Cmnput.Bid. Med. Vol. 27. No.6,pp.493-505, 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0010-4825/97 $17.00+0.00
PII: soo10-4825(97)ooo22-I
MICROPROCESSOR BASED SPATIAL TENS (TRANSCUTANEOUS ELECTRIC NERVE STIMULATOR) DESIGNED WITH WAVEFORM OPTIMALITY FOR CLINICAL EVALUATION IN A PAIN STUDY D. W. REPPERCER,* C. C. Ho,? P. AUKUTHOTA,~ C. A. PHILLIPS,$ D. C. JOHNSON* and S. R. CoLLtNst * Armstrong Laboratory, Wright Patterson AFB, OH 45433, U.S.A. t VA Medical Center, Dayton, OH 45428, U.S.A. $ Wright State University, Dayton, OH 45435, U.S.A. (Received
21 June
1996; revised
18 April
1997)
Abstract-A microprocessor based TENS device is developed which utilizes a spatial procedure in the administration of electrical fields to actively interfere with pain signals reaching the brain. This unusual design also has the advantage of requiring the frequency characteristics of the electrical waveform produced to be optimally tuned to the mechanical impedance properties of the skin/tissue. Hence a much more efficient procedure for the transfer of electrical energy from the TENS device to the human tissue is provided. Data are presented involving patients from the Dayton VA Medical Center in Ohio, USA being tested with this new microprocessor system compared to the treatment obtained via a traditional stimulator, 0 1997 Elsevier Science Ltd. Microprocessor biomedical device Optimal electrical power transfer
Sensory aid
Pain therapy
1. INTRODUCTION With the continuing advance of microprocessor technology, alternative methods to administer electrical fields to human tissue are provided. There appears to be great utility in these innovations, e.g., in the area of pain management. In the United States, one of the primary problems affecting the VA (Department of Veterans Affairs) medical community is the treatment of pain from various etiologies. As a crude measure of the immensity of this problem, the VA medical system treats about 10% of the population of the United States, 28 million people. It is reported that about 30-40% of these patients may experience pain from such sources as surgery, back pain related to military or other accidents, arthritis, phantom pain from amputation, and a host of other causes. The traditional TENS devices in the marketplace to&y experience success with only about 50% of the patient population. This leaves over 5 million patients in the VA medical system having to deal with this affliction by other means. The alternatives to TENS therapy, surgery or prescription drugs, are not the primary choices of treatment for the patients that we have run in our studies. In particular, with respect to narcotic drugs, patients dislike them because they do not wish to compromise, to even the smallest degree, any other activities of daily living through the utilization of prescription drugs. Alternatively, the percent of success with surgery is not high enough for patients to feel comfortable in accepting the risks associated with this procedure. This study had the original [l] intention of investigating whether a wireless TENS unit could effectively replace the traditional units in clinical use today. After performing over 125 clinical trials with a host of etiologies (back problems associated with accidents, arthritis, post surgery pain, post polio syndrome, and from other sources), it became clear that a modified approach to pain therapy may be in order to help improve and administer this type of rehabilitation to a large number of veterans. The microprocessor device described herein allows many new and unusual waveforms to be generated as contrasted to 493
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the traditional TENS which generally only manipulates temporal patterns of electrical signals. The wireless device developed from the study [1] also has some unique characteristics [2,3] which have been shown to be effective for patients who may not respond with great success to the traditional TENS. The property of “non-isolation”, discovered in [2,3], with the wireless device has added a new dimension in the administration of pain therapy. As described in the sequel, this “non-isolation” property allows more efficient utilization of battery life, provides more randomness in the waveform (to reduce accommodation to pain), and seems to alter and sometimes increase extinction characteristics of the electrical stimulator (extinction being defined as the time when pain returns after the stimulator is turned off) for certain patients. Space precludes an extensive discussion on studies related to pain management. Some of the well-known references in this area include the book by Melzack and Wall [4], and other sources consulted by the authors [5-81 which describe the familiar concepts regarding pain reduction (gate theory, endorphin theory, and possibly local biochemical interactions) as well as a host of other issues. In the interests of brevity, it can be summarized as the state of the art that the sources and control of pain are still not widely understood and its treatment needs much additional research. The three modalities of pain control [9] include pharmacological, neurosurgical, and sensory. The sensory control (TENS related) of pain has had the longest history, the least serious consequences, and may be the most effective method for the long-term management of chronic pain. The electrical approach (TENS or electrical analgesia) was used by the ancients via electric fish as Aristotle, Pliny and Plutarch wrote of its numbing effects and Scribonius described this technique to deal with pain from gout and of headache [9, lo]. Other methodologies have also been considered for pain management. For example, massage, manipulation, hot poultices, liniments, and ice packs have had a long history [4,9]. Acupuncture, moxibustion, scarification, and cauterization have also been applied. In order to design an electronic stimulator device to generate electrical fields that have some optimality property which may work to alleviate pain, an analogous method will be borrowed from studies in electrical circuit theory and power systems. THE
PRINCIPLE
OF OPTIMALITY IN ELECTRICAL DESIGN
WAVEFORM
Studies on the optimal transfer of power in electrical systems lend themselves to an interesting concept for the contrivance of a TENS device based on some of these fundamental principles. It is known from empirical studies that the impedance of the human skin/tissue has certain low pass filter properties [11-141 and the technique of designing such systems may assist in the construction of a TENS device. The objective is to find a method to better devise a stimulator’s electrical properties so that it is more efficient in transferring energy from the battery source to the skin/tissue material and then to the nerves. This may also have some benefit related to the management of pain. To illustrate the philosophical method for the design of interest considered here, it is important to study an analogous problem involving the optimal synthesis of an electrical circuit for maximum power transfer. Design of an electrical circuit for maximum power transfer
Figure 1 illustrates an electrical circuit in which the source of power is on the left-hand side of the diagram. The voltage supply V, describes the power that is available, but the source, itself, has the constraint that it has an internal electrical impedance Z, denoted as: Z,=R,+jX,
(1)
where j indicates the complex number d( - 1), R, is a pure resistance, and X, is the reactance of the source of the power. On the right-hand side of the diagram in Fig. 1 is the load or the destination where the power is to be delivered. The load impedance Z, satisfies
Microprocessor
based spatial TENS
Source
495
I Load Fig. 1.
the condition: Z,=R,+jX,
(2)
In this problem formulation, the load impedance (human skin/tissue) is fixed and we, as the designers, have the option to change only the source device (the TENS system or V,, R,, and X,) to deliver the maximum power to the load. We are free to manipulate the values of these variables. To find the maximum power transfer characteristics, the electric current in the circuit is first calculated via: I= v,/(z,+z,) (3) where the quantities Z, and Z, are complex numbers. The magnitude of the current can be expressed: IZl=VsI.\/(R,+R,)2+(Xs+X,)2 and the real power delivered to the load is given by: Power At Load=P,=12RL
(4) (5)
This can be expressed:
PL=[V~IRLI[(RS+RL)~+(XL+XS)~I As shown in the Appendix, the maximum following two conditions are met:
(6)
power transfer to the load is achieved when the xg= -x,
(7)
and: Rf=O
(8) or Rf>O is to be made as small as possible. The superscript * indicates optimal value. The maximum power that can ever be transferred to the load is specified by: P:= V;IRL (9) Since the load is fixed for this application (the skin/tissue impedance), the best design that can be achieved will be contingent on a judicious design of the TENS device which is predicated on the source variables R, and X,. It is noted that the optimal conditions (7) and (8) when applied to equations (1) and (2) yield a complex conjugate reactance of these impedances but the real parts differ. Also, it is unreasonable to presume the source impedance R,=O, but the smaller this variable, the better. Thus the circuit elements have little flexibility except for what has been shown. The next step would be to modify the frequency content of the stimulator signal to be more in tune with the skin/tissue material. Hence the load variable will be now characterized to help in the design of the TENS system. The load variable Z, In order to better design the TENS device (and its corresponding electrical waveform properties), it is important first to be able to characterize the impedance properties of the
496
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D.W
REPPERGER etal.
0 = Prepared
-90
4 i.oo.z (0.5) 2f! d- 0.10 . B G
A = Unprepared -75 a~ -60
3 b-45
0.01 -
10 100 1K IOK IOOKlM Frequency (Hz)
IO 100 1K IOK IOOKIM Freww (Hz)
Fig. 2.
load to which the waveform will be applied. Prior studies [ll, 121 have demonstrated the low pass filter nature of the skin/tissue electrical impedance and we characterize the load via the following transfer function representation: H(s)=K,/(l+s/(Y)
P-3
which is a first order, low pass filter representation of the electrical impedance of the skin/ tissue combination. cyis approximately 27r (1020) rad/sec for the patients and equipment used in our study (Fig. 2). The transfer function H(s) represents a ratio between an input variable (voltage applied) and the measured output variable (current) [ll] which characterizes a complex impedance function. The waveform design Traditional thinking in TENS development has designed a typical waveform of the type displayed in Fig. 3. This high frequency signal produces a strong stimulation sensation but may not be efficient in the transfer of the energy from the power source of the TENS device to the skin/tissue. Figure 4 illustrates the waveform design for the device described in this paper. It has the traditional charge balanced property (the area under the curve for one cycle equals zero) to prevent charge accumulation and subsequent burning, but the signal is much lower in frequency than the traditional waveform displayed in Fig. 3. With a Fourier analysis of the waveform of the TENS system reported in this paper, the component frequencies were kept at least a factor of 10 below the half power point of the load characteristic in Fig. 2. This allows a significantly larger percentage of the source power and energy to be delivered to the skin/tissue and hopefully may promote a more efficient manner of delivering the electric fields to actively interfere with the pain signals. The
Electric Current
Time 0
Fig. 3.
Axis
Microprocessor based spatial TENS
(charge
491
BALANCED)
Tl t-
T, - 30N set
Fig. 4.
experimental paradigm is now described and investigates conventional devices used in the marketplace. SUBJECTS
AND
METHODS
Subjects Over 125 clinical trials have been conducted involving 40 subjects recruited from the Dayton VA Medical Center. The age levels ranged from 37 years to 76 years. One female veteran subject was run and the remainder of the patients were male veterans. The sources of pain included such etiologies as back pain due to military or other accidents, arthritis, pain due to surgery, post polio syndrome, and from other sources. The early stages of the study did not provide reimbursement for participation. After funds were obtained for patient reimbursement ($5 per visit and 28 cents a mile for travel), a regular pool of patients was maintained. The data reported herein involved 8 patients who were involved with at least 4-5 days of testing with both the traditional TENS and the wireless device. Development of the wireless TENS There were three stages of development of the wireless device described in [2,3]. Figure 5 illustrates the gradual evolution of preliminary prototypes with the last prototype used with subjects appearing on the far left as indicated. It is slightly bigger than a US 50 cent piece and has a battery source as illustrated. The first prototype was tested on about 20 patients initially and had limited success due to the level of output power achieved. It was then decided that the real element of success, as far as pain management was concerned, was due to waveform generation, electrode placement, and spatial generation of the electric fields (to be described in the sequel). This gave rise to a special waveform function generator used to simulate a host of special waveforms that might help the patient. The waveform generator was found, in certain cases, to provide pain relief to patients when the traditional TENS would fail. The latter investigations were then focused on which etiologies may be helped by the spatial and time patterns of the electrical signals produced by the wireless TENS. A comparison between these two devices is now presented. The traditional
TENS
In clinical use today, the traditional TENS has found wide acceptance with at least 50% of the patients who require pain therapy. It has the following capabilities in the generation of electric waveforms for the mitigation of pain: (1) The waveforms can be changed in a time sense by varying amplitude, frequency, and
498
D. W. REPPERGER
ef al.
Fig. 5.
pulse width. It also has one or more burst modes, which helps reduce accommodation to the stimulator. The burst mode provides a changing signal (in time) which “fools” the brain into accommodating to the stimulator. After a while, however, a large percentage of patients have to increase the amplitude of the device because the pain returns even with the stimulator on. The wireless TENS is now described to compare it to the traditional TENS unit. The wireless TENS The motivation for building the wireless device was to eliminate the long, entangling wires which over 90% of the patients we interviewed, preferred to do without. These long wires cause disruption during application of the traditional TENS; they reduce its reliability, increase the waste of electric power, and can sometimes short and interfere with other activities of daily living. The new (wireless) TENS has the following properties. Properties of the wireless TENS in [2, 31 (1) This device has all the same time-varying properties as the traditional TENS including changing waveform amplitude, frequency, and pulse width. It has an equivalent burst mode to reduce accommodation. It has no wires, except a connection between the battery source and the stimulator which can essentially be mounted on the electrodes (if 4 or more are used, cf. Fig. 6(a-b) for its use in a 4-electrode situation). It is noted that there must always exist a path between the battery source and the electrode; however, if the battery can be made proximal to the electrode, then the wire problems can be substantially mitigated and the device can be considered “wireless” in terms of not having long, entangling wires. (2) The wireless TENS has a spatially varying pattern (cf. Fig. 7(b)) which allows both time and space variations of the electric signals that are generated to interfere with the pain. In Fig. 7(b) it is seen, for a 4-electrode pattern, that the electric fields can transverse from electrodes 1 to 3 (as the for traditional TENS in Fig. 7(a)) and can also transverse from
Microprocessor
based spatial TENS
499
electrodes 1 to 4 (which will never happen with the traditional TENS). In addition, the directions of the electric fields can be reversed both in time and space (thus the directions of the arrows can be reversed in Fig. 7(b)), which adds another dimension of randomness to this device. The advantage of this design is to fight the ability of the brain to accommodate to the stimulator (which occurs with the traditional TENS device). The manner in which a spatial dimension is added with this device can be described as follows (using a property called “non-isolation”). The “non-isolation
” property
of the wireless
TENS
In Fig. 7(a), for the traditional TENS having the “isolation property”, the path of the electric fields between the electrodes follows two isolated channels. This keeps a small amount of area affected by the system isolated between these two channels. This isolation is caused by the fact that traditional devices have separate electric grounds for each (a)
1
(b)
Fig. 6.
500
D. W. REPFZRGER
er 01.
channel. By contrast, Fig. 7(b) illustrates the electric field pattern for the wireless TENS device. In the wireless device, a ground is common and shared between all four electrodes. This allows the paths of the electric fields to be controlled by a microprocessor element at the chip on the electrode. Comparing the areas affected by the traditional TENS versus the wireless version in Fig. 7(a-b), one can see that using the “non-isolation” property can almost double the area affected. In addition, the randomness nature of the device does not only have to depend on time, but also can depend on spatial characteristics as well. Additional
advantages
of the non-isolation
property of the wireless
device
(a) It is noted in Fig. 7(a-b) that twice the area can be affected for the same electric power input. This makes the new device more efficient (in an electric power sense) per unit area. (b) Both accommodation and extinction are also affected. Accommodation is reduced because it becomes more difficult for the brain to recognize the pattern of stimulation. The new TENS is far more random (varying in space and time) versus the traditional TENS having only time variations. As mentioned previously, the waveform generation procedure being tuned to the load variable adds to the effectiveness of this device. These points discussed so far represent a few of the reasons for the design of the
(isolated
channels
- no common electrical
ground) -AreaAl
Electrodes , (;,;,
3
---_
-cc
--______---Current
,, I 2,
--
ch 2
\
---_
f-
Ana A’
-\\
-0’
Effective
Current
4
./’
Flow Area
(b) (non-isolated
channels
- with a common
electrical
ground) AteaAl /
A2
\ Fig. 7.
AreaAl
Microprocessor based spatial TENS
501
prototype discussed herein. Further details are available, to the interested reader, in [2,3]. A more detailed description of the experimental paradigm is given next. The experimental paradigm
To investigate various issues of sensitivity and efficacy of the new wireless TENS developed in this study as compared to the traditional TENS device, the procedure to test each patient during a data run was as follows: (i) After the patient arrived, the first item on the agenda was the completion of the “McGill-Melzack” Pain Questionnaire. Five parts were completed including determining the location of the pain (on the day of testing), describing the pain verbally, indicating how the pain changes with time, numerically evaluting how strong the pain was, and an estimation on an analog scale of how the pain feels on this day of testing was obtained. (ii) The second item on the daily agenda was the selection of a pain site where the 4 electrodes could be tested and another area where a control group of measurements could be taken (non-pain site). Of course, the pain site and non-pain site had to have similar (symmetrical body location) anatomical structure to prevent any confounding due to different skin condition measurements. (iii) An experiment was then conducted on just noticeable differences (JNDs) at both the pain site and the non-pain site. Both the traditional and wireless TENS were presented in a random manner and the subject was blind to which stimulator was in use. The following four measurements were obtained (chronologically) at the pain site for both units: (a) The JND when the stimulator was first perceived to be on. (b) The stimulator level when 50% or more pain was mitigated. (For some patients this number could not be achieved, but a lower percentage was acceptable if it could be quantified.) (c) The maximum level of stimulation that could be tolerated was recorded. (d) The stimulator was then returned to zero and the patient noted when the stimulator was not perceived any longer. Typically this JND level was higher than the first JND when the stimulator was first perceived as being on. Electric power measurements were recorded for both stimulators during all four of the above measurements. Measurements of inter-electrode impedances were obtained prior to stimulation and after stimulation was finished. At the JND levels, volts (AC RMS) were recorded and, from a cathode ray oscilloscope, the maximum amplitude of the waveform was determined. Measurements of power could then be calculated. As mentioned previously, the pain site and non-pain site were randomized in their presentation. At the non-pain site, only 3 JND type of measurements were recorded: (e) The JND when the stimulator was first felt. (f) The maximum tolerated stimulator level. (g) After the maximum level was recorded, the device was returned to zero and the measurement of when the stimulator was not felt was noted. As with the pain site, this number was typically much higher than the measurements obtained in (e). This completed the sensitivity or JND portion of the measurement testing. The next item on the schedule was the evaluation of which spatial and temporal patterns worked best for that patient (on that particular day). It included the following steps: (h) The waveform function generator was connected to the four electrodes and the following modes were possible to be studied: (I) Crossover or no crossover. This allows the subject the choice between spatially varying electric fields versus the isolated channels typical of the traditional TENS in use today. The independent variable in this case was exclusively a spatially varying profile variable. (II) Modulation or non-modulation-This choice allowed the patient the option of a burst-type mode versus a consistent time pattern (the frequency of the source would change). The independent variable in this case was exclusively a time variable. (III) The subject could then select the pulse width to be small or large. This indicated the necessary charge intensity of the electric signal.
502
D. W. REPPERGER
t-f al.
Table 1. Percentage of responses characterized by etiology Crossover On-Off Modulation On-Off Pulse Width Large-Small
On-88%
OR6796
on-75%
On-100%
On-55%
On478
on-50%
On-100%
Small-678
Small-67%
Small-75%
Small-100%
Since there were two possibilities in (I), (II), and (III), there were actualy 23=8 combinations. After this evaluation was completed, the patient was then subjected to 20 minutes of stimulation of the pattern he selected for that day. On the next visit, the following two questions were asked: (1) When did the pain return after the stimulator was turned off? (extinction question) (2) Was there any adaptation necessary during the 20 minutes? (The pain would then return and it would be required to increase the voltage amplitude of the TENS device.) Since this was a preliminary study to demonstrate the efficacy of the wireless device to replicate the traditional TENS in performance, the results reported at this time mainly focused on demonstrating how a wireless device can compare to the traditional TENS in the marketplace today. RESULTS We report results involving four etiologies of pain and responses to three questions: prefer crossover on or off (this refers to spatial distribution being preferred over the normal time variations of a traditional TENS); prefer modulation on or off (this refers to spatial and temporal randomization); and prefer pulse width short or long (this refers to the duration of the leading pulse). These results are illustrated in Table 1 for the four etiologies abbreviated as follows: Back=back related problems due to accidents, Surg=pain due to surgery (e.g. cancer), Arth=pain due to arthritis, and Polio=pain due to post polio syndrome. The results are displayed in Table 1 with the dominant response indicated. Please note that there were a different number of subjects in each group, so the overall averages are not the mean of the averages in each row. The overall results across all runs were: crossover was preferred by 81% of all patients tested, the modulation was preferred to be on by 56% of the trials, and the pulse width was preferred to be small by 68% of the patients tested. The results of the JND tests are also of interest. These data were obtained across 8 subjects with a total of 29 runs included. Figure 8 illustrates a plot of the minimum detectable stimulus level for the experimental TENSJND2 versus this quantity for the traditional TENS-JNDl. The slope of the regression line is about unity indicating little difference. Figure 9 compares the voltage level during equivalent pain relief. The slope of 60 50 40 30 20 10
0
5
IO
I5
20 JNDI
(volts)
Fig. 8.
23
30
35
40
Microprocessor Comparison
based
of Stimulus Commercial
spatial
TENS
Voltage Levels vs Experimental
80r
503
Providing TENS
* .
Pain
Relief
.
-.
.
.
.
. . .
.
.
I IO
0
I
I
I
I
I
I
20
30
40
50
60
70
Stimulus
Level
(ma)
Commercial
TENS
Fig. 9.
the line is slightly less than one indicating that the wireless TENS provides the same pain relief for slightly smaller voltage levels. Figure 10 compares the two TENS devices at equivalent pain relief conditions for their amplitude versus the skin/tissue impedance prior to stimulation. In this diagram, the wireless TENS has a small advantage (consistent with Fig. 9) of having equivalent pain relief at a slightly lower voltage for a wide range of skin resistant values. DISCUSSION This study has focused on the development of a wireless TENS device to produce equivalent or greater pain reduction as compared to the traditional TENS used in the clinical environment. One unique aspect of the design was the tuning of the frequency characteristics of the stimulator waveform to be more akin to the load electrical impedance (skin/tissue). Secondly, the development of the wireless device altered the manner in which the electric fields were produced. This introduction of a “non-isolation” property, in conjunction with lower frequency exciting electric signals, seems to indicate that there may be better methods to approach the application of electric analgesia to patients in the VA medical system. Amplitude of Pain Relief Stimulus vs Transcutaneous Resistance for Commercial vs Experimental TENS Units 60.0 0
$ 70.0 .. :! 60.0 -- . 4 50.0 1 “oo = 40.0 .. 8
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0
0
8 ’
8
0
0
E 30.0 .. 8 P8 s 3 g
B 20*o 10.0
..
.
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00.0 4 0.00
100.00
200.00 Resistance
300.00 ( k ohms Fig.
400.00 1
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CONCLUSION Wireless TENS devices have great potential to study pain management problems. They provide new alternatives to this therapy and may be able to attack that 50% of the present VA patient population which have not experienced success with traditional TENS devices. It is felt that the reason why only 50% success has been seen is because the traditional devices offer limited options. With the modem technology that now exists in developing these systems, it is hypothesized that a better job of mitigating pain can be accomplished since many more options are available to treat patients in a more efficient manner. Acknowledgement-This work was supported by a joint VA-DOD Phase I merit Review Study, “Design and Clinical Application of A Wireless TENS (Transcutaneous Electric Nerve Stimulator) in Pain Management,” B 93-620AP.
REFERENCES 1. C. C. Ho, D. W. Repperger, C. A. Phillips, and P. Aukuthota, Design and Clinical Application of A Wireless TENS (Transcutaneous Electric Nerve Stimulator) in Pain Management, VA-DOD Phase I merit review proposal, B93-620AP 2. D. W. Repperger, D. C. Johnson, and Charles C. Ho, A Wireless TENS (Transcutaneous Electric Nerve Stimulator), US Government Invention, Disclosure Number 23,201. 3. D. W. Repperger, D. C. Johnson and Charles C. Ho, The Anti-Accommodation Nonisolation Transcutaneous Electric Nerve Stimulator, US Government Invention Application, June, 1995. 4. R. Melzack and F?Wall, The Challenge of Pain, Penguin Books, NY (1988). 5. A. L. Nachemson, Low Back Pain-Its Etiology and Treatment, Clin. Me& 78, 18 (1971). 6. M. J. Ebershould, E. R. Laws, and H. H. Stonnington, Transcutaneous Electric Stimulation for Treatment of Chronic Pain: A Preliminary Report. Surg. Neural. 4,96-99 (1975). 7. F? A. McGrath, Pain in Children (Nature, Assessment and Treatment), New York: The Guilford Press, (1990). 8. F?Prithvi Raj, Practical Management of Pain, St. Louis: Mosby Year Book, 1992, pp. 1025-1037. 9. R. A. Stemback, TENS: A Pain Management Alremative, TENS Clinical Monograph, Medtronix, Medical Education Division, San Diego, (1984). 10. K. Kane and A. Taub, A History of Local Electric Analgesia, Pain 1, 125- 138 (1975). 1I. D. C. Johnson and D. W. Reppetger, Skin Impedance Implications of TENS Function and the Development of an Improved Stimulation Waveform, Proceedings of the 1995 IEEE International Conference on Engineering, Medicine, and Biology, September, 1995, pp. 137-139. 12. A. M. Sagi-Dolev, D. Pmchi and R. H. Nathan, Three-Dimensional Current Density Distribution Under Surface Stimulation Electrodes, Medical and Biological Engineering and Computing 95 33(3), 403-408 (1995). 13. J. Resell, J. Colominas, P. Riu, R. Pallas-Amey and J. G. Webster, Skin Impedance from 1 Hz to I MHz, IEEE Transactions on Biomedical Engineering, vol. BME-35.649-65 1 (1988). 14. D. K. Swanson and J. G. Webster, A Model For Skin Electrode Impedance, in H. A. Miller and D. C. Harrison (Eds), Biomedical Elecrrode Technology, Academic Press, New York, 117- 128 (1974).
APPENDIX To show that the electric power is maximized be written:
to the load, the expression for power can
~L=~~s12r~~~~~~s+~L~2+~~~+~~~2 II
(11)
and the objective is to maximize PL with respect to the independent variables R, and X, with the quantities V,, R, , and R, presumed to be fixed. It is noted that PL is always positive since RL is positive and the remaining quantities are squares of real variables. The two necessary conditions for optimality require:
ap,iax,=o
(12)
aP,laR,=o
(13)
and which yields the two candidate solutions: x*--x s-
L
(14)
and R$=-R,
(1%
Microprocessor
based spatial TENS
505
To verify if these candidate values are optimal with respect to maximizing PL, we check the value of the second variation of P, assessed at the candidate values. It is easily shown that: #P,l13~X,<0
for XQ= -XL
(16)
a2P,ld2R,<0
for R$= - R,
(17)
and thus, the conditions (14, 15) are sufficient, as well as necessary, for a maximum of P,. However R,>O and a negative R, cannot be achieved and results in nonfinite power. The R, condition is changed such that as R, 30, P, in equation (11) is maximized. It is noted that X, as specified in equation (14) still retains its optimal&y property. About the Author-DANIEL W. REPPERGER received his B.S.E.E. and M.S.E.E. degrees from Rensselaer Polfiechnic Institute, Troy, N.Y. and the Ph.D. in Electrical Engineering from Purdue University. He is a member of Eta Kappa Nu, Tau Beta Pi, and Sigma Xi. From 1973-1974, he was a National Research Council Postdoctoral Fellow, then joining the federal government at Wright Patterson Air Force Base in Ohio to the present time. He has authored or co-authored over 40 journal publications, I4 technical reports, and over 150 conference papers. The author of 10 patents and 20 Air Force Inventions, he has applied this technology to disabled people in the health care sector in joint programs involving the US Air Force and the Department of Veterans Affairs. In 1985, he ran experiments on two space shuttle missions. Dr. Repperger serves as an Associate Editor of the IEEE Transacrions on Conrroi Sysrems Technology, Control Engineering Practice, and Intelligent and Fuzzy Systems. In 1996 he was elected Fellow of the IEEE (Institute of Electrical and Electronic Engineers). About the Author--&.mLEs C. Ho, MD, Ph.D., is the Assistant Chief of the Rehabilitation Medicine Service of the Dayton VA Medical Center, Dayton, Ohio. He received his B.S. degree in Chemistry from Cheng Kung University, Tainan, Taiwan, his MS. in Biochemistry from the Ohio State University and his Ph.D. in Pharmacology/Physiology from Wayne State University, Detroit, Michigan. He received the M.D. degree from University of Juarez, Juarez, Mexico and is Board Certified by the American Academy of Pain Management and the American Board of Physical Medicine and Rehabilitation. Dr. Ho serves on the Editorial Advisory Board of American Journal of Pain Management and reviewer for Federal Practitioner and Journal of Rehabilitation. He also serves on the Research, and Awards and Prizes Committees, American Congress of Rehabilitation Medicine and has performed a Postdoctoral Fellowship in 1980 for the National Institute of Drug Abuse. Dr. Ho has over 40 journal publications and has received numerous grants related to rehabilitation research in the VA Medical System. About the Author-PAN1 AKUTHOTA received his MD from Osmania Medical College, Hyderabad, India in 1968, his Diplomat from the American Board of Physical Medicine and Rehabilitation in 1981, and his Diplomat from the American Board of Electrodiagnostic Medicine in 1991. His area of specialties include rehabilitation in amputee, stroke, musculosk~letal disorder, and spinal cord injury &luding electrodiagnosis. His nresent position is Chief of Rehabilitation Medicine Service, Dayton VA Medical Center inl)ayton, O&o and Hlso serves as Medical Director, Department of PM&R,-Good Samaritan Hospital, Dayton, Ohio and Medical Director, Geriatric Rehabilitation, Maria Joseph Center, Dayton, Ohio. Dr. Aukuthota serves as an Assistant Clinical Professor in PM&R, Wright State University, in Dayton, Ohio and has been a Staff Physiatrist at Long Island YAMC, in Northport, New York. He has served on a number of research projects involving the VA Medical Center including Functional Electrical Stimulation, and a Carpal Tunnel Syndrome study involving electrodiagnosis in Pre-and Post-operative Set up. Ahout the AU~~O~-CHANDLER A. PHILLIPS received his A.B., Biological Sciences from Stanford University, his MD from the University of Southern California, Los Angeles in 1969, and the A.B. in Classical Languages from Wright State University, Dayton, Ohio in 1982. His current position is Professor of Biomedical Engineering and Human Factors Engineering in the Department of Biomedical and Human Factors Engineering at Wright State University. Dr. Phillips has over 250 publications including six United States patents and three books. He is on the Editorial Advisory Boards for the journals: Automedica, Journal of Biomechanics, Journal of Clinical Engineering, and Prosthetics and Orrhorics Engineering. He also reviews for numerous other journals and grant organizations. He was elected Fellow of the IEEE and Fellow (Honorary). American Academy of Orthopedic and Neurological Surgeons. About the Author-DAVID C. JOHNSON received his B.S.E.E. and M.S.E.E. from The University of New Hampshire, New Hampshire. After graduation, he joined the U.S. Air Force as a first lieutenant and served a three year tour at Wright-Patterson Air Force Base in Dayton, Ohio. During this three year tour, he published about 5 papers and made 4 patent applications which are still under review. His specialty areas include the development of a Wireless TENS device and other biomedical devices, which have emphasis on the sensing and measurement of biological signals. After the tour with the US Air Force, Mr. Johnson formed a company, Johnson Kinetic Systems Corporation, which continues to work on the development of biomedical devices, sensors, and diagnostic systems.