limit to the cross sectional area of piezoelectric material that can be machined and if the cross sectional area of the stack is made too small there is a risk of breaking the generator as force is applied.

The output power of the generator will increase as the amplitude and frequency of the input muscle force increases. Muscle force increases as the cross-sectional area of the muscle increases and will depend upon what muscle is chosen to run the generator. Estimates of the maximum contraction forces can be found by multiplying the muscle’s physiological cross sectional area by a conversion factor of 35 Ncm−2.10 For sustained operation of the generator it will be necessary to use submaximal muscle contractions. The cross-sectional area of small forearm muscle such as the brachioradialis has been reported to be between 1.5 and 4.7 cm2.7, 15, 16, 20 It is 7.5–25 cm2 for a midsized muscle such as the latissimus dorsi14, 15, 19 and 25–60 cm2 for a large muscle such as the gastrocnemius.7, 15, 16, 20 Based on these cross-sectional areas and a conservative submaximal force level of 10–30% of maximum, an estimate of the range of possible input muscle forces was determined to be 25–250 N. The upper limit of the sustained frequency of the input force will be dictated by the rate at which the muscle can sustain contractions without fatigue. Table 1 summarizes the system parameter constraints.

TABLE 1. Summary of system parameter constraints.
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Simulations were performed with SPICE software (EMA Design Automation, Inc., Rochester, NY) to predict the theoretical output power of the generator as the system parameters were varied within the constraints imposed by the properties of the piezoelectric material and by the physiological constraints. The output power was calculated using Eq. (3), using the simulated steady state output voltage across the load resistor (R L ). Once the parameters that result in maximum output power were identified, the predicted output power for three scenarios was found. Scenario 1) is a 2.5 cm long generator with an input force of 50 N, such as would be appropriate if the generator was developed for use with a brachioradialis muscle. Scenario 2) is a 4 cm long generator with a 100 N force, for use with a muscle such as the latissimus dorsi. Scenario 3) is an 8 cm long generator, with an input force of 250 N, such as for use with a gastrocnemius muscle. The rest of the parameters were held constant across the three scenarios at values corresponding to those found in the parameter simulations to result in maximum output power within the constraints of the system.

Muscle stimulation power requirements (Input Power)

Some of the generated power will be used to electrically stimulate the muscle which drives the generator. This will be referred to as input power. The amount of required input power consists of two parts, stimulation power and controller power. The amount of stimulation power required depends upon the pulse width and amplitude of the stimulating current pulse, the frequency and duration of the stimulus and the rate of stimulation, resulting in a range of possible stimulation power requirements. At the high end of this range, is the estimate of 6 μW of power necessary for tetanic contractions. This is based on 500 μs pulses of 1 mA, applied at 50 Hz for 250 ms per contraction at a rate of 1 contraction per second, assuming a 1 kΩ impedance. The low end of the range is an estimate of 50 nW, for the power necessary for 1 Hz muscle twitches. This is based on single current pulse of 500 μA for 200 μs through a resistance of 1 kΩ, operating at 1 Hz. In addition to the power necessary for stimulation, power will also be needed for a stimulator controller. A controller for a single channel stimulator continuously consumes an average power of approximately 40 μW when the device is on.24 Therefore, a conservative estimate of the required stimulation power for our design is the controller power plus the stimulation power, or approximately 46 μW. However, it is likely that this amount could be reduced by using a simpler controller.

Experimental methods

Force was applied to a non-optimized prototype system with a material testing system (MTS) machine (MTS Systems Corporation, Eden Prairie, MN) to verify the accuracy of the software simulations and to explore possible sources of power loss within the system. A lead zirconate titanate (PZT) piezoelectric stack generator (part number T18-H5-104, Piezo Systems, Inc. Cambridge, MA), with a volume of 0.5 cm3 (5 mm × 5 mm × 18 mm), was used in the experimental trials. The piezoelectric material of the stack had a piezoelectric constant of 0.013 VmN−1 and a relative dielectric constant of 5400. The thickness of each layer was 0.11 mm and the stack contained approximately 164 layers. These values were specified by the manufacturer.

The piezoelectric generator was connected to the circuit shown in Fig. 2. A 100 μF filter capacitor (C L ) was chosen to balance between charging time and voltage ripple. C p was measured to be 1.86 μF, so a 540 kΩ load resistor (R L ) was used, which was calculated using Eq. (4). The MTS machine was used to apply compressive force directly to the piezoelectric stack. The applied force consisted of 250 ms triangle force pulses at 1 Hz with peak values of 25, 50, 100, 150, 200 and 250 N. For each trial, the pulses were applied for 240 seconds while the voltage was recorded across R L . The output power of the system was calculated with Eq. (3) using the resulting steady state voltages from the six trials. The parameters values of the piezoelectric stack and load circuit used in the mechanical experiments were entered into the circuit model and software simulations were performed using the same force values as used in the mechanical experiments. The experimental output power was compared to the software simulations in order to verify the accuracy of the model.

A mechanical device was built as a holder and connector for the piezoelectric generator. A picture of the mechanical holder is shown in Fig. 4. Since the muscle-tendon unit will always be producing tension, the mechanical device was designed to convert the tensile force produced by the muscle into a compressive force applied to the stack. The MTS machine was also used to apply tensile force to the mechanical device containing the piezoelectric generator. The applied tensile force consisted of 250 ms triangle force pulses at 1 Hz with peak values of 25, 50, 100, 150, 200 and 250 N. The pulses were applied for 240 seconds and the recorded steady state voltages across R L were used to calculate the output power. The differences in output power between force applied directly to the stack and force applied to the piezoelectric stack in a mechanical device was compared to determine losses due to the mechanical coupling.

Figure 4.
figure 4

Photo of mechanical holder. A mechanical device was built to hold the piezoelectric stack and convert the tensile force of muscle into a compressive force applied to the piezoelectric stack. When tensile force is applied between the two attachment sites a compressive force results between the top and bottom plates of the holder. The piezoelectric stack experiences the compressive force since it is held in place between the top and bottom plates.

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Results

Model results

Figure 5 contains the results of the SPICE simulations that were performed to predict the output power of the system as the system parameters were varied within their constraints. Using the relationship found between g 33 and E r , the maximum output power occurs when g 33 is approximately 0.0325 VmN−1 and E r is 1427 (Fig. 5(a)). The output power increases with increasing length (L) (the thickness of one layer times the number of layers) and decreases with increasing cross sectional area (Fig. 5(b)). The output voltage can be increased by increasing the thickness of the individual layers, while keeping the overall length constant. This will not increase the output power since the number of layers will decrease. However, by changing the thickness of the layers the output voltage of the system can be controlled and appropriately matched to the load connected to the generator. Figure 5(c) illustrates how the output power increases as the rate of the applied input force increases. However, muscle fatigue will likely occur at higher frequencies. The output power increases quadratically as the amplitude of the input force increases, as shown in Fig. 5(d). Example of muscles that can produce force in the three highlighted ranges is also given. The values used for the parameters when they were not varied were, g 33  = 0.0325 VmN−1, F m  = 50 N, L = 0.018 m, E r  = 1427, f = 1 Hz, A = 5 mm × 5 mm.

Figure 5.
figure 5

Simulation results within parameter constraints. A. Output power vs. the piezoelectric constant (g33) using the relationship between E r and g 33 found in Fig. 3. The g33, E r pair that results in maximum power is g33 = 0.0325 VmN−1, E r  = 1427. B. The length (L) (the thickness of one layer times the number of layers) is varied from 0 to 10 cm for three different cross sectional areas. The output power increases with increasing length and decreases with increasing cross sectional area. C. The output power increases as the rate of the applied input force increases. The higher the frequency, the more likely muscle fatigue will occur. D. The output power increases quadratically as the amplitude of the input force increases. An example of a muscle that can produce the force in the three highlighted ranges is given. The values used for the parameters when they were not varied were, g33 = 0.0325 VmN−1, F m  = 50 N, L = 0.018 m, E r  = 1427, f = 1 Hz, A = 5 mm × 5 mm.

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The results of the simulations performed to predict the output power of the three generator scenarios is shown in Fig. 6. The predicted output power for the three generator scenarios was: 1) 8 μW for a 2.5 cm generator with 50 N peak input force; 2) 54 μW for a 4 cm generator with 100 N peak input force; 3) 690 μW for an 8 cm generator with 250 N peak input force. The power required for a stimulator controller and for the range of possible stimulation power requirements is also shown in Fig. 6 for comparison.

Figure 6.
figure 6

Simulation of three generator scenarios. SPICE simulations of the output power for three generator scenarios: (1) A 2.5 cm long generator with 50 N peak input force, which would be appropriate if the generator was connected to the brachioradialis muscle. This scenario resulted in 8 μW of power; (2) A 4 cm long generator with 100 N peak input force, resulting in 54 μW. An example of a muscle for this scenario is the latissimus dorsi; (3) An 8 cm long generator with 250 N input force could be used with a muscle such as the gastrocnemius, resulting in 690 μW. All other parameters were constant for the three scenarios and were: g33 = 0.0325 VmN−1, E r  = 1427, f = 1 Hz, A = 5 mm × 5 mm. These parameter values correspond to those found in the parameter simulations to result in maximum output power, within system constraints. The range of power required for motor nerve stimulation and the power required for a single channel stimulator controller are shown for comparison.

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Experimental Results

The output voltage resulting from direct repetitive compression of the piezoelectric stack with the MTS machine is shown in Fig. 7. The voltage across R L increases from zero to a steady state value. The output voltage is proportional to the applied force and increases as the force increases. The steady state voltage ranged from 0.33 V when 25 N force pulses are applied to 6.1 V when 250 N force pulses are applied. The steady state voltages were used with Eq. (3) to determine the output power of the generator system when it was subjected to direct compression. The output power was also calculated from the steady state voltages resulting from repetitive tensile force applied to the mechanical holder containing the piezoelectric stack. These experimental output power values were compared to the simulated output power results in Fig. 8.

Figure 7.
figure 7

Output voltage from repetitive force application. Triangle force pulses with a 250 ms pulse width were mechanically applied with a MTS machine at 1 Hz for 240 s with six different peak force values, 25, 50, 100, 150, 200 and 250 N, to a non-optimized piezoelectric generator connected to the circuit shown in Fig. 2. The output voltage was proportional to the applied force and increased as the force was increased. The steady state voltage when 25 N force pulses are applied was 0.33 V. It was 1.26, 2.23, 3.52, 4.85 and 6.1 V for 50, 100, 150, 200 and 250 N force pulses respectively. The steady state voltages were used with Eq. (3) to determine the output power of the generator system.

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Figure 8.
figure 8

Simulation and experimental output power comparison. The simulated output power over a range of input force from 25 to 250 N is compared to the experimental output power resulting from mechanical force applied directly to the piezoelectric stack and to the stack in the mechanical holder. The experimental output power was calculated using Eq. (3) with the steady state voltage levels measured across the load resistor. The simulated output power corresponds well with the experimental output power, demonstrating the accuracy of the software model. There is essentially no difference between the output power when force is applied in compression directly to the stack and when it is applied in tension to the mechanical holder. This demonstrates that the mechanical holder can be used without significant mechanical coupling losses.

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The output power results obtained in the simulations matched the output power resulting from direct compression of the piezoelectric stack. An average difference of 4 μW was observed over the range of input forces, from 25 to 250 N (Fig. 8). When the output power resulting from direct compression of the stack is compared to the output power resulting from tensile force applied to the mechanical device, the output power was essentially the same over the range of 25 to 250 N (Fig. 8). The average difference was 0.08 μW.

Discussion

Our results provide evidence that a stimulated muscle powered piezoelectric generator system may be feasible for extending the life of, or possibly eliminating, the batteries of implanted electronic devices. It also may be possible to use the generator to allow for periods of untethered FES device functionality. Simulations of the software model of our system were used to identify parameter values which maximize the output power of the system, within the system constraints. Our simulations predict that with an 8 cm long generator and 250 N input force pulses, 690 μW of power may be achieved by an implanted, muscle powered piezoelectric generator. This is greater than the conservative estimate of the necessary input power of 46 μW, which includes the power requirements of a stimulator controller and for motor nerve stimulation. It is predicted that a 4 cm long generator with 100 N input force pulses will produce 54 μW of output power, also in excess of the stimulation power required to drive the generator. For a 2.5 cm long generator with 50 N input force pulses, a lower power stimulator will need to be developed in order for the generator to produce more output power than required stimulation power.

It may be possible to reduce the amount of required stimulation input power by using a simpler controller. If the stimulation pattern is continuous and unchanging and no sensing is needed, it should be possible to reduce the controller’s power requirements. Another possible way to reduce the input power requirements is to design one controller that combines the control functions needed for both the stimulations to drive the generator and another functional electrical stimulation application. Additionally, current research may lead to reductions in the power requirements of stimulator controllers. For example, Wong et al. developed a pacemaker that combined the sensing, controlling and stimulation delivery into a single, very-low-power integrated circuit that consumed only 8 μW of power25. The theoretical output power of our generator was based on continuous operation. The power requirements of targeted applications may require large bursts of power during short periods of time. Thus, electrical circuitry will be needed to match these different duty cycles and may cause increased power losses within the system.

The two key parameters in our design will be the selection of the muscle used to drive the generator and the rate of muscle contraction. A large muscle will produce more force and output power than a small muscle. However, implementation may be easier with a small muscle and the use of a redundant muscle is attractive in order to minimize the effect of the loss of functionality of the muscle used to run the generator. The presented analysis may be used to determine the required muscle sizes for novel applications. The force produced by muscles also varies depending on the stimulation frequency. Low frequency single pulse stimulations will require less stimulation power, but will result in low force muscle twitches. High frequency stimulation pulse trains will produce maximal tetanic force, but will require greater input stimulation power. Additionally, the rate at which muscle contraction can be sustained depends on the fatigability of the muscle. Studies have shown that 500 ms tetanic contractions can be sustained without fatigue at a rate of 40 contractions per minute in conditioned muscle.9 Since twitch contractions are less fatiguing then tetanic contractions, it may be possible to sustain twitch contractions a higher rate, however, studies have shown that twitch contractions repeated at 2 Hz in conditioned muscle produced fatigue after 116 minutes.2 Clearly, the trade-offs between amplitude and rate of force production, input power, and fatigue will be critical when specifying the motor nerve stimulation patterns.

We expect that the muscle contractions produced as part of the muscle-powered piezoelectric generator will be tolerable to the users. This is based on the experience of spinal cord injured individuals who utilize implanted neuroprostheses for hand function.12 In order to build and maintain muscle bulk and fatigue resistance, these individual’s muscles are exercised through electrical stimulation for eight hours a day. This repetitive stimulation of the paralyzed muscle is usually performed at night while the individual is sleeping and discomfort as a result of the stimulations has not been reported.12

There was good agreement between the simulated and experimental results demonstrating that the software model accurately represents the piezoelectric generator system and can be used to evaluate system performance. The software model electrically represented a piezoelectric generator operating at low frequency, similar to the methods used elsewhere to model piezoelectric generators.4, 6, 8, 13 The software model developed for this study, along with data from the literature, will be used to investigate the major trade-offs of the system and will be used to identify the stimulation patterns that result in maximum output power. In addition, the software model will be used to develop and assess design changes in an effort to improve system performance.

Our results demonstrate that a mechanical device can be used to hold the piezoelectric stack and convert tensile force into a compressive force applied to the stack, without significant mechanical coupling losses. However, strategies for in vivo attachment between the tendon and the mechanical device and between the device and the bone need to be developed further. The sharp corners of the current holder were convenient to machine, but will need to be rounded in future implantable versions. The tendon attachment strategy will likely use artificial tendon. Artificial tendon is a commercially available product (for example, CardioEnergetics, Inc., Cincinnati, OH) that has been used for other purposes. For example, Trumble et al., found that connecting their ventricular assist device to artificial tendon made of polyester fibers and incorporating it into the natural tendon was more stable than connecting the device directly to natural tendon.23 Additionally, it is likely that existing bone attachment strategies developed for orthopedic prosthetics can be used to attach our generator to a bone in close proximity to the tendon. Ideally, the muscle-tendon-generator system will be attached across the length of a single long bone so that no limb movement is produced during electrical stimulation of the muscle. The next step of development towards a tangible implantable generator requires demonstration of closed-loop operation of a prototype system in an ex vivo or in vivo animal model. A prototype system should include a low power consuming stimulator and electrical circuitry which allows closed-loop operation and storage of excess power.

Conclusion

The results of this study provide evidence that a stimulated muscle powered piezoelectric generator system may be feasible for extending the life of the batteries of implanted electronic devices or for allowing periods of FES device use untethered from external power sources. Simulations performed in this study predict that approximately 690 μW of power can be achieved by a muscle powered implanted piezoelectric generator that is 8 cm long and to which peak force pulses of 250 N are applied. This is greater than the necessary input power, conservatively estimated to be 46 μW. These results suggest that this concept has the potential to be an implantable, self-replenishing power source and should be investigated further.