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original signal h(k) and the process is repeated at the next occurrence, ki. This approach works well with signals having short time constants and long delays. The long delays insure satisfying the requirements for enough points between occurrences and the short time constants mean that errors in identification or subtraction tend to die out before the next set of operations. Also, this method, when applied to stable signals, uses the initial part of the signal where the components are largest in contrast to the reverse method that uses the tail of the signal. V. EFFECTS OF ERROR The preceding results have assumed that h(k) is exactly of the form given in (1). In practice this is generally not the case due to the effects of modeling and measurement errors. By use of the pseudo-inverse to solve (8) and by using a search where the error in (13) is minimized rather than made zero, the procedure can be applied to noisy signals. For this case where (8) is not solved exactly, b, and therefore Ki, will depend somewhat on the number of points K + I used. Since the delays ki only take on integer values, their determination should not be affected by noise unless it is fairly large. No general results have been obtained on this problem yet.

VI. CONCLUSIONS In this paper a new approach to the identification of the response of lumped systems with time delays has been developed based on a matrix formulation of Prony's method. Several algorithms and possible variations were discussed which will work equally well with real and complex natural frequencies. A real advantage of this approach is its non-iterative nature. An application is concluded in a finite number of steps and questions of convergence, stability, etc., do not occur. On the other hand, certain conditions were shown to require inversion of ill-conditioned matrices and no real theory of the application to noisy signals has yet been developed. Although continually stated as an identification procedure, there are obvious applications in the analysis of radar, seismic, and biological signals and to time domain synthesis problems. ACKNOWLEDGMENT Our appreciation is extended to Dr. Neil Branston whose research in bioengineering initiated this research.

REFERENCES

[11 [21 [31 [4] [5]

[6] [71

[8] [9] 1101

R. Prony, "Essai Experimentale et Analytique," Journal de l'ecole Polytechnique (Paris), 1, pp. 24-76, 1975. R. N. McDonough, "Representation and Analysis of Signals Part XV. Matched Exponents for the Representation of Signals," Johns Hopkins Univ. EE Dept. Report, April 1963, Catalogued by DDC as AD 411431. R. Fischl, "Optimal lb-Representation of Signals by Exponentials on a Finite Point Set," Proceedings of the Second Annual Houston Conference on Circuits, Systems and Computers, Houston, Texas, April 20, 1970. R. E. Kalman, "Design of a Self-Optimizing Control System," Trans. ASME, vol. 80, pp. 468-478, Feb. 1958. C. S. Burrus, T. W. Parks, and T. B. Watt, "A Digital ParameterIdentification Technique Applied to Biological Signals," IEEE Trans. Bio-Med. Engr., Vol. BME-18, pp. 35-38, Jan. 1971. D. F. Tuttle, Jr., "Network Synthesis for Prescribed Transient Response," D. Sc. Thesis, MIT, 1958. W. C. Yengst, "Approximation to a Specified Time Response," IRE Trans. CT, CT-9, No. 2, pp. 152-162, June 1962. P. E. Mantey, "Convergent Automatic-Synthesis Procedures for Sampled-Data Networks with Feedback," SEL-Tech. Report No. 6773-1, Stanford University, Oct. 1964. C. S. Burrus and T. W. Parks, "Time Domain Design of Recursive Digital Filters," IEEE Trans. Audio and Electroacoustics, vol. AU-18, pp. 137-141, June 1970. D. F. Tuttle, Jr., Part V in Aspects of Network and System

Theory, edited by R. E. Kalman and N. De Claris, Holt, Rinehart and Winston Inc., pp. 591-612, 1971. [11] T. Y. Young, "Epoch Detection-A Method for Resolving Overlapping Signals," Bell System Technical Jour., vol. 44, pp. 401426, March 1965. [12] W. R. Robinson and A. C. Soudack, "A Method for the Identification of Time Delays in Linear Systems," IEEE Trans. Automatic Control. vol. AC-iS, pp. 97-101, Feb. 1970.

An LED-Transistor Photoplethysmograph ALISON L. LEE, ALBERT J. TAHMOUSH, AND J. RICHARD JENNINGS Abstract-A commercial transducer combining a gallium arsenide infrared emitting diode and silicon phototransistor has been adapted for use as a photoelectric plethysmograph. This device is superior to the tungsten lamp-photoconductive cell plethysmograph generally available.

INTRODUCTION Photoelectric plethysmography is a simple non-invasive technique for the study of relative changes in peripheral circulation. This technique requires the placement of a light source and light detector over a vascular bed. Blood volume changes in the vascular bed produce variations in the percentage of incident light reflected to the photodetector. Continuous tracings of blood volume pulses (BVP) and blood volume (BV) are obtained when the photodetector is appropriately connected to a recording system (Fig. 1). The photoelectric plethysmograph generally available contains a minature tungsten lamp and photoconductive cell [ 11, [2] . Several problems occur when this device is used to study peripheral circulation. The major problem is the influence of prior light exposure on the output of the photoconductive cell to standard signals. Storing the plethysmograph in room light results in a DC output significantly different from that of the same plethysmograph stored in darkness [2]. A second problem is the broad spectral output of the tungsten lamp (Fig. 2). Since in vitro light transmittance is independent of blood oxygen content only in the near infrared spectrum 13 1, it appears probable that vascular bed reflectance from a tungsten lamp source will be affected by both changes in peripheral circulation and blood oxygen content. Finally, the tungsten lamp-photoconductive cell plethysmograph is often bulky and requires pressure application to the recording site. GENERAL DESCRIPTION A plethysmograph employing a commercially available LEDphototransistor integrated circuit minimizes the above problems. The basic component is a STRT-850A reflective transducer manufactured by Sensor Technology, Inc.' The transducer combines a gallium arsenide infrared emitting diode (LED) and a silicon N-P-N phototransistor in a compact package measuring 0.25 X 0.18 X 0.19 inches and weighing Manuscript received July 11, 1974. The authors are with the Walter Reed Army Institute of Research, Washington, D.C. 20012. 1Sensor Technology, Inc., 21012 Lassen Street, Chatsworth, Calif. 91311.

249

COMMUNICATIONS

vCC REFLECTING SURFACE OC 2 1K

.25SW Fig. 1. Representative record with the subject performing a Valsalva maneuver as indicated by the arrow. The top tracing is the DC coupled blood volume signal. The bottom tracing is the AC coupled blood volume pulse. Gain on the bottom channel is four times that on the top channel.

OUT PUT

TF Fig. 3. Schematic of transducer with biasing resistors. Vcc is supply voltage; Ic is transistor collector current; and IF is LED input current.

WAVELENGTH, )L

Fig. 2. The relative spectral response for silicon and the radiant spectral distribution of a tungsten lamp and a gallium arsenide LED.

0.4 gms. The radiating surface of the LED and sensing face of the phototransistor are positioned so that only reflected light is detected. The peak spectral emission of the LED is 0.94 ,um with a .707 peak band width of 0.04 ,um (Fig. 2). The silicon phototransistor is sensitive to radiation between 0.4-1.1 Jim. The narrow radiation band of the LED and high phototransistor sensitivity to this band maximizes power efficiency and therefore reduces heat output. The transducer is used as an emitter follower and biased as diagrammed in Fig. 3, with V,, equal to + 4 volts. The resistors in the circuit are placed at the terminal box away from the transducer to minimize heating and bulkiness. With this circuit configuration, 0.25 mW is generated by the LED and the phototransistor output changes in a linear fashion when exposed to Munsell color chips2 of known infrared reflectance. A Beckman dynograph with the 9853A coupler serves as voltage source for the transducer and provides filtering and amplification of the signal. An AC-coupled (TC = I sec) and DC-coupled mode are employed to record BVP and BV signals, respectively. A buffering amplifier is used to apply offset voltages allowing sensitive recording of the DC signal. Careful placement and application of the device is essential in order to prevent movement artifacts and artifacts due to mechanical distortion of the skin. In our application, the photoplethysmograph is centrally placed on the ventral aspect of the distal phalanx. A small strip of stomaseal (3M) is 2Munsell Color Corporation, 2441 N. Calvert Street, Baltimore, Md. 21218.

Fig. 4. Application of plethysmograph to finger. The integrated circuit has been attached to a square of stomaseal surrounding the measurement site. Plethysmograph position is stabilized with

collodion.

applied to the area surrounding the measurement site. The face of the transducer rests directly over the skin with the edges of the transducer attached to the stomaseal. Collodion is applied about the edges of the transducer to prevent any displacement from the stomaseal (Fig. 4). The hand is pronated and placed on a perforated metallic support to minimize large movement artifact and maintain constant position. EXPERIMENTAL TRIALS The LED-transistor plethysmograph has been tested for stability and light history using standard reflectance surfaces. The transducer was placed 3 mm. from a rotating wheel containing four color chips with different known infrared reflectances. During multiple 12 hour test sessions, transducer DC and AC output was found constant. Storing the plethysmograph in the dark or in bright light had no detectable effect on the output. The LED-transistor plethysmograph has been used with human volunteers in a 12 hour study of peripheral circulation. The subjects felt no discomfort or heating from the device, and consistently good records with minimal movement artifact were generally obtained. The sensitivity of the device to standard physiological maneuvers has been demonstrated. Fig. 1 shows a classical vasoconstrictive reaction to a Valsalva maneuver. REFEIkENCES [1] J. Weinman, Photoplethysmography, in A Manual of Psychophysiological Methods, P. H. Venable and 1. Martin, Ed. Amsterdam: North-Holland, 1967, pp. 185-217.

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[21 R. A. Novelly, P. J. Perona, and A. F. Ax, Photoplethysmography: System calibration and light history effects. Psychophys. vol. 10, pp. 67-73, 1973.

[3] K. Kramer, J. 0. Elam, G. A. Saxton, and W. N. Elam. Influence

of oxygen saturation, erythrocyte concentration and optical depth upon the red and near-infrared light transmittance of whole blood. Am. J. Phys., vol. 165, pp. 229-246, 1951.

D.

E.

G.

F

I

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Frequency Stability of an Implantable Pressure Telemetry Capsule GERALD W. TIMM, MEMBER, IEEE, JAMES S. LIST, WILLIAM E. BRADLEY, AND F. BRANTLEY SCOTT

Fig. 1. Structural diagram of pressure telemetry capsule. A. Inlet tubes; B. Coil; C. Electronic components; D. Teflon form; E. Silastic diaphragm; F. Ferrite rod; G. Epoxy potting; H. Chamber exposed to cuff pressure; I. Sealed air chamber.

EXPERIMENTAL PROCEDURE The pressure transducer (Fig. 1) consists of a diaphragm of 0.50 mm thick Dacron reinforced Silastic sheeting, 12.5 mm in diameter, exposed on one side to cuff pressure and on the other side to a sealed air chamber. To the center of the diaphragm is attached a ferrite rod which modulates the inductance of the tuning coil of the oscillator [71 designed to operate at 107 kHz with a 140 microwatt power consumption. The telemetry capsule is activated when an external magnet is brought to within 5 cm of a reed switch connected in series with the battery. The experimental set-up is shown in Fig. 2. Four stages of evaluation were performed in order to determine the effects of simulated implantation on the frequency of the pressure telemetry transmitter. Initially a response curve was taken by measuring the frequency versus pressure at room temperature. The pressure inManuscript received January 18, 1974; revised July 5, 1974, and September 5, 1974. This work was supported in part by the National Institute of General Medical Science under Grant GM 21178. G. W. Timm and J. S. List are with the Department of Neurology, University of Minnesota Hospitals, Minneapolis, Minn. 55455. W. E. Bradley is with the Department of Neurology, University of Minnesota Hospitals, Minneapolis, Minn. 55455, and the Department of Urology, Baylor College of Medicine, Houston, Tex. 77025. F. B. Scott is with the Department of Urology, Baylor College of Medicine, Houston, Tex. 77025.

Transducer

Syringe

Abstract-An implantable pressure telemetry capsule was developed to permit monitoring cuff pressure in an artificial urethral sphincter during chronic conditions. Following implantation, the baseline frequency of the capsule was observed to increase by nearly 2 percent. A series of experiments was then conducted to determine whether this increase was caused by the temperature rise after implant, by fluid migration through the Silastic diaphragm, or by permeation of water vapor through the epoxy encapsulating the electronics. Elevated temperatures accounted for 84.5 percent of the frequency increase, migration through the diaphragm 11.85 percent of the total, and water permeation through the epoxy 3.65 percent

INTRODUCTION Telemetry of pressures from within animals was previously reported [ 1] -[61. When a telemetry capsule was constructed and implanted to monitor cuff pressures in an artificial sphincter system [61, the baseline frequency of the transmitter at a pressure of zero cm H2 0 increased. These experiments, which simulated animal implantation, were conducted to determine the cause of this frequency change.

cilm

. Digital Cou nter

~~~~~~~~~~~~~~I Oscil loscope

Pressure Indicator

Fig. 2. Schematic diagram of experimental apparatus.

side chamber H was varied accordingly by injecting or removing air. The pressure ranged between - 200 and +200 cm H2 0 to include the operating range of an artificial sphincter system [6]. The frequency of the signal from the transmitter was measured at increments of 50 cm H2 0. The pressure was first increased from - 200 to +200 cm H2 0 and then decreased from +200 to -200. The barometric pressure and relative humidity were recorded at the time of each measurement, but with no significant correlation between them and the frequency of the signal being found, these factors were not of concern in subsequent calculations. In the second stage the capsule was placed in a watertight container and submersed in a water bath at 370C. After allowing the capsule to remain in the bath for one hour, a response curve was taken by injecting 370C water into chamber H. The water was removed from the capsule following this measurement and the inside was dried by passing a stream of air through chamber H. The measurement and drying procedures were repeated at irregular intervals until the baseline frequency of the transmitter stabilized. Next, while maintaining the capsule temperature at 370C, response curves were taken by injecting 25% Hypaquel solution, the fluid used in the artificial sphincter [61, into chamber H. Unlike the second stage, the Hypaque solution was not removed between measurements. Again the baseline frequency was allowed to stabilize. Finally, the capsule was removed from the watertight container and immersed in a physiological saline bath. 1

Sodium diatrizoate, Winthrop Laboratories.

An LED-transistor photoplethysmograph.

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, MAY 1975 248 original signal h(k) and the process is repeated at the next occurrence, ki. This approach...
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