USING ACOUSTIC REFLECTOMETRY TO DETERMINE BREATHING TUBE POSITION AND PATENCY

Journal of Sound and Vibration (1995) 188(2), 167–188

USING ACOUSTIC REFLECTOMETRY TO DETERMINE BREATHING TUBE POSITION AND PATENCY J. P. M  G. R. W School of Electrical and Computer Engineering and Hillenbrand Biomedical Engineering Center, Purdue University, West Lafayette, Indiana 47907-1285, U.S.A. (Received 18 March 1994, and in final form 13 October 1994) A new technique to guide and determine the patency of tubes placed within the human body was developed using the principles of time domain acoustic reflectometry. An audible sound pulse is introduced into the proximal end of the tube or catheter and the sonic reflections from the tube lumen and body cavity are analyzed to provide patency and position information, respectively. The information can be used to initially place the tube and monitor its position and patency thereafter. A dedicated instrument was developed for use with breathing tubes, known as endotracheal tubes (ETT), that are necessary for the mechanical ventilation of patients. The incident sound pulse is generated and it is measured along with the resulting reflections in a small wave tube connected to the ETT. When the ETT is properly placed in the trachea below the vocal folds, a characteristic reflection from the airways is measured and the timing between the incident pulse and this reflection is used to determine ETT position or movement. The reflection from the discontinuity between the distal ETT tip and the airway is used to estimate the diameter of the airway at this point. In addition, reflections from the ETT lumen are used to generate a profile of the lumen area over the length of the tube. This information allows reliable differentiation between proper and erroneous tube placement, quantification of movement over time, and provides the location and degree of obstructions within the lumen. 7 1995 Academic Press Limited

1. INTRODUCTION

1.1.    In time domain reflectometry, a system is interrogated with a short duration perturbation and the reflections that arise are measured and interpreted to estimate inhomogeneities. This technique has been employed in a wide variety of areas such as sonar and radar to locate moving targets, electrical transmission lines to detect faults [1], in seismography to survey the composition of layers of underground deposits, and in medical diagnostics such as ultrasound to non-invasively image body structures. Figure 1 depicts an example of time domain reflectometry in which the perturbation is an acoustic pulse generated by a speaker and the measurement is performed by a microphone. The pulse propagates down a wave tube into an object of unknown composition and the resulting reflections that propagate back up the wave tube are measured with the microphone and interpreted to obtain information about the object in question. The timing of the reflections that arise from physical discontinuities in the object can be used to locate these discontinuities if the propagation speed is known. The orientation and amplitude of the reflections can detail the nature of the discontinuities as a function of distance from the microphone. This acoustic technique has been used to estimate the cross-sectional area 167 0022–460X/95/470167+22 $12.00/0

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Figure 1. Overview of time domain acoustic reflectometry.

[2] of both the vocal tract [3] and the airways [4, 5] assuming that both structures act as rigid conduits with constant propagation speeds. 1.2.      The use of tubes and catheters in medical diagnosis and therapy is growing rapidly. These devices are placed in a number of tube-like body cavities such as arteries and veins, the digestive and urinary tracts, and the airways. Frequently, the advancement of catheters to their desired location is performed with no guidance or under X-ray fluoroscopy, and thus the procedure can be complicated by branching pathways or poorly visualized anatomy. Even if properly placed, any subsequent movement of the tube or catheter relative to the patient may not be detected until it produces a deleterious clinical result. Clearly, there is a need for technologies that provide position information in a continuous and non-invasive manner. 1.3.    A breathing or endotracheal tube (ETT) is typically inserted into the mouth and advanced past the vocal folds into the trachea (see Figure 2) to provide mechanical ventilation for patients with respiratory failure or during surgical procedures. Ensuring

Figure 2. Endotracheal intubation.

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Figure 3. Improper placement of a breathing tube: (a) into the esophagus; (b) past the carina into the right bronchus.

that an ETT is correctly positioned and free of obstructions is of major clinical concern. Several scenarios can complicate the proper placement of the ETT, known as endotracheal intubation. Since there are two distinct pathways the ETT can follow when inserted into the vocal tract, the trachea and the esophagus, an ETT can be inadvertently placed in the esophagus as shown in Figure 3(a). As the esophagus is located posterior to the trachea, it is the likely path that a hastily placed ETT will follow. Another possible placement error is the over-advancement (or post-placement movement) of the ETT tip past the bifurcation of the trachea (carina) into the right or left airways (primary bronchi) (Figure 3(b)). Also,

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mucous build-up inside the ETT over extended periods of intubation can in extreme cases completely close off the tube lumen and cease ventilation. Failure to immediately detect misplaced, dislodged, or obstructed tubes is a serious problem with potentially life-threatening consequences. 1.4.    In this study, a new method to guide, place, and monitor the position and patency of tubes within the human body was developed based upon time domain acoustic reflectometry. It is shown for the case of ETT placement that one can quantitatively estimate the geometry of the airways and the relative distance between airway structures and the ETT to determine where the ETT is located and if it moves over time. Each of the possible passageways the ETT can enter (trachea, bronchus, and esophagus) has a distinct geometry, and therefore, a distinct acoustic reflectance that delineates position and movement. ETT patency is ensured by analyzing acoustic reflections arising from obstructions within the tube lumen which determine blockage location and severity. 2. PRINCIPLES OF ACOUSTIC REFLECTOMETRY IN TUBES

Two fundamental pieces of information lie in sound pressure recordings of the reflected waveforms arising from a system: the locations of where structural changes occur and the nature of these changes. Since our use of acoustic reflectometry deals with the interpretation of reflected sound from tube-like structures, it is necessary to understand how sonic reflections arise in tubes. Here, the simplest case of a lossless and rigid tube is considered, followed by a discussion of deviations from this ideal case as a result of the non-rigid and lossy tubes in the body. 2.1.          Whenever a sound wave travelling in a tube encounters a change in acoustic impedance, Z(v), a reflection will occur. Z(v) is a frequency dependent parameter defined as the complex ratio of sound pressure p(v) in dynes/cm2 to volume velocity U(v) in cm3/s [6], or Z(v)=p(v)/U(v),

(1)

where Z(v) is in dynes · s/cm5. For planar wave propagation in a lossless, rigid tube of infinite extent, Z(v) equals the characteristic impedance Zc , which is determined by the propagation medium and the cross-sectional area of the tube, Zc=r0 c/S,

(2)

where r0 is the density of the gas in g/cm3, c is the wave propagation speed in cm/s as determined by the density and stiffness of the medium, and S is the cross-sectional area of the tube in cm2. Note that for wave travel in a medium of constant density and stiffness, the numerator remains constant, and Zc is inversely proportional to S. To highlight this point in terms of reflections, consider the tube depicted in Figure 4 with a decrease in cross-sectional area from S0 to S1 at x=x0 , and a corresponding increase in characteristic impedance from Z0 to Z1 . When the incident sound pressure wave, pi , encounters the boundary at x=x0 , a portion of it is transmitted, pt , and a portion reflected, pr , in the opposite direction. Assuming spatial continuity of pressure and volume velocity at the boundary, then pi+pr=pt

(3)

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Ui−Ur=Ut ,

(4)

and

3

where the U are in cm /s. From equations (1), (3), and (4), a dimensionless reflection coefficient is obtained as the expression R=pr /pi=(Z1−Z0 )/(Z1+Z0 ).

(5)

With the assumption that r0 c is constant throughout the medium, combining equations (2) and (5) yields R=pr /pi=(S0−S1 )/(S0+S1 ).

(6)

Note that if S is changing from larger to smaller, as is the case in Figure 4, the value of R will be positive and therefore the time domain pr will be a scaled version of pi . Alternately, a change of S from smaller to larger will yield a negative R and a corresponding pr that is inverted relative to pi . If values of pi and pr are measured and the initial cross-sectional area S0 is known, then an estimation of S1 can be made by rearranging equation (6) as S1=

0 1

1−R S. 1+R 0

(7)

2.2.         The timing of the reflections that arise from changes in S in a lossless and rigid tube provides longitudinal distance information of where these changes take place. Assuming a constant speed in the propagation medium, the distance d between the microphone and boundary which caused the reflection is given as d=ctd /2,

(8)

where td is the time delay between incident and reflected pulses. Note, the factor of 2 in the denominator takes into account that the round trip path length of the sound pulse is equal to twice the separation distance. 2.3.   , -  The tube-like structures found in the body are not ideal since they are filled with lossy media and their wall impedances are finite and complex. As a result, body structures

Figure 4. Behaviour of a propagating acoustic pulse in a tube containing an abrupt change in cross-sectional area. Top: hypothetical tube with change from S0 to S1 at x0 . Middle: impedance of the tube. Bottom: diagram illustrating an incident pressure wave pi , its reflection pr from the discontinuity, and the transmitted wave pt .

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exhibit responses that can deviate significantly from the ideal case. The lossy media can be characterized by viscous and thermal resistances, while additional losses arise from wall motion as well as radiation of energy into the surrounding structures. The overall effect of these losses is a diminished reflected response over certain frequencies in contrast to the ideal case [7]. The effect of yielding walls on the reflection response can be estimated by incorporating the wall properties in terms of their inherent resistance, inertance, and compliance. The wall soft tissue is represented by the following specific acoustic parameters [8]: a frequency-dependent resistance [dyne · s/cm3 ] of Rw (v)=hn(v)/r 2,

(9)

where h is the wall thickness in cm, n(v) is the wall viscosity in dyne · s/cm2 which grows with the square root of frequency, and r is the tube radius in cm; an inertance of Mw=hrw ,

(10)

where Mw is in dyne · s2/cm3 and where rw is the wall tissue density in g/cm3; and a compliance of Cw=r 2/hY,

(11)

where Cw is in cm3/dyne and where Y is the Young’s modulus in dyne/cm2. A complex specific acoustic radiation impedance zrad (v) (ratio of sound pressure p(v) to particle velocity u(v)) which accounts for the loading effects of the surrounding structures in contact with the outer tube walls can also be included. Because of the difficulty in accurately identifying and characterizing the surrounding structures that give rise to zrad (v), these effects are typically lumped with the Rw , Mw and Cw values to yield an approximate overall wall response prediction. The resulting complex specific acoustic wall impedance zw (v) is zw (v)=

$

%

p(v) 1 =Rw (v)+j vMw− , u(v) vCw

(12)

which contains both resistive (real) and reactive (imaginary) components. The wall resonance fw=

1 2p

X

1 1 = Mw Cw 2pr

X

Y rw

(13)

occurs when the reactance is zero yielding a minimum wall impedance equal to Rw (v). Note that fw is inversely proportional to the lumen radius and the square root of wall density and proportional to the square root of wall stiffness. This wall resonance is not, however, dependent on tube length or wall thickness. At frequencies fw , Re {zw (v)} is small due to the frequency dependent viscosity and Im {zw (v)} is negative, indicative of compliant behavior. At these frequencies the tube wall exhibits an elastic behavior and alters cross-sectional area in response to pressure changes. At frequencies fw , Re {zw (v)} becomes significantly large and Im {zw (v)} is positive, indicative of mass-like behavior. At these high frequencies, the walls appear massive and with increasing f are essentially rigid. Near fw , the wall impedance is small resulting in an increased wall velocity and thus net displacement at the air/wall interface and a decreased lumenal pressure. In addition, a portion of the energy involved in the radial motion of the tube wall is dissipated as a consequence of the wall viscosity. Therefore, the attenuation per unit length of a sound

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pressure wave propagating down a non-rigid tube is minimal at frequencies significantly below and above fw , and maximal at frequencies near fw . 2.4. -  The Ware–Aki algorithm uses a technique that determines the impedance of a medium as a function of travel time from the reflected impulse response [2]. Once the impedance is obtained, the application of equations (2) and (8) yields the cross-sectional area as a function of distance. The algorithm assumes a lossless medium and is of a marching nature—using previously calculated impedances close to the sound source in conjunction with the impulse waveform to calculate subsequent impedances further distances away. Since the algorithm assumes a lossless medium, which is seldom the case in practice, it is important to consider what losses exist in the actual medium to determine if the algorithm will produce accurate results. The overall effect of losses is to cause the estimated impedance to diverge from the actual impedance with increasing distance and therefore reflection arrival time. Another inherent problem of the technique lies in fact that at each impedance discontinuity the amount of transmitted energy is less than the incident energy; this means that for distant structures, the amount of acoustic energy that is actually incident upon and returns from that structure may be relatively small, resulting in a reduced signal-to-noise ratio. For example, for a tube with frequent and sizeable area changes over a small distance, the accuracy of the algorithm over distance would rapidly deteriorate because a large portion of the incident energy will be reflected at each discontinuity, reducing the total transmitted energy, and effectively reducing the signal-to-noise ratio of reflections arising from latter discontinuities. Therefore, it is expected that the technique will yield somewhat accurate values over considerable distances in structures with few losses and few abrupt discontinuities, while yielding increasingly inaccurate values over relatively small distances in lossy or highly variable structures. When the latter case is true, caution needs to be taken when interpreting the results from this technique in a quantitative fashion. 3. ACOUSTIC REFLECTANCE MODEL OF THE AIRWAYS

The airways consist of a complex branching structure of tubes with varying cross-sectional areas, lengths and wall properties. The ends of the largest airway, the trachea, are characterized by the larynx (which contains the vocal folds) cranially and the first bifurcation, known as the carina, caudally. The tracheal wall, comprised of a fibrocartilaginous coat enclosing rings of cartilage in a layer of elastic tissue, provides for a more rigid conduit than the succeeding smaller airways with walls containing mostly smooth muscle. The airways formed by the carina are the right and left primary bronchi, which themselves branch into bronchi of smaller cross-sectional areas and lengths. This branching pattern is repeated until the most distant bronchi are finally reached, terminating into the alveoli, small air-filled sacs where oxygen–carbon dioxide gas exchange takes place. An interesting property of the lungs is that even though the cross-sectional areas of the individual tubes grow smaller with increasing path length from the larynx, the number of tubes due to branching increases in such a manner that the total cross-sectional area of the airways increases with distance until the alveoli are reached [9]. The acoustical properties of the airways are very complex, depending primarily on branching structure, wall properties, and cross-sectional area. It has been hypothesized that over the frequency range 1000–6000 Hz, the acoustical response of the large airways is strongly affected by the total cross-sectional area and relatively less affected by wall

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properties, which leads to the simplified notion that the airways behave in a similar manner to a flanged horn with a low impedance boundary condition at its terminal end [10]. It was expected that the rapidly changing terminal end of this horn would produce an acoustic reflection of inverted phase and significant sound-pressure amplitude. To provide better insight into the quantitative acoustical behavior of the airways, an asymmetric canine airway model with non-rigid walls [8] was simulated in the audible frequency range 100 Hz–10 kHz. The goals of this modelling effort were to ascertain the shape and size of the airway reflections, the locations at which reflections arise, and the effect on the reflected signal of variations in input pulse frequency content. 3.1.    The modelling approach that was taken, an extension of the work by Jackson et al. [8], was used to interpret input acoustic impedance measurements made at the mouth in the canine. Briefly, an asymmetric branching model was simulated that accounts for 47 different branches which are combined using the ‘‘self-consistency’’ hypothesis put forward by Horsfield et al. [11]. The simulation begins at the terminal branch (named the 0th generation) and builds an asymmetric branching airway network by storing in memory the acoustic impedance looking into each generation and recalling these impedances at the higher level generations. At a given generation n, the two parallel daughter impedances are the previously calculated impedances looking into generation n−1 and generation n−H(n), where H(n) is the Horsfield order of generation n. If H(n) is set equal to 1 for all generations n, then the model branching defaults to the symmetric case. The airway walls are represented by estimates of their inherent acoustic inertance, compliance and resistance as a function of generation. In our simulation, the airway wall resistance was assumed to be proportional to the square root of frequency, as has been shown for many biological tissues [12]. Also, an airway length scaling factor in the model was set to 0·80 to account for the size of dog used in our experimental measurements. The input acoustic impedance of the airways Zin (v) was estimated from 100 Hz to 10 000 Hz. The reflection coefficient R(v) was then calculated using equation (5), where Z1 equals Zin (v) and Z0 is the initial characteristic impedance of the airway model, or R(v)=

Zin (v)−r0 c/S0 , Zin (v)+r0 c/S0

(14)

where the initial area S0 was chosen to be equal to the cross-sectional area of the trachea. The reflected impulse response h(t) was determined by taking the real part of the inverse Fourier transform of R(v), or h(t)=Re {F−1{R(v)}}.

(15)

The effect of the input pulse spectral content was investigated by simulating the responses of a trachea intubated with a 15 mm inner diameter (I.D.) ETT with different input sound waveforms. 3.2.   3.2.1. Impulse response Examining the airway model impulse response along with its total cross-sectional area versus distance relationship provides insight into where the airway reflections arise and how these reflections are influenced by wall properties. Figure 5(a) depicts the total cross-sectional area of the model versus distance from the top of the trachea. Note that the area remains constant at 2·3 cm2 for 20 cm (the length of the trachea), then grows rapidly to 5·5 cm2 over

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Figure 5. (a) Total cross-sectional area of the asymmetric airway model versus distance from the top of the trachea and (b) impulse response of the model with rigid walls (solid line) and non-rigid walls (broken line) versus estimated distance d via equation (8).

a relatively short distance of 7 cm, and finally decreases as a result of terminating bronchioles. The asymmetric airway model impulse responses h(t) for rigid and non-rigid walls is depicted in Figure 5(b) with the abscissa converted from delay time to distance d using equation (8) for ease of comparison to Figure 5(a). For the rigid case, a significant inverted reflection arises from the structures between 21 cm and 27 cm owing to the corresponding rapidly growing area (decrease of Z) as seen in Figure 5(a). A smaller positive reflection immediately follows the inverted reflection and corresponds to the decreasing area (increasing Z) of the airways between 27 cm and 32 cm. With the inclusion of non-rigid wall properties in the model, the resulting impulse response appears to be almost identical to the rigid case until approximately 23 cm, ignoring the slight offset between the two cases. This indicates that the effects of wall properties in this region (the larger airways) are relatively small. After 23 cm, the reflection amplitude is smaller, indicative of an increased contribution of energy loss due to the walls. The slight shift in the location of the minimum point and the diminished pulse width for the non-rigid case may indicate that at some point after 23 cm in the smaller airways the energy losses due to the non-rigid walls dominate over the effects of increasing cross-sectional area. 3.2.2. Input frequency content The effects of exciting the model airways with input pulses of differing time duration is summarized in Figure 6(a). Three acoustical pulses of 0·15, 0·24, and 0·36 ms duration were used, each containing equal amounts of energy. The spectral content of each of the respective pulses is shown in Figure 6(b) with −3 dB cut-offs of 3400, 2000 and 1400 Hz, respectively. Figure 6(c) shows the model responses. The inverted reflection of 0·4 ms is

Figure 6. (a) Input sound pressure pulses of 0·15, ——; 0·24, – – –; 0·36 ms, · · · ·; duration; and (b) their corresponding spectral magnitudes. Acoustical responses of (c) canine airway model with ETT; and (d) actual intubated canine airways for the three different input pulses. Note that the large, inverted reflection at 0·4 ms arises from the change in area between the ETT and the trachea.

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Figure 7. Acoustical instrument for determining ETT position.

due to the abrupt area change between the ETT and the trachea while the smaller and broader reflection at 1·7 ms is the airway reflection that was shown in Figure 5(b). Note that the size of this reflection does not significantly change when the high frequency content of the input pulse is increased, indicating that it is primarily the low frequency energy that is reflected from this region where the airway cross-sectional area grows rapidly. The same input pulses were emitted into an intubated and anesthetized canine’s airways through an ETT and the measured response is shown in Figure 6(d). The airway reflection is similar in shape to the one predicted by the model and is likewise relatively unaffected by an increase in the high frequency content of the input pulse. The departure from baseline of the signal between the ETT tip reflection and the airway reflection indicates that the trachea is not of constant cross-sectional area over its length as was assumed in the model. As the pulse duration is decreased, the airway reflection size remains constant while the reflections preceding it increase in size. Evidently, reflections arising from the impedance changes in the larger airways are much more sensitive to higher frequencies, as was expected from the discussion in section 2.3. Therefore, since we were interested in detecting the airway reflection for the purposes of tracking relative movements of the ETT, we chose to excite the system with the low frequency pulse (0·35 ms duration) to minimize the size of the extraneous airway reflections relative to the desired airway reflection. 4. INSTRUMENT DESIGN

4.1.   The instrument that was designed to guide the placement of breathing tubes and determine tube patency based on acoustic reflectometry is depicted in Figure 7. Pulse generation and reflection analysis is performed by a computer (PC based 486 33 MHz) through a menu-driven program developed in C under a windows environment. With the valve in the down position, a digital-to-analog board (Qua Tech WSB-100 with WSB-A12 module) generates an a priori inverse filtered, short duration electrical pulse (see section 4.2.2) which is fed into an audio amplifier (Denon DRA345R) and then converted into a short duration sonic pulse (Q120 dB SPL re 0·0002 mbar) by a miniature speaker (Sony Driver model 150-50-8911) located in the wall of a PVC wave tube 20 cm in length. Two separate incident sound pulses are generated successively, one for airway

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reflection detection purposes (time duration=0·35 ms and spectral energy up to 1400 Hz), and the other for ETT lumen patency estimation (time duration=0·15 ms and spectral energy up to 3400 Hz). For each speaker excitation, two pulses propagating in opposite directions emanate from the speaker. A majority of the left-travelling sonic pulse is absorbed by a foam rubber material with a characteristic impedance closely matched to that of the wave tube (see section 4.2.1). The right travelling pulse propagates down the wave tube, and is recorded as it passes over a microphone (Sony model EMC-155) mounted flush with the inner tube wall, and continues to propagate down and out of the distal end of the ETT. All reflections are recorded by the same microphone as they propagate back up the wave tube and are finally absorbed by the foam rubber termination. The response of the microphone is flat to 23 dB over the 50 Hz–15 kHz frequency range. The analog output of the microphone is digitized by an A/D board (Metrabyte DAS-16) at a sampling rate of 100 ksamples/s (see section 4.2.4), and then stored, analyzed, and displayed on the computer. The instrument uses the inverted airway reflection to track any changes in longitudinal location of the ETT (section 4.2.5). An estimate of the diameter of the airway just beyond the ETT tip is provided by analyzing the reflection arising from the tube tip (section 4.2.5). In addition, a patency profile of the ETT lumen is generated by applying an area–distance algorithm to the reflection signals from inside the ETT (section 4.2.5). 4.2.   To provide a relatively small device with high reliability, the initial concern was to ensure that the device delivered a sonic pulse that yielded a sizeable airway reflection. Design issues addressed included source tube configuration, microphone placement, valve design, and acoustic pulse generation. Signal processing algorithms were also developed to extract information such as changes in ETT longitudinal position, estimated airway dimension just beyond the ETT tip, and an ETT lumen patency profile. 4.2.1. Source tube and microphone configuration Several factors need to be considered when designing a system to effectively deliver a sound pulse into an object and measure the reflected signal. A primary concern is to minimize any extraneous reflections due to the delivery system that may temporally overlap with the desired object reflections measured by the microphone. A delivery system consists of a sound source located at the proximal end of a rigid tube of selected length with a microphone mounted in the wall at a distance far enough from the object to ensure that the incident pulse and the reflected waveforms do not significantly temporally overlap with one another. The minimal distance between the microphone and the object can be determined by utilizing equation (8), where td is the incident pulse duration. To ensure that the measured reflections arising from the object precede all secondary reflections off the speaker diaphragm requires the distance between the speaker and the microphone to be at least as long as the length of the object. Allowing for an incident pulse duration of at most 0·50 ms required that the microphone be located at least 9 cm from the distal end of the source tube. Assuming an airway length of approximately 40 cm and a maximum ETT length of 40 cm, a source tube of at least 89 cm was deemed necessary. Our initial source tube made of rigid Plexiglas of almost a meter in length worked very well but was extremely awkward to maneuver. We felt that a significant reduction of source tube size was absolutely necessary to yield a practical device. One approach was to coil the source tube while ensuring that the internal cross-sectional area of the tube was constant over its length. Since the frequencies employed by the system are low enough to ensure plane wave propagation, there should not be a significant difference

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between a straight tube or a coiled tube. A source tube made of a soft PVC was used and worked very well, although it was still somewhat bulky to work with during actual intubations. The present design, as seen in Figure 7, involved reducing the total length of the source tube by placing foam rubber over the proximal end and embedding the sound source in the wall of the tube. Matching the impedance of the foam rubber material to that of the tube resulted in a source tube that appears to be of infinite length to the left. This impedance matching was performed by measuring the reflected amplitude of an incident sound pulse, as shown in Figure 8, and altering the density of the foam material until the reflected amplitude was close to zero. The speaker was embedded in the wall of the tube so as to minimize the change in cross-sectional area experienced in the tube at the speaker interface. We were unable to completely eliminate this change in cross-sectional area and also, since the speaker diaphragm is not rigid, a small reflection does arise at the speaker–tube interface when probed with an incident sound pulse. However, this reflection is small enough in amplitude that it does not significantly alter the measured airway reflections. 4.2.2. Pulse generation Since the task at hand was to produce reflected signals that were well-defined and detectable in order to reduce the complexity of the signal processing algorithms, a primary objective was to design a sound delivery system that could generate a monophasic pulse of varying duration. We found that simply driving a miniature speaker with a monophasic electrical pulse did not produce a monophasic pressure pulse due to the bandpass frequency characteristics of the speaker. To remedy this problem, an a priori inverse filtering technique was employed [13]. After the sound source was selected and mounted onto the source tube, it was driven with a very short electrical pulse ( the natural period of the source) and the resulting pressure signal, the approximate impulse response, was recorded. This impulse response of the sound source was then used to determine the electrical waveform which, when applied to the speaker, produced a desired monophasic pressure pulse. The output pulse waveform that we used in the instrument was a Hanning function [14] of selectable duration between 0·1 ms and 0·5 ms, with a 0·35 ms pulse used for the majority of measurements.

Figure 8. Normalized reflected response of valve, speaker and foam rubber termination. This measurement was taken by replacing the ETT with a tube 1 m in length containing a speaker and microphone, launching a sound pulse towards the valve and source tube, and measuring the resulting reflections.

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4.2.3. Valve design The task of interfacing a mechanical ventilator with the prototype is complicated for a number of reasons. Simply connecting a ventilator hose in a T or Y configuration to the source tube would result in a composite reflection waveform consisting of reflections arising from both the airways and the hoses. Thus, a valve was designed with two specific goals: first, to isolate the respirator hoses from the source tube during acoustical measurements; and second, to make the valve ‘‘invisible’’ to the acoustic measurement by preserving the cross-sectional area of the source tube across the valve (matching the impedance of the valve to that of the source tube). The present valve configuration, as depicted in Figure 7, consists of a spring-loaded shaft, which when in the normal up position, creates a pathway between the ETT and the ventilator hose and when in the down position, creates a clear pathway between the source tube and the ETT. 4.2.4. Sampling rate It is apparent that decreasing the sampling period of the microphone signal (increasing the sampling rate) increases the potential accuracy of the distance estimate yielded by equation (8). Therefore, given the bandwidth of the pulse and reflected signals, we chose a high sampling rate of 100 kHz (sampling period=10 ms) which yields an inherent distance error to within 20·18 cm which is small enough for breathing tube applications. This error could potentially be reduced with interpolation techniques to determine the location of a peak that actually falls between two successive samples if the need for higher distance accuracy arose. 4.2.5. Tracking algorithms The algorithm to detect and track the inverted airway reflection consists of defining a search window which will always contain this reflection and simply locating the minimum sample within this window. If the absolute amplitude of the sample is less than 5% of the incident pulse, then the reflection is not considered large enough to be an airway reflection and the system does not confirm detection. The time delay td measured between the incident pulse and a confirmed airway reflection spatially corresponds to the distance d between the microphone and the boundary where the airway area grows rapidly. Once the ETT tip is inserted just past the vocal folds and the airway reflection tracking algorithm is activated, any subsequent longitudinal changes in position of the ETT are detected. An estimation of the cross-sectional area just beyond the ETT tip is performed by calculating the dimensionless reflection coefficient at the ETT tip, or Rtip=ptip /pin ,

(16)

where ptip is the amplitude of the reflected sound-pressure pulse arising from the ETT tip and pin is the amplitude of the incident sound-pressure pulse. The cross-sectional area of the airway Sairway is then calculated, with reference to equation (7), as Sairway=

0

1

1−aRtip S , 1+aRtip ETT

(17)

where SETT is the known cross-sectional area of the ETT and the calibration coefficient a which is obtained by inserting the ETT into a tube of known cross-sectional area Stube prior to the intubation and solving for a using a=

0

1

1−Stube /SETT 1 . 1+Stube /SETT Rtip

(18)

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This calibration coefficient is provided to account for any sound energy losses that may occur between the microphone and ETT tip. Examples of such energy losses include the reduction of transmitted sound energy at the ETT connector interface due to reflections and the attenuation resulting from viscous and thermal losses inside the wave tube and ETT. The ETT lumen area profile is estimated using the Ware–Aki algorithm discussed in section 2.4. The input parameters to the algorithm are the reflected impulse response h(t) of the source tube and ETT and the initial cross-sectional area of the source tube. To increase the ability of the algorithm to accurately track abrupt changes in cross-sectional area, a separate input pulse of duration 0·15 ms is used when taking this measurement. The impulse response h(t) is obtained by separating the incident pressure waveform pi (t) and the reflected pressure waveform pr (t) from the microphone signal, and calculating h(t)=F−1

6

7

Pr (v) G(v) , Pi (v)

(19)

where Pr (v)=F{pr (t)} and Pi {v}=F{pi (t)}, and G(v) is a lowpass filter with cut-off frequency identical to the highest frequency in Pi (v) with magnitude above −3 dB. Since the energy of the input signal Pi (v) is within a finite frequency band, it is not possible to recover h(t) at frequencies outside this band. Note that at frequencies above those contained in Pi (v), the denominator becomes very small and the expression becomes very large. The filter serves to eliminate these erroneous values. After h(t) is calculated, the area–distance function S(d ) is then estimated for the source tube and ETT lumen. The system is calibrated before intubation by connecting it to a patent ETT and obtaining the acoustical estimate of Scal (d ). A degree of constriction profile Dconstr (d ) is then calculated for any subsequent estimate of S(d ) as Dconstr (d )=

Scal (d )−S(d ) . Scal (d )

(20)

5. EXPERIMENTAL RESULTS

The instrument was evaluated in four canines who were undergoing surgery for other purposes. Four specific items were investigated: (1) the effects of input pulse duration on the detectability of the airway reflection (see section 3.2.2); (2) the effectiveness of using the airway reflection time delay in determining changes in ETT location; (3) the use of diameter estimation to distinguish between tracheal, and erroneous bronchial or esophageal placement; and (4) the ability to detect ETT obstructions. 5.1.    Figure 9 shows the sound pressure signal recorded during endotracheal intubation at three different tip insertion distances of 21, 25, and 29 cm past the canine eye tooth (used as an anatomical reference point). In addition to the time axis on the bottom of the graph, an acoustically estimated distance axis is provided on the top of the graph. The peak of the incident pressure pulse is referenced as time=0. The positive going reflected pulse located at 0·5 ms is due to the changing area from larger to smaller (1·13 cm2 to 0·79 cm2 ) between the source wave tube and the ETT. The remaining reflections arising from the ETT tip and the growing airway area are similar to those predicted by the airway model depicted in Figure 6(d). As the ETT is advanced 4 cm into the airways, the estimated

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Figure 9. Acoustical measurements at three different ETT insertion distance of (a) 21, (b) 25, and (c) 29 cm (relative to canine tooth) in the trachea versus distance d calculated via equation (8). Note as the ETT is advanced 4 cm in each case, the airway reflection (airway boundary) moves a calculated distance of approximately 4 cm closer to the incident pulse (microphone).

distance d between the microphone and the airway boundary tracks these changes almost exactly. Figure 10 depicts the relationship between the acoustically estimated insertion distance and the measured insertion distance from seven insertions performed on the four dogs. After the ETT tip was advanced past the vocal folds, both the estimated and measured insertion distances were set equal to zero so that the insertion distances of any subsequent advancements of the tube indicated the distance relative to the initial placement. A nearly one-to-one relationship between the measured and estimated insertion distances was

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Figure 10. Acoustically estimated insertion distance d versus measured insertion distance x from data obtained on multiple intubations of four canines. The slope of close to unity (0·99) of the least-squares fit indicate a strong one-to-one relationship between d and x with a correlation coefficient R close to unity (0·995).

observed. Figure 11 is a histogram of the estimated error (estimated distance minus measured distance) for 115 individual distance measurements from the four dogs. A Gaussian distribution curve was fitted to the data with a mean of −0·09 cm and a standard deviation of 0·41 cm. It should be noted that the error includes the inability to manually advance the flexible ETT into the airways a precise distance. 5.2.    Since the device is capable of providing an estimate of airway diameter just past the ETT tip, this feature can be used to determine if the tip is erroneously advanced from the larger diameter trachea into the smaller diameter bronchus. In two of the animals, the carina was visualized using X-ray fluoroscopy and its location relative to the ETT insertion distance was determined by guiding the ETT into one bronchus and then the other bronchus and noting the point at which the tube tip started to follow either bronchial pathway. Figure 12 shows a representative cross-sectional area estimation as the ETT was advanced at 1 cm increments beginning in the trachea and ending past the carina in a bronchus. The

Figure 11. Histogram of the esitmation error (estimated distance d minus measured distance x) over 115 measurements. The fitted Gaussian curve has mean of −0·09 cm and standard deviation of 0·41 cm.

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Figure 12. Acoustically estimated cross-sectional area versus measured insertion distance past the vocal folds. The abrupt change in area between 8 and 9 cm indicates that the ETT tip has moved from the larger trachea to the smaller bronchus.

estimated area in the trachea is consistently larger than that of the ETT and the estimate in the bronchus is consistently smaller than that of the ETT. Also, there is a sharp decrease in area when the ETT is advanced past the carina, as located fluoroscopically. 5.3.   The estimated cross-sectional area versus measured insertion distance from esophageal intubation is shown in Figure 13. It was noted that the consistent and inverted boundary reflection used for tracking longitudinal tube movement in the airways was absent in the esophagus. A comparison of Figures 13 and 12 shows that the estimated cross-sectional area of the collapsible esophagus was consistently less than that of the ETT, a markedly dissimilar finding to that of tracheal intubation. 5.4.     The system’s ability to detect and assess an inter-lumen constriction using the Ware–Aki algorithm is illustrated in Figures 14(a) and (b). Figure 14(a) depicts the acoustically estimated area profile obtained from a source tube (12·5 mm I.D.) connected to an ETT (9 mm I.D.) with and without a 3 cm long constriction of 6 mm I.D. The thin line represents the actual area profile. Figure 14(b) shows the estimated and actual degree of constriction versus distance calculated via equation (20). Note that a degree of constriction equal to one indicates a totally obstructed lumen.

Figure 13. Acoustically estimated cross-sectional area versus measured insertion distance x which is markedly different from case for ETT inserted into the trachea (Figure 12).

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Figure 14. Detection of ETT inter-lumen constriction. (a) Acoustically estimated cross-sectional area (via Ware–Aki algorithm) versus distance d for source tube connected to ETT; – – –, without constriction, —— with constriction; (——) actual source tube and ETT area profile is plotted for comparison. (b) ——, Acoustically estimated degree of constriction; ——, actual degree of constriction versus distance d as measured in source tube and ETT. Degree of constriction is calculated from equation (20) and ranges from 0 (no constriction) to 1 (total obstruction).

6. DISCUSSION AND CONCLUSIONS

Correctly positioning catheters or tubes within the body and assessing lumen patency is an important clinical issue that can be addressed by using acoustic reflectometry. This technology can provide a real-time estimate of the structures that lie within the tube lumen and beyond the tip and thereby detect lumen obstructions or tube misplacement. It also offers the capability to continuously monitor tube position for correctness in cases where the body cavity contains a landmark boundary from which a sizeable reflection arises, as is the case for the airways. A prior knowledge of the characteristics of the cavity in which the catheter will be placed, such as tube geometry, branching structure, wall effects, and propagation medium, is essential for choosing an appropriate frequency range of excitation. To ensure planar wave propagation, a knowledge of the tube geometry and propagation velocity is also required. This is accomplished by selecting frequencies with wavelengths that are greater

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than at least twice the largest diameter tube. Taking an adult trachea diameter of a=0·8 cm and a propagation speed c=354 m/s in air at 37°C yields an upper frequency limit of 11 000 Hz. Of course, if the propagation medium were a fluid such as blood (c=1570 m/s), the upper frequency limit would be much higher than for air. Non-rigid tube walls were shown to significantly attenuate propagating pressure waves at frequencies close to the wall resonant frequency. For example, a tube of radius r=0·8 cm correspond of soft tissue (r=1·06 g/cm3 [15] and Y=0·392×106 dyne/cm2 [8]) has a wall resonant frequency fw,s=119 Hz (equation (15)) while a tube composed of cartilage (r=1·14 g/cm3 [15] and Y=39·2×106 dyne/cm2 [16]) has a wall resonant frequency fw,c=1190 Hz. Since the trachea is composed of both soft tissue and cartilage, the wall resonant frequency or frequencies will likely occur somewhere between fw,s and fw,c . For a smaller tube of radius r=0·05 cm composed mainly of soft tissue, as is found in the smaller bronchi, fw,s=1904 Hz. Therefore, to a rough approximation, one can expect the large airways, of which there are relatively few, to attenuate low frequencies (Q1000 Hz) to some extent, and the smaller airways which are relatively numerous, to attenuate higher frequencies (q1000 Hz) appreciably. In the past, various researchers have attempted to use the Ware–Aki algorithm to extract quantitative area information from complex structures such as the vocal tract and airways through acoustic means. In the airways, the algorithm’s additive error is a major shortcoming when trying to obtain quantitative data beyond the trachea. The time domain approach taken in this study circumvents this limitation by exploiting the pulse response from these more caudal airways to guide breathing tubes. The appearance of the sizeable airway reflection was used to indicate that the ETT was in the trachea and then to track any longitudinal movements of the ETT. During tracheal intubation, the airway reflection was present and the use of the delay time between the incident pulse and the reflected airway pulse to track changes in ETT position via equation (8) proved to be very reliable as shown in Figures 10 and 11. When the ETT was placed in the esophagus, the inverted airway reflection was absent and the system was unable to track movements of the ETT. The reflection arising from the ETT tip was used to estimate the cross-sectional area in which the tube is placed via equation (7). The potential uses for this estimate are threefold: (1) it provides the user with a means by which to ascertain if the ETT is of appropriate diameter relative to the trachea; (2) a significant reduction in the estimated area from that measured in the trachea indicates that the ETT tip has entered the narrower bronchus; and (3) a clear indication of an erroneous esophageal intubation is provided when, immediately upon ETT insertion, the estimated area is less than that of the ETT due to the collapsed esophageal walls around the tube tip. Another important feature of this device is the ability to monitor ETT lumen patency. Any obstruction of the ETT lumen such as mucous deposition or kinking of the ETT will produce acoustic reflections due to the decrease in lumen area. An area profile (Figure 14(a)) as well as a degree of constriction profile (Figure 14(b)) can be generated from these reflections. It is noteworthy that the Ware–Aki technique is unable to accurately estimate the degree of constriction immediatley after the constriction, a weakness of this general technique that was discussed in section 2.4. Besides the potentially pathological effects that an obstructed ETT might have, it will also render the position tracking features ineffective by significantly reducing the amount of acoustic energy transmitted to and received from the airways. For this reason, it is imperative that an obstructed tube is cleared to permit unimpeded ventilation and sound propagation. Several methods exist to reduce the source tube to an arbitrarily short length. One such method investigated by Marshall [17] uses a signal processing approach to remove the

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multiple reflections from the speaker diaphragm which may obscure the desired object reflections. Another method reported by Louis et al. [18] uses a two microphone system and signal processing to extract the desired reflected response. The strength and limitations of these two techniques, as compared to using a nearly-matched termination impedance on the wave tube, need to be evaluated for each particular application. The acoustical guidance system developed in this study offers the potential to become an inexpensive and reliable clinical device. The system is non-invasive since it emits audible sounds at maximum sound pressure levels Q120 dB SPL (re 0·0002 mbar) which are comparable to those found within the lower vocal tract during normal speech [19]. It consists of relatively simple and inexpensive components. The accuracy of distance estimation measured in the trachea to 20·8 cm over the entire insertion range is adequate to be useful in adults as well as infants. For prospective clinical use, once the ETT tip is placed through the vocal folds, the system can confirm that the tube is in the trachea and not in the esophagus through the detection of the airway reflection and an estimated cross-sectional airway area that is greater than that of the ETT. The tube can then be advanced a desired distance past the vocal cords as guided by the system. A safety zone could potentially be defined, where any inadvertent movements of the ETT outside this zone will be indicated through an alarm. If a safety zone breach does occur, the system could assist the user in guiding the ETT back to its original, correct position. In addition, any condition that reduces lumen patency such as excessive build-up of mucous or a kinked tube will be detected by the system, at which time corrective measures can be taken.

ACKNOWLEDGMENTS

This work was supported in part by a grant from the Showalter Trust, a National Science Foundation Young Investigator Award to George R. Wodicka (BCS-9257488), and the Trask Fund of the Purdue Research Foundation.

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