Acoustic Measurements of Bubbles in Biological Tissue

Transcription

1 Cavitation: Turbo-machinery & Medica Appications WIMRC FORUM 8 Warwick University, UK, 7 th -9th Juy 8 Acoustic Measurements of Bubbes in Bioogica Tissue Georges L. Chahine*, DYNAFLOW, INC. Miche Tanguay, DYNAFLOW, INC. Gregory Loraine, DYNAFLOW, INC. * gchahine@dynafow-inc.com ABSTRACT An acoustic based instrument, the ABS ACOUSTIC BUBBLE SPECTROMETER, was investigated for the detection and quantification of bubbes in bioogica media. These incude viscoeastic media (bood), materias of varying density (bone in tissue), non-homogenous distribution of bubbes (intravenous bubby fow), and bubbes migrating in tissue (decompression sickness, DCS). The performance of the ABS was demonstrated in a series of aboratory experiments. Vaidation of the code was performed using a viscoeastic poymer soution, Poyox, in which the bubbe size distribution and void fraction were determined by ABS measurements and with image anaysis of high speed videos. These tests showed that the accuracy of the ABS was not significanty affected by viscoeasticity for bubbes smaer than microns. The ABS detection and measurement of non-homogenous bubbe distributions was demonstrated using a bubby fow through a simuated vein surrounded by tissue. The scatter of acoustic signas due to bones in the acoustic pathway was aso investigated. These in-vitro experiments were done using meat (beef) as a tissue simuant. Decompression experiments were done using beef meat which was hed underwater at high pressure (9.9 atm.) then rapidy decompressed. Bubbe size distributions and void fraction cacuations in these experiments were then vaidated using image anaysis of high speed video. In addition, preiminary experiments were performed with the US Navy Medica Research Center, demonstrating the utiity of the modified ABS system in detecting the evoution of bubbes in swine undergoing decompression sickness (DCS). These resuts indicate that the ABS may be used to detect and quantify the evoution of bubbes in-vivo and aid in the monitoring of DCS. INTRODUCTION This paper describes a study conducted to deveop a nove technique and instrument for non-invasive in vivo detection and characterization of bubbes in bioogica fuids and tissues/organs. The detection of bubbes in the human body has a number of important appications in medica research and cinica practice incuding study of decompression sickness (DCS), monitoring of hyperbaric treatment, and detection of emboi [-7]. The acoustic-based approach investigated here is based on our previous work concerned with the measurement of bubbe distributions in iquids [8-]. This method consists of emitting and receiving acoustic bursts at different frequencies and determining the sound speed and attenuation of the waves as functions of frequency. Tiny bubbes that form in the tissue and the body iquids after decompression act as sma acoustic osciators. These osciators have natura frequencies that depend on the bubbe sizes and the ambient pressure. The response of the osciators to an externa excitation varies with bubbe size and the frequency of the excitation, and causes dispersion and attenuation of the sound waves in the medium. In order to appy the ABS ACOUSTIC BUBBLE SPECTROMETER (ABS) technique of bubbe size distribution measurement to tissues or biofuids containing gas bubbes, the appicabiity of the mode and software for non-newtonian rheoogica properties [-5] as we as to compex geometries was investigated. The technique was tested in the aboratory using viscoeastic fuids, ges and meats, and the resuts were compared to those obtained from microphotography. Since the instrument was originay designed for the detection of bubbes for engineering appications such as in conduits and containers, this research focused on assessing the accuracy of the ABS in a bioogica environment. The studies were divided into four sections: viscoeastic media, soft tissue, wave scattering from hard tissue and preiminary in vivo test. The advantage of acoustic monitoring is that even at very sma concentrations gas bubbes have a arge impact on the overa compressibiity of the medium. This is in contrast to scattering-based approaches (such as Dopper utrasound) where the scattering signature of a bubbe is difficut to distinguish from that of a soid scatterer [-]. This approach computes bubbe size density distribution based on the acoustic transmission over a broad frequency spectrum unike current Dopper utrasound systems. ABS BACKGROUND The ABS ACOUSTIC BUBBLE SPECTROMETER system empoys a pair of acoustic transducers. One transducer emits controed sound bursts into the iquid whie the second hydrophone senses the transmitted sound waves after they have traversed the bubbe/iquid mixture. The presence of bubbes modifies both the phase speed and the ampitude of the sound waves. The time of fight between the two transducers can be obtained from the time ag between the emitted and received signa and provides the sound speed, whie the ampitude decay provides the attenuation. The detais of the modification depend on the properties of the iquid, on the size, number, and

2 distribution of the bubbes as we as on the frequency of the sound wave. By utiizing a set of discrete frequencies and the mathematica modes deveoped in [8-], information about the corresponding range of bubbe sizes can be obtained. Determination of the bubbe distribution requires soution of an inverse probem. In such a probem, the input (emitted signa) and output (received signa) are known, whie the characteristics of the system (here, the medium properties) that produce the resuting output are sought. The probem is mathematicay i-posed, i.e. the bubbe distributions that are obtained from the measured output signas are very sensitive to changes in these measurements. In addition, noise in the system introduces a eve of uncertainty in the measured inputs and outputs. Knowing the characteristics of the emitted and received sound waves, the bubbe distribution in the iquid is obtained using an inverse methods deveoped in [8]. Figure. Sketch of ABS setup for bubbe measurements. Bubbe Dynamics in Viscoeastic Media For a singe spherica bubbe osciating in a Newtonian iquid with pressure fied p(t), the dynamic equation describing forced radia osciations in a sighty compressibe Newtonian iquid is given by [6-7]): R R R R d R RR R pb p 4 () C c c c dt R R where pb is the pressure inside the bubbe and,, and the iquid density, viscosity and the sound speed respectivey. σ is the surface tension. The bubbe pressure is a function of the vapor pressure, the amount of non-condensabe gas inside the bubbe and the temperature fied inside the bubbe. It is important to note that irreversibe heat transfer during bubbe osciation is one of the primary mechanisms for energy dissipation. Assuming that the gas pressure is approximatey uniform, the rate of change of the pressure can be written as: c are T p g K pg R, R r rr () where K is the therma conductivity, is the ratio c / c of the gas specific heats at constant pressure and voume respectivey, and the tota bubbe pressure is pb pg pv. () The temperature in the gas can be obtained by [8]: T r T T pg K T pg K r. t p r (4) r c c r r r g g p g p p v For sma perturbations about the bubbe equiibrium size, this equation can be simpified to: T p g K T r y, y,, (5) t gcp gcp R y y y R which can be soved in the frequency domain to provide: p g R p g gc pr i gc pr i T r, - sinh y / sinh, (6) gcp r gcp K K where is the frequency. In order to compute the rate of change of the gas pressure, we can write the temperature gradient at the bubbe wa as: T p g R gcpi R gcpi coth, (7) r R r R gc p K K and the pressure fuctuations, p g, can be reated to the radius fuctuations, R, by the expression [8]: T i pg K i pg R, R r rr p g R with, p R g K,. R gcp i i coth i The above reationship between the pressure and the bubbe radius can be introduced in the inearized equation for the bubbe motion (Equation ()): i R R R RR p g R 4 i. p c R R R (9) Assuming that the Mach number of the bubbe wa motion R / C R / C is much ess than unity, the bubbe motion can be represented by the foowing approximate expression: i R R R R O C RR pg R 4 i. p C R R R () The above expression can be cast in the form of a second order harmonic osciator: p ib o R, R o pg R b. R R C In order to address bioogica media of viscoeastic nature such as tissue [], the mathematica mode for the description of a two-phase medium was modified to account for inearized viscoeasticity. The modified Rayeigh-Pesset mode was generaized for an arbitrary fuid (viscous, eastic, viscoeastic) [9]. If we assume that the viscoeastic effects are imited to a region near the surface of the bubbe where compressibe effects are negigibe, the resuting equation can be written as: R R RR R C C () R R d pb p dr pb p, C R r R C dt R where r is the radia distance to the bubbe center and is the radia stress. In the iterature, a standard mode for the viscoeastic nature of bood is the Carreau-Yasuda fit [-]: pg, R R (8) ()

3 o ( n) / a a ( S ), o Pa s, Pa s, () a., n.68,.86 s. From this mode, the effective viscosity of the bood changes between 4cp and cp. However, this form is not readiy appicabe to a inearized formuation and ony represents the viscous component of the stress tensor. Instead, by using a three-parameter inear Odroyd mode or the Jeffreys mode [4-5, 4-6] mode for inear viscoeasticity, we were abe to appropriatey account for the changes in the bubbes natura frequency and damping factor. The three-parameter Odroyd mode can be written as: S S, (4) t t where the shear rate in the radia direction is defined as: ur S rr. (5) r The dependency of on the radia position can be found from (4) and the veocity fied of the iquid around a spherica bubbe (assuming that it is effectivey incompressibe in this region). The strain rate in the radia direction can be written as: ur R R R R S rr. (6) r r r r For sma perturbations about the bubbe equiibrium radius, the stress term can be expressed in the frequency domain as: R R i 4i i. (7) r Consequenty the integrated stress term of Equation () can be written in the inearized bubbe dynamics mode as: i R R i R RR p g R 4 i p, C R R i R (8) where is the iquid viscosity at ow frequency. It is important to note that this inear viscoeastic mode exhibits shear thinning effects (reduction in viscous stress at high shear rate) with the transition between the ow and high frequency viscosity occurring at a frequency near f ~ ½ πλ. In the transition region, the stress term has a non-zero imaginary component that reates to the eastic nature of the fuid (that is generates stress in phase with the radia dispacement instead of in phase with the radia veocity). Casting the resut of Equation (8) into the form of a damped second order osciator, we can express the natura frequency and damping factor as a function of bubbe size and the forcing frequency: p g 4 o, R R R (9) pg R b. R R C In order to assess the impact of viscoeasticity on the mode, the natura frequency and damping factor from Equation (9) were computed for a viscoeastic mode. For this cacuation, the properties of bood were based on fitting the mode of Equation (4) to the Carreau-Yasuda correation of Equation () and resuted in the vaues shown beow: cp, sec, sec, 6 () 6 kg/m, C 584 m/s. Using the above vaues, the bood becomes a purey viscous fuid near an osciating frequency of khz. Under these conditions, the maximum deviation of the vaue of the natura bubbe frequency is % when compared against the viscosity of water. Moreover, if we base a computations on a fixed vaue of viscosity equa to the high frequency imit, the potentia error in the frequency is ess than 9%. Since the natura frequency is the main parameter in determining the bubbe size, we can expect a shift of the order of % of the bubbe size if we erroneousy assume that the medium is water. Simiary the damping factor exhibits a correction of ess than % due to viscoeasticity. The infuence of the damping factor is primariy in term of the popuation density of bubbes (a other factors being equa, twice the bubbe density resuts in neary twice the damping factor) thus considering the bood media as water coud resut at most in a % error in computing the quantity of bubbes (i.e. % error in the void fraction). With respect to typica ABS operations, these errors are very sma considering that the investigated bubbe sizes range from 5 to 5 microns and the bubbe popuation varies by over four orders of magnitude. To further iustrate the impact of the difference between bood and water, the sound speed and attenuation for given bubbe density distribution (Gaussian, centered at a radius of microns) were cacuated using the viscoeastic behavior of bood and then fed to the ABS inverse probem sover. The resuts shown in Figure iustrate the difference in the computed bubbe distribution if the viscoeastic nature of bood was ignored and the medium was treated as pure water. The errors in the mean bubbe radius and the magnitude of the density refect the corresponding error estimated above. Bubbe density distribution (m -4 ).E+ E+ 8E+ 6E+ 4E+ E+ 7% deviation Visco-eastic inverse probem Water inverse probem.4% deviation Bubbe radius (m) Figure. Comparison of inverse probem soution in a viscoeastic media with and without viscoeastic correction. ABS Vaidation Experiments in Poyox The ABS data was compared against optica measurements in water and poyethyene oxide poymer (Poyox WSR-, average moecuar weight 4 x 6 ) soutions of 5 mg/l and 5, mg/l. The viscosities of these soutions were measured to be.,.4 and 9.8 cp for water, Poyox 5 mg/l, and 5, mg/l, respectivey. In comparison, the range of bood viscosity

4 is 4 to cp depending on the shear rate. Bubbes were generated using a muti-wire eectroysis grid. The video data was coected using a high speed video imaging system with frame rates up to 8, frames/sec. The images were anayzed using the Matab Image Processing Toobox. Each frame was saved as a jpeg image and the sequence was then processed by Matab where the background was subtracted and threshoded, the outine of individua objects was traced, and continuous regions were fied soid. An equivaent radius for each object was computed based on its shaded area. There was reativey good agreement between the ABS and image anaysis regardess of the viscoeastic properties of the fuid as iustrated in Figure which shows a comparison between the ABS and image anaysis resuts for the most viscous conditions (5 mg/l Poyox). Based on these resuts and theoretica anaysis, we concuded that the viscoeasticity of the media does not significanty impact the accuracy of the ABS for bubbes smaer than microns. Bubbe density distribution (m -4 ) 4 Image anaysis ABS Acoustic Bubbe Spectrometer Bubbe radius (m) Figure. Bubbe density distribution of 5 mg/l Poyox, using ABS and image anaysis. Sound Propagation in Gas Saturated Tissues In order to assess the impact of the medium inhomogeneities (i.e. non-uniform bubbe distribution and/or non-uniform tissue properties), a numerica mode was impemented to represent the propagation of acoustic waves in an arbitrary two-phase medium. A continuum medium approach was used to mode propagation of pressure waves in tissues containing gas bubbes [-]. Foowing this approach, the foowing main assumptions were considered: The medium consists of two phases: compressibe bubbes and a sighty compressibe iquid phase (tissue); The acoustic waveength is much arger than the bubbe size and the tissue sma scae inhomogeneities (ces, capiary vesses, etc.), so that the medium can be considered as ocay acousticay homogeneous; The characteristic time of bubbe growth/dissoution due to gas diffusion is much arger than the characteristic period of the acoustic waves imposed. In addition, since we are interested in prevention, i.e. detection prior to the bubbe void fraction α becoming significant, we assumed that α is much smaer than one. The effects of bubbe coaescence/fragmentation were negected and bubbes were approximated by spheres. In the code mutipe bubbes with different equiibrium conditions can be modeed. The void fraction can be cacuated as the sum over the bubbe size distribution N for each equiibrium size: 4 x, t Ri x, t Ni x, t. () i Foowing the assumption of ow void fraction, the effective conservation equation for mass and momentum of the two-phase medium can be written in the form: u, t () u uu p O, t where p, ρ, and u are the medium pressure, density, and veocity respectivey. The right-hand side of the momentum conservation equation incudes terms proportiona to the void fraction which are assumed to be negigiby sma for the present computations. Given this simpification, the void fraction does not appear expicity in Equation (). Instead, the couping between the phases is manifested through the equation of state for the bubby medium. For ow void fractions, the pressure in the bubbe aden tissue is approximatey that of the iquid-tissue phase. The non-inear behavior of the tissue is represented here using an equation of state that expresses the pressure in terms of the inear and quadratic changes in density. This formuation is consistent with the modeing of utrasonic wave propagation and data regarding the constants for different types of tissue is readiy avaiabe [7-9]. The non-inear equation of state for the two-phase media can be written as: B p p c, A (), where the B/A parameter is a standard non-inearity coefficient found in the iterature. The subscript refers to undisturbed parameters for the tissue. It is important to note that in the mode described above, a viscous stresses as we as a anisotropic eastic stresses have been negected. This effectivey prevents the formation and propagation of shear waves and focuses on capturing the acoustic propagation ony. Additionay, based on the sma ampitudes associated with acoustic propagation, the dispacement of the interface between different tissue-types is assumed to be negigibe. Sound propagation modeing in the forearm In order to study scattering effects due to differences in tissue properties and bones, a mode of a human forearm was studied. The forearm was seected since the geometry is simiar to that of a pig foreimb which was tested during preiminary anima experiments at NMRC. Since the precise modeing of the interface between various tissues is beyond the scope of this research, a simpified approach was adopted where the domain is a singe materia with spatiay varying properties (i.e. initia density, sound speed, B/A). Since the materia is assumed to exhibit negigibe dispacement during the course of the simuation, these properties are considered fixed with respect to the computationa grid. In order to input the materia properties of the various tissues, a rectanguar matrix is read from fie with 4

5 a materia indicator index. An image from Gray s anatomy [] was used for the cross-section of the forearm. Figure 4 shows a grey map with each tissue identified with a different intensity vaue and a rectanguar section added to represent the receiving hydrophone of the ABS. The materia properties of the piezo ceramics were used. The arrow at the bottom of the image indicates the emitting boundary. Foowing the dimensions of the actua hydrophones (red box in Figure 4), the emitting portion of the boundary is inch wide for the D cacuations and x inch for the D cacuations. Athough the receiving piezo-ceramic is shown to have some thickness, ony the pressure at the contact surface with the skin (the red ine in Figure 4) was used to determine the measured signa. The properties of the various tissues used are isted in Tabe. Figure 4: Forearm cross-section indicating different tissue types. The eft and right images show hydrophone configurations studied here. Materia Density Sound speed (g/cc) (m/s) B/A Grey eve Air.. White Skin Dark grey Musce/marrow Medium grey Cortica bone Back Trabecuar bone.8. Light grey Hydrophone Darkest grey Tabe : Materia properties used in forearm simuations. The two-phase medium is assumed to be at rest initiay. The acoustic signas are generated at the skin. The generated signa had a duration of 5 cyces at a given nomina frequency. The outer domain composed of air has a non-refective boundary condition at the edge of the domain. The non-refective boundary condition is based on a oca decomposition into characteristic waves. Considering the mass and momentum conservation in vector form: u v w u uu p uv uw, (4) v vu vv p vw w wu wv ww p t x y z we can decompose the fux vector into a matrix times the state vector. Let us consider the x-fux first: u uu p c u u u vu uv v u v wu uw w u w u w v u c u c u u. uc v v u c c c v cu w w u c c c w (5) Foowing the decomposition of the above matrix into eft and right eigenvectors, the governing equation can be written as: w u w v u u v u v u c v w u c w uc u c c c c c cu c u c c t x c c (6) w v w v uv uw. uc c c vv p vw cu c c wv ww p y z In order expoit the characteristic propagation, we assume that the matrix of eft eigenvector is approximatey constant in the vicinity of the boundary (both spatiay and temporay). This aows for the insertion of the matrix into the derivatives and to recast the state variabe into eft and right propagating waves: w v u L, uc c c v cu c c w u w v w u v uv uw Lt L x uc u c c c vv p vw cu u c. c c wv ww p y z (7) If we further assume that the right-hand side of the above equation is approximatey zero (i.e. wave with norma incidence to the boundary), then the non-refective boundary condition can be formuated as foows for the right boundary: L x u u u u u u L, x u u u w u u u u v u uu p u uc c c uc x vu cu uc c c wu. (8) The above expression reates the spatia derivatives of the characteristic vector to the finite difference derivative of the fux vector whie considering the outgoing waves ony and assuming no inbound wave propagation. From this expression for the 5

6 derivative, we rewrite the fux gradient in terms of the finite difference of the fux variabe: u u u u c u c v v w w u u c u c u L, x v v u c w w u c w v u c c c c u c c c u c u c c v u u c u v c u u u c u v w u c u u u c c u c vc w c u u u u uu p, x v u wu Received pressure (Pa) u uu p vu wu x (9) u uu p x vu. u u wu u Time (ms) Figure 6: Pressure measured at the receiving hydrophone. It is important to note that athough the above expression is not exact since the veocity is not constant as a function of space and time, it ony introduces an error of the order of the Mach number (u/c) and is therefore very robust. The main weakness of this approach is with respect to waves incident at some shaow ange. For such cases, the right hand side of Equation (6) is no onger negigibe. Consequenty, the decomposition presented here is not fuy representative of the true characteristics and resuts in a progressive deterioration of the non-refective properties. The spatia derivatives for this study were obtained using a compact high-order finite difference scheme where the derivatives at a given ocation are aso a function of the neighbouring derivatives. The scheme used in this study is 6th order accurate and can be written as: ' 4 i i' i' i i i i. 9 x 9 4 x No bubbes -6 Void fraction -5 Void fraction Figure 7: Pressure contours for simuation of acoustic propagation of 5 cyces at 5 khz in a human forearm popuated with m radius bubbes in the musce tissue. () No bubbes -6 Void fraction -5 Void fraction Received pressure (Pa) To obtain the derivative of a variabe, a tri-diagona matrix must be soved for each grid ine (vertica and horizonta) in the domain. The derivative obtained from the boundary condition coses this probem. Once the spatia derivatives of the fuxes are cacuated, the time derivatives of the state vector are integrated using a 4th order Runge-Kutta integration Time (ms) Figure 8: Pressure measured at receiving hydrophone for second configuration. Figure 5: Pressure contours from the simuation of the acoustic propagation of 5 cyces at 5 khz in a human forearm popuated with microns radius bubbes in the musce tissue. The D mode described above was aso extended to D (see Figure 9). Since the height of the emitter in the mode was roughy one quarter of the distance between the hydrophones, three dimensiona effects were minima as seen in Figure. 6

7 By normaizing the received ampitude with bone by the reference ampitude, much in the same way as the damping due to bubbe attenuation is cacuated by the ABS, V A cwater og bone A flgap reference, () we can pot an effective damping due to the presence of the bone and is shown in Figure for different positions. Data was coected with cm and cm gaps between the hydrophones. Aso shown in Figure, is the damping due to the bone but through meat rather than through water. As can be seen in Figure, the more centra the ocation of the bone, the arger the attenuation. The attenuation was higher at Position foowed by Position or 4. In addition, the degree of attenuation decreases as the gap separating the hydrophones increases (soid ines and dashed ines in Figure ). Figure 9: Snapshot of acoustic simuation of D wave propagation in human arm mode for 5 cyce forcing at khz..6 D mode D mode Received pressure (Pa) Figure : Comparison of the damping due to scattering of a bone. The damping is cacuated reative to the signa strength without the bone present time (ms) Figure : Comparison of received pressure between D and D numerica mode for signas emitted at khz. Scattering Anaysis in Presence of Bone The D simuations (Figure 5 to Figure 8) indicated that the presence of bones in the acoustic pathway woud attenuate the signas. These resuts were confirmed by comparing experimentay signas with and without a sma bone (diameter ~.7 cm) present. Two cases were considered: one with the bone submerged in water and one with a bone inserted between two sabs of meat (beef). As shown in Figure, the received signa is ceary atered by the presence of the bone insert. The inset in Figure iustrates the different bone ocations that were tested. In Position the bone was directy in between the two hydrophones. In Position the bone was sti between the hydrophones but was off-center, and in Position 4 the pathway was ony partiay obstructed. In addition to the acoustic measurements with the bone, a reference measurement was done with no bone present. The experimenta set up was modified so that the acoustic waves propagated through meat, a tissue simuant, rather than water. Signas were coected through cm of beef with and without the bone present. The bone was ocated near the edge of the transducer (position of Figure ). As can be seen in Figure and Figure, the bone affected both the sound speed and the attenuation reative to meat ony, as was predicted by the numerica simuations. M eat and bone M eat ony 8 kh z forcing M eat and bone M eat ony kh z forcing.5.5 Received signa (V). Received signa (V) Time (ms) Time (ms) Figure : Comparison of signa with and without bone insert for 8 and khz forcing. 7

8 V U Frequency (khz) Frequency (khz) Figure : Sound speed ratio and damping of bone insert. No bubbes are present in this case. The impact of an acoustic scatterer such as bone is of keen interest to the operation of the ABS. The software impicity assumes that the acoustic path is a straight ine between the emitter and receiver. Based on preiminary resuts such as Figure, we can anticipate that the scattering wi introduce a frequency dependence on the effective acoustic path. For norma ABS operation both reference (no bubbe) and test (with bubbes) measurements woud be conducted with the bone present. The main assumption woud be that any impact of the bone on the effective acoustic pathway woud not be affected by the presence of bubbes. Therefore, the presence of the bone woud not impact the measurement of the bubbe popuation as ong as its ocation and that of the hydrophone are fixed. Preiminary tests were conducted where bubbes were injected in a vesse phantom inside the meat (simiar to experiments presented beow). ABS measurements were compared with and without a bone insert and against optica measurements inside the tube. In Figure 4, we can note that the bubbe density distribution determined by the ABS matched cosey with optica measurements over the range of vaidity of each approach (see Figure 4a). Aso shown are the resuts from the same experiment with a bone insert next to the vesse phantom (see Figure 4b). The bone insert did have an impact on the abiity of the ABS to capture the presence of bubbes between -µm but did not seem to impact measurements outside this range. This suggests that the ABS coud be operated cose to bone structures with the caveat that the instrument woud be bind to a specific bubbe size range. This imitation coud be potentiay ifted through additiona anaysis of the impact of the bone scatterer on the signas. Non-homogeneous bubbe distributions In aboratory conditions, the bubbe coud to be measured by the ABS has typicay a uniform distribution between the transducers. However, this is not necessariy the case in rea-ife scenarios. For exampe, bubby fows such as in a bood vesse are of particuar importance since they are the basis for the operation of current Dopper utrasounds detectors [-]. In order to assess the performance of the ABS in spatiay nonuniform bubbe fieds, we conducted tests where a bubby mixture was injected in a imited voume of the space between the transducers through a pastic tube (see Figure 5). In a first instance, a proportionay ower density (conserving the tota bubbe voume in between the transducer) was assumed to be prevaent over the entire width between the two transducers. This was then compared to the actua bubbe density appied ony over a thin region between the transducer. If we consider the anaytica expression for the D propagation in a concentrated distribution, we can write the transfer function reating the measured votage to the emitted one as: i L Lcoud i Lcoud u iv Vreceived exp exp Vemitted, C Ciquid iquid () i L Lcoud u ivlcoud exp Vemitted, where, u and v are the sound speed ratio and damping due to the ocaized bubbe coud. For a uniform diuted bubbe distribution, we can write the same transfer function as: i L ue ive Vreceived exp Vemitted, Ciquid () where, ue and ve are the effective sound speed ratio and damping due to the uniform bubbe coud. An effective coud is obtained by spreading the bubbes over the entire region. It is equivaent to reducing the bubbe density by the ratio of voumes (Lcoud/L). Using the fundamenta expressions for the definition of the sound speed ratio and damping, we can express these effective vaues in terms of the origina ones: RNuniform R ue ive 4 Ciquid o ib dr, (4) L N uniform R coud N R. L Expanding the above expression, the effective vaues of ue and ve can be written in terms of those from the origina ocaized bubbe distribution: ue ive u iv ue ive RN R L coud 4 Ciquid o ib dr, L RN R 4 Ciquid o ib dr, L coud L u iv, i L L Vreceived exp coud L Ciquid Figure 4. ABS bubbe distribution and optica measurement for bubbe injection through meat with and without bone insert. Ciquid (5) u iv Vemitted. At first gance, the transfer functions for the concentrated () and uniformy diuted (5) distributions are not identica. However, if we consider a ow void fraction case where u and v then the foowing approximate reationship hods: 8

9 L L coud L Nyon Tube u iv L Lcoud u iv O u iv, (6) L Lcoud Lcoud u iv, hydrophone s which, is approximatey equa to the expression in Equation () up to second order terms. Therefore, for the measurement of non-homogenous bubbe density distribution at ow void fraction, we can reate the density distribution measured by the ABS (homogeneous)) to the density observed by correcting by the geometrica factor Lcoud/L. Spatiay Non-Uniform Bubbe Distributions Experiments were performed to test the abiity of the ABS to measure spatiay non-uniform bubbe distributions akin to what woud be expected in a bioogica media where bubbes woud be carried away through the bood stream. To vaidate the ABS under this configuration, air bubbes were generated using a sma in-ine eectroysis system inside a nyon tube (4. mm ID,. mm thick was) with water pumped through it. Two one-inch ABS square transducers were paced. cm away from each other with the tube passing through the midde. The experimenta setup is shown in Figure 5. Bubbe size distribution was determined by both ABS and high-speed video image anaysis. The video images were taken as the bubbes exited the tube. The average fow rate in the tube generated by the pump was approximatey.5m/s. If we compare against typica fow rates in the arteria suppy, the area and fow rate corresponds approximatey to a arge artery [4]. Since the bubbe coud is ceary non-homogenous in this case, the bubbe density distribution measured by the video was corrected foowing the method discussed in the previous section. The void fraction within the tube, α is cacuated using: Vgas Vtube (7), where Vgas is the gas voume within the tube and Vtube is the voume of the tube section between the two hydrophones. The void fraction between the two hydrophones, α, is given by: Vcyinder Atransducer Dtransducer, (8) where Atransducer is the area of the transducer face and Dtransducer is the distance between the two transducers. Bubbes were injected into a fow of water through a tube inserted between two ayers of meat (beef.4 cm thick on each side). Optica vaidation was performed. In order to test the ABS in reaistic conditions, the transducer-meat-tube assemby was tested whie exposed to air as we as when it was submerged. The setup was modified such that the optica measurements were done inside a sma tank of water whie the transducermeat assemby was seated in another vesse which coud be fied with water for the wetted case without having to disrupt the assemby, Figure 7. In addition to the wet/dry tests, another series of measurements were conducted with a sma bone insert. The bone has a cross-section which varied from 7 to 9 mm in diameter and was fuy wetted prior to testing. Surfaces were covered by gycerin ge before joining and the overa assemby was hed together by eastic bands. Eectroysis Power In-ine eectroysis generator Figure 5. Experimenta setup for measuring bubby fows through a tube. Figure 6: Bubbe density distribution comparisons of ABS and image anaysis for bubbes in tube experiments, ( )ABS through water,( ) through meat. The comparison between the ABS and the image anaysis was done using the bubbe density distribution and the overa void fraction. Figure 6 presents the comparison of ABS measurements and image anaysis data. Within the range of vaidity of the ABS and the optica measurement technique, the bubbe distributions from the two methods agreed reasonaby we with each other. Based on these tests, we can concude that spatiay non-uniform bubbe distributions can be accuratey captured if one accounts for the voume ratio. Figure 7: Picture of ABS tube-in-meat experiments. The void fraction was controed by the votage appied to the eectroysis array. The votage was varied between 5 and vots. This greaty changed the void fraction inside the tube. The 9

10 void fractions cacuated by image anaysis at 5,, and V were.7 x -, 4.4 x -, and. x -, respectivey. These vaues were corrected for the voume samped by the hydrophones as discussed above and are inset in Figure 8. Figure. The resuts were not as cose here may be because the optica measurement did not give the meat bubbe popuation. Figure 9. Diagrams iustrating the operation of the pressure ce for decompression tests. Figure 8. Bubbe density distributions of bubby fow through tube measured by the ABS through water and meat, and image anaysis ( void fraction of. x -5, V ). These experiments indicate that the ABS is capabe of accuratey measuring bubbe sizes and void fractions in a vesse over a range of void fractions. Decompression Experiments The previous section discussed the capabiities of the ABS in detecting the presence of ocaized bubbes in a bioogica environment. However, the size and quantity of bubbes were controed by the eectroysis votage and the water fow through the tube. In order to achieve a good comparison in a more reaistic environment, we conducted a series of experiments where the bubbes were generated by the rapid decompression of the testing chamber. A diagram of the experimenta set-up is shown in Figure 9. The pressure chamber consisted of a Pexigas cyinder with.5 inch thick was, and inch stee pates on the ends hed in pace by compression. Coaxia cabes for the hydrophones passed through the pates in bukhead fittings and were epoxied into pace. The vesse was partiay fied with water. Pressure was appied from a compressed air cyinder to a pressure of 9.9 atm (45 psi) above ambient pressure. The headspace gas was bubbed through the iquid using an eectric micro-pump suspended from the id of the pressure chamber to equiibrate gas concentration in the water. After equiibrium was obtained ( minutes), a vave was reeased and the pressure dropped rapidy to ambient. As the pressure decreased, the iquid became supersaturated with gas and bubbes formed and rose towards the surface. In these experiments ABS readings were taken through meat. Thus, the bubbes detected were in the tissue itsef not in the iquid as opposed to the previous tests discussed above (viscoeastic fuids and bubby fow through tubes). To confirm the vaidity of the ABS measurements through the meat these resuts were compared to ABS measurements in water, and high speed video taken under the same conditions. The video images were taken directy above the meat in the buk iquid. The bubbe density distributions for two experiments are shown in Figure. Bubbe density distribution due to decompression in meat, ABS measurements through meat, ABS in water, and image anaysis. Preiminary anima experiments We contributed to tests conducted at the Navy Medica Research Center (NMRC) on iving animas exhibiting symptoms of decompression sickness in the course of an ongoing research study on the benefits of oxygen pre-breathe on decompression sickness conducted by Dr. Mahon s group. The experiments invoved two 7 kg swine which were subjected to a saturation dive and hed at a pressure equivaent to 6 ft of seawater (.8 ATA) for hours. The animas were then surfaced at a rate of ft per minutes for two minutes. ABS data was coected on two animas prior to entering the hyperbaric chamber and after surfacing. Data was coected at severa ocations on the animas; ears, tais, hind egs and fore egs. The pre-dive data coected for the ears and tais of both animas showed good signa quaity. One anima, designated as 5467, exhibited skin bends characterized by marbing of the skin, at 9 minutes after surfacing and was euthanized after minutes. Prior to this, a set of data was coected through an ear from to minutes after surfacing. Additiona ABS measurements were taken postmortem, at the ear, tai, and eg. The thickness of the ears, tai,

11 significanty with time, whie the number of arge bubbes remained at the same order. This coud suggest that the anima succeeded in eiminating the smaer bubbes, whie the arger one may require a onger time. The anima 5467 shows simiar trends post-mortem with a bubbe sizes reducing in number over time. There is a marked increase in the pre-mortem fu bubbe popuation between and 6 minutes..5 E - 5 p ig e u th a n iz e d p ig p ig E - 5 Void fraction and eg were measured with caipers at the ocation where the transducers were paced. This provided estimates for the distance between the hydrophones of 4 mm for the ears, mm for the tai, and mm for the hind eg. The other anima designated 5466, survived for the entire duration of the experiment (over 9 minutes) and was ater euthanized and anayzed post-mortem. Measurements were taken at severa time periods from 4 minutes to 7 minutes after surfacing. In a post-dive measurements, pairs of data sets were coected within a few seconds of each other. Combining the pre- and post-dive data provided the attenuation and sound speed ratio for the each anima as a function of time. Resuts for sound speed ratio and damping are shown in Figure and Figure. The error bars on these figures are representative of the differences observed between the measurements. 5 E - 6 P r e - d iv e r e f e r e n c e P o s t - d iv e t im e ( m in u t e s ) V Figure. Evoution of the void fraction as a function of time for each anima. Note that the zero measurement is based on the pre-dive reference conditions ony F re q u e n c y ( k H z ) Figure. Comparison of signa damping as a function of frequency for pig No at various times after resurfacing Bubbe density distribution (m-4) 5 Pig Pig 5466 minutes 6 minutes minutes 4 minutes 6 minutes 64 minutes 7 minutes Bubbe density distribution (m-4) Bubbe radius ( m) U Bubbe radius ( m). Figure 4. Evoution of the computed bubbe density distributions for each anima F re q u e n c y ( kh z ) Figure. Comparison of sound speed ratio of pig No as a function of frequency for various post-dive times. The most interesting aspect of the resuts shown in Figure is that the void fraction for pig number 5466, which actuay experienced successfuy the dive, continuousy decreased with post-dive time, probaby indicating a positive sow return to pre-dive body bubbe content. On the other hand, pig number 5467, which was experiencing great post-dive difficuties, saw its bubbe content or void fraction continue to increase post dive unti the time it was euthanized. This correates with the difficuties experienced by the anima. Postmortem, void fraction dropped over 6 min. to the pre-dive eve. The deduced bubbe density distributions (Figure 4) provide a picture of the changes in the bubbe popuation with post-dive time. As shown in Figure 4, the bubbe density for pig number 5466 appears to shift from sma bubbes to arger bubbes with time. The number of smaer bubbes decreases These very imited anima tests provide significant observations in terms of void fraction and bubbe popuation as a function of post-dive time. These can be summarized as foows: Changes in the void fraction as a function of time were observed in both animas, demonstrating the capabiity of the ABS to detect bubbe generation during DCS. There seems to be a correation between the shape of the void fraction time history curve and the resistance of the animas to decompression. The strong pig started recovering fast after the post-dive and exhibited a continuous decay of the void fraction at the times of the tests. The weak pig showed a continued increase in void fraction unti death. Bubbe size distribution appears to indicate that smaer bubbes are desorbed faster. CONCLUSIONS This study has demonstrated the feasibiity of using the acousticay based detection system, the ABS A COUSTIC BUBBLE SPECTROMETER, for the detection of microbubbes in bioogica media such as bood and other tissue. The agorithms used by the ABS to detect and quantify bubbes in water were

12 modified so that the existing hardware system coud be used in bioogica media. Severa technica chaenges associated with the acoustic measurement of gas bubbes in bioogica media were addressed. These incuded the effects of viscoeasticity on the response of bubbes in an acoustic fied, scattering due to dense materias such as bone, non-homogenous distribution of bubbes in the bood vesses and tissues, and the effects of perfusion of bubbes through tissue during DCS and ischemia. ACKNOWLEDGMENTS This work was supported by the Nationa Institute of Heath US Dept. of Heath and Human Services. We woud aso ike to thank Cmdr. Richard Mahon MD of the Navy Experimenta Dive Unit, Nava Medica Research Center, US Navy. REFERENCES. F. Crawey, J. Styga, S. Lunn, M. Harrison, M. M. Brown, S. Newman, Comparison of Microemboism Detected by Transcrania Dopper and Neuropsychoogica Sequeae of Carotid Surgery and Percutaneous Transumina Angiopasty, Stroke,,9-4,.. J. Buckey, D. Knaus, D. Avarenga, M. 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