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Peter Johansen*Bioengineering Department,Penn State University,University Park, PA 16802,Department of Cardiothoracicand Vascular Surgery,Aarhus University Hospital Skejby Sygehus,8200 Aarhus N., DenmarkKeefe B. ManningBioengineering Department,Penn State University,University Park, PA 16802John M. TarbellDepartment of Biomedical Engineering,The City College of New York (CUNY),New York, NY 10031Arnold A. FontaineSteven DeutschApplied Research Laboratory,Penn State University,University Park, PA 16802A New Method for Evaluationof Cavitation Near MechanicalHeart ValvesEvaluation of cavitation in vivo is often based on recordings of high-pass filtered randomhigh-frequency pressure fluctuations. We hypothesized that cavitation signal componentsare more appropriately assessed by a new method for extraction of random signal components of the pressure signals. We investigated three different valve types and found ahigh correlation between the two methods 共 r 2 :0.8806 0.9887兲 . The new method showedthat the cavitation signal could be extracted without a priori knowledge needed for settingthe high-pass filter cut off frequency, nor did it introduce bandwidth limitation of thecavitation signal. 关DOI: 10.1115/1.1613297兴Hans NygaardDepartment of Cardiothoracicand Vascular Surgery,Aarhus University Hospital Skejby Sygehus,8200 Aarhus N., DenmarkBackgroundPatients with heart-valve dysfunction are most often treated surgically with implantation of mechanical heart-valve prostheses.Currently, over 175,000 heart valves are implanted in the worldeach year 关1兴. Although this mostly is a life-saving procedure,patients with these prostheses face potential complications. Themost common of these complications are thromboembolic andbleeding disorders, but material damage of mechanical heart-valveleaflets has also been observed.Since cavitation is known to expose nearby structures to strongerosive forces 关2兴, this phenomenon has been suggested as a possible contributor to the thromboembolic complications and material failures 关3兴. Previous, evaluation of cavitation near mechanical heart valves has primarily been based on visualization ofcavitation bubble formation in transparent media 关4 –9兴. Thesestudies have shown that cavitation bubbles can form and collapseat the inflow side of the valve immediately after its closure. Thesecavitation ‘‘clouds’’ have been visualized at specific locations depending on valve design, suggesting a variety of mechanisms forinception of cavitation. Since the visualization method is not ap*Corresponding address: Department of Cardiothoracic and Vascular Surgery,Aarhus University Hospital Skejby Sygehus, Brendstrupgaardsvej, 8200 Aarhus N.,Denmark. Phone: 45 8949 5486; Fax: 45 8949 6016; e-mail:peter.johansen@iekf.au.dk.Contributed by the Bioengineering Division for publication in the JOURNAL OFBIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division November 14, 2002; revision received April 17, 2003. Associate Editor: A.Yoganathan.Journal of Biomechanical Engineeringplicable in vivo, a method using measurements of high-frequencypressure fluctuation was developed 关10兴. Garrison et al. recordedpressure fluctuations at beats with and without cavitation. Theyfound that beats with no cavitation had no frequency componentsabove 35 kHz, whereas beats with cavitation had higher frequencycomponents. Mechanical resonance generated by the closure ofthe mechanical heart valve was found to have frequency components up to 35 kHz. By removing these components through ahigh-pass 共HP兲 filter, Garrison et al. isolated the cavitation signal.The root mean square 共RMS兲 value of the high-pass filtered datawas calculated, and its magnitude correlated well with the degreeof cavitation observed visually.However, when applying this technique, appropriate selectionof the HP filter cutoff frequency should be based on knowledge ofthe individual valve’s closing sound characteristics 关11兴. Furthermore, since there may be a frequency overlap between valve closure resonance and cavitation signal components, this methodmight remove components from the cavitation signal.Consequently, using this method in vivo either during animalexperiments or carrying out a clinical patient-related protocol maycause difficulties in choosing the right parameters needed for setting up the analysis. A method which requires no a priori knowledge is desired. Therefore, a slight different approach could beutilized. The cavitation signals recorded using pressure transducers or hydrophones are caused by the momentary large pressuresgenerated when the contents of a collapsing bubble become highlycompressed 关12兴. The resonance frequency of a bubble is relatedto the bubble radius, such that smaller bubbles have higher reso-Copyright 2003 by ASMEOCTOBER 2003, Vol. 125 Õ 663
Fig. 1 The top three schematics of the investigated valves show areas„shaded of highest probability to find cavitation. The transducer positionis illustrated as the dark shaded rectangle on the atrial aspect with the wireleaving. Below the schematics are three photographs which visualizes thecavitation.nance peak frequencies than larger bubbles. Cavitation formationsthat have been observed near mechanical heart valves containednumerous single cavities, each having its own frequency spectrum. This variation in bubble size perhaps creates the broadbanded frequency signature of the pressure signal observed. Sincethere is also beat-to-beat variation in the number and size ofbubbles, it can be assumed that the sound generated exhibits randomness in the form of a non-deterministic frequency pattern. Thework of Oba et al., which found stochastic behavior of desinentcavitation supports this theory 关13兴.HypothesisSeparation of cavitation and valve closure signal componentscan be accomplished by separation of deterministic and nondeterministic components without a priori knowledge of valveclosure resonance.Aim of StudyTo develop an alternative signal analysis method than high-passfiltering, for the separation of cavitation from valve closingsounds. The new method must be applicable to different valvetypes.Material and MethodsThree different 29 mm mitral valves with an intact suture ringwere investigated: The Björk-Shiley monostrut, the MedtronicHall, and the CarboMedics CPHV standard mitral bileaflet valve.They were operated in a custom-made single-shot valve-closingmodel similar to the one described by Kini et al. 关14兴 and Chandran and Aluri 关15兴. The model was manufactured from acrylic foroptical access. It encompassed two chambers. The smaller ventricular chamber was sealed and connected to a pneumatic pressure regulator system 共Air compressor pulsatile pump, VitamekInc., Houston, TX兲. The larger atrial chamber was held open to theatmosphere in order to provide a stable hydrostatic pressure tosimulate ventricular preload. A transparent blood analog fluid consisted of 40% glycerin and 60% water to mimic blood’s viscosityand density ( 3.5 cP, 1.1 g/cm3 ). The tap water used wasfiltered and stored for degasing for at least 24 hours. The mixedsolution was also set to degas for at least 24 hours.A high-speed video camera system 共Kodak Motion Corder Analyzer, RedLake MASD, San Diego, CA兲 was used to visualize the664 Õ Vol. 125, OCTOBER 2003atrial side of the mitral valve with 3,000 image frames per second.A Millar micro tip pressure transducer was positioned in theventricular chamber to measure the left ventricular pressure usedfor evaluation of dp/dt. A pressure transducer 共PCB 132M30,Depew, NY, USA兲 positioned in the atrial chamber was used todetect high frequency pressure fluctuations 共HFPF兲. The transducer was positioned at a skewed angle of 45 , 5 mm in front ofthe potential cavitation areas, which were determined prior to theexperiments. Figure 1 shows the potential cavitation areas of eachof the valves and the position of the pressure transducer relative toeach valve in a frontal view. The shaded semi-transparent areasillustrate the potential cavitation sites for each valve. Below thesedrawings are frames obtained by high-speed imaging showingcavitation in these areas. The areas where cavitation was observedand location of the pressure transducer were similar to those recorded in other studies of the three investigated valves 共BjörkShiley 关10兴, CarboMedics 关16兴, and Medtronic Hall 关9,17兴兲.Different loading conditions (dp/dt) were imposed by adjusting the pulsatile pump heart rate 共60–170 bpm兲, systolic duration共20– 400 ms 5– 40% of each heart cycle兲 and the maximumleft ventricular pressure. The latter was adjusted between 120–220 mmHg and verified with a Millar catheter. Nine differentloading rates were planned based on pilot experiments to allowdifferent levels of cavitation, going from ‘‘not visible’’ to ‘‘severe’’ cavitation.The dp/dt was assessed on a LeCroy 9310 oscilloscope 共Chestnut Ridge, NY兲 for each adjustment prior to and after a series ofrecordings during one stable hemodynamic situation as describedin the data analysis section.The high-frequency pressure signal was sampled through theLeCroy 9310 oscilloscope at 2 MHz. A time segment of 1 msec ofpre-triggered data was acquired followed by 4 msec of posttriggered data. The data were transferred through general purposeinterface bus 共GPIB兲 to a standard PC. A custom made program inLabVIEW 共National Instruments, Austin, TX兲 was applied to control data transfer from the digital storage oscilloscope.Data Analysis. For each setting of the pulsatile pump, thedp/dt was calculated according to the guidelines set by the FDA关18兴, as the average P/ t over the last 20 msec before the mitralvalve closure. Hence, dp/dt was estimated as P20 msec/20 msec.As an indicator of cavitation intensity, the root mean square共RMS兲 value of the HFPF data was calculated after it was highTransactions of the ASME
Table 1 Criteria for separating the different hemodynamic situations into various degrees of cavitationCavitation degreeValveBjörk-ShileyNoneModerate 1Moderate 2HighNo visiblecavitationFormation of bubblecavitation on the discsurface.Max. duration 2/3 ms.Formation of bubblecavitation and indicationof cavitation at the edgeof the leaflet.Max duration 2/3 ms.Extensive formationof bubble cavitationand cavitation at theedge of the leaflet.Duration 2/3 ms.Formation of cavitationnear leaflet edge.Max duration 2/3 ms.ExcludedExtensive cavitationformation near leafletedge with a duration 2/3 ms.ExcludedFormation of bubblecavitation on the discsurface.Max. duration 2/3 ms.Extensive formationof bubble cavitationand cavitation nearseat stop.Duration 2/3 ms.CarboMedicsMedtronicHallpass filtered using Garrison et al.’s method 关10兴, later modified byJohansen et al. 关11兴. Hence, the cutoff filter matched the naturalharmonic components of each valve. The cutoff frequencies chosen were for the Björk-Shiley: 40.9 kHz, CarboMedics: 53.7 kHz,and Medtronic Hall: 49.9 kHz. The high-pass filter was configuredas a fifth-order Butterworth. The RMS value was calculated as:RM S 冑冕1TR xy 共 t 兲 x 共 t 兲 丢 y 共 t 兲 Tp 2 共 t 兲 dt(1)0where T represents the data length 共5 msec兲 and p(t) is the recorded pressure data. The mean RMS value was calculated basedon 30 value closures.To isolate and quantify the non-deterministic energy as a representation of cavitation, the deterministic energy was subtractedfrom the total signal energy:E non-deterministic E total E deterministic(2)The Enon-deterministic was compared with the RMS calculated fromthe same data, using Spearmans Rho non-parametric correlationanalysis 关19兴.The total energy was calculated from the mean energy densityspectrum of the raw data. The energy parameter was derived as:NE fs冕f s /2G 共 f 兲 d f0(3)where N is the number of samples, f s is the sampling frequency,and G( f ) is the amplitude spectrum squared. The amplitude spectrum is calculated based on discrete Fourier transformation 共FTD兲Eq. 共4兲. FTD:X 共 e j T 兲 兺n x 关 nT 兴 e jn T(4)where x 关 nT 兴 is the input sequence, is the cyclic frequencyand T is the time between samples. Based on this, the amplitudespectrum is the square root of the sum of the squares of the real共Re兲 and imaginary 共Im兲 parts of the complex transformation result Eq. 共5兲Amplitude spectrum兩 X 共 f 兲 兩 : 冑Re2 Im2(5)The total energy was thus calculated using equation 3 withx 关 nT 兴 x total关 nT 兴 being used in Eq. 共4兲 where x total关 nT 兴 is theraw data input sequence of data.The deterministic signal energy (Edeterministic) was calculated from the ensemble average of the heart cycles x ea 关 nT 兴using Eq. 共3兲.Journal of Biomechanical EngineeringIn order to line up the data in the time domain prior to ensembleaveraging, a cross-correlation function was developed. First, arepresentative beat was chosen as a template to line up the rest ofthe data. The cross correlation 共Rxy兲 between two signals (x(t)and y(t)) for continuous data is given by冕 x 共 兲 y 共 t 兲 d (6)where 丢 denotes the cross correlation.Considering two signals in discrete form 共X and Y兲 where:X has n elements,X关j兴 0 for j 0 and j nY has m elements,Y关j兴 0 for j 0 and j mThe cross-correlation can be implemented initially by calculation of an intermediate variable h j :n 1h j m 1兺 兺k o j 共 n 1 兲x k y j k(7)The cross-correlation can then be calculated as:R xyi h i 共 n 1 兲(8)Having calculated the cross-correlation, a result in the rangefrom 0 1 共where 1 is the highest correlation兲 was obtained bynormalizing the result with the template chosen, 共represented asT 关 n 兴 in digitized form兲, as:R xy 关 n 兴Normalize: N 1兺n 0(9)T 关n兴2The time, ref , where the template auto correlates with 1, is setas a reference for the line up. The maximum correlation betweenthe template and each of the heart cycles is determined and thedifference between each and ref was used to adjust the temporalposition of the recorded heart cycles.Based on the high-speed visualization, each hemodynamic situation was assigned to one of three groups of cavitation intensity:none, moderate, or high. The moderate category was further divided into two sub groups. The criteria for each group are listed inTable 1.The CarboMedics valve was expected to act with asynchronousclosure, due to its bileaflet design 关20兴. The time between first andsecond leaflet closure was measured graphically by placing twocursors at the start of each leaflet closing signal.OCTOBER 2003, Vol. 125 Õ 665
Fig. 2 The different dp Õ dt obtained for the different investigated valves. Themean dp Õ dt Ástandard deviation was 2926Á1183, 2286Á824, and 2585Á1296 mmHgÕs for the Björk-Shiley, CarboMedics, and Medtronic Hall, respectively.ResultsAdjusting the pump settings allowed us to obtain a range ofdifferent dp/dt values for each of the three valves as illustrated inFig. 2. The high-speed visualization data showed that the level ofcavitation was a function of dp/dt. By subjectively dividing thedegrees of cavitation according to the guidelines set previously共Table 1兲, a degree of cavitation could be assigned to each operating condition. Figure 3 depicts image frames obtained at thevarious degrees of cavitation. Each frame represents 1/3 msFig. 3 Images acquired at different loading rates. The data aredivided in three degrees of cavitation based on visual judgments and criteria. Only frames with visual cavitation areshown, except for the non-cavitation category. Each frame represents 1Õ3 msec. Successive frames are shown with time increasing downward. Contrast and brightness of the imageshave been adjusted to enhance details.666 Õ Vol. 125, OCTOBER 2003共frame rate 3000 fps.). The degree of cavitation was also associated with the number of frames showing cavitation bubbles.In processing the high-frequency pressure signal, before calculating the ensemble average, the data were temporal lined up using cross-correlation. The maximum temporal displacement ofvalve closures in a data series determined by the time constant was about 700 samples 共 350 s兲, which constitutes 7% of therecording window width.Figure 4 shows an example of the spectra calculated. Both thefrequency axis and the signal energy are plotted with logarithmicaxes. At low frequencies and up to approximately 10 kHz most ofthe total signal energy is comprised of the deterministic part. Atfrequencies above 10 kHz the non-deterministic signal energy isabout a factor 10 higher than the deterministic part.Figure 5 shows the non-deterministic energy and dp/dt plottedas a function of the degree of cavitation based on the visual criteria 共Table 1兲 for the three valve types. All valves show a tendency to exhibit increases in both non-deterministic energy anddp/dt as cavitation intensity increases. The Medtronic Hall valvethough, has one measuring point with a lower non-deterministicenergy level at higher visual cavitation level than those in themoderate cavitation degree. Furthermore, the same valve has twopoints in the high-cavitation-level group that are in the same rangeas points in the moderate-cavitation-level group.Figure 6 shows the non-deterministic energy plotted as a function of dp/dt. The r2 varies from 0.56 0.99 for the three valves.Both the Björk-Shiley and the CarboMedics data have a far endpoint. The two tilting disc had higher levels of non-deterministicenergy than the bileaflet valve.The RMS cavitation parameter is plotted as a function of thenon-deterministic energy evaluated in Fig. 7. Analogous to thenon-deterministic energy the RMS values were also higher for thetilting discs than the bileaflet valve. There appears to be a linearcorrelation between the two variables. The non-deterministic energy of the CarboMedics valve was in the range 150 2,100 kPa2 when visible cavitation was detected. The level increased as cavitation became more extensive spatially and temporally. The two tilting disc valves had higher ranges of nondeterministic energy than the bileaflet valve. They were 9,000 14,000 kPa2 共Björk-Shiley valve兲 and 500 16,700 kPa2共Medtronic Hall valve兲. These ranges were observed when cavitation could be visually confirmed on the high-speed video images. The dp/dt ranges for the tilting disc valves were roughly thesame. Fewer measurements were taken at low dp/dt conditionsTransactions of the ASME
Fig. 4 The spectra calculated are the total energy spectrum, the deterministic energy spectrum calculated from the ensembleaverage signal, and the non-deterministic spectrum being the difference between the total and the deterministic energy spectrum. Legends Light gray: Total energy density spectrum; Dark gray: Deterministic energy density spectrum; Black: Nondeterministic energy density spectrum.with the Medtronic Hall valve than the Björk-Shiley valve. Thenon-deterministic energy levels increased with increasing dp/dt.Table 2 lists the mean times and standard deviation for the duration between the two leaflet closures in the CarboMedics valvebased on 40 consecutive valve closures.DiscussionThe in vitro model used in this study made it possible to adjustthe dp/dt for different valves over a wide range. The higher values were well above the normal physiological range. These valueswere included to follow the severe development of cavitation andto cover a large scale of fluid dynamic situations, making theevaluation of the new method more robust. The video imagesshowed a clear tendency of more extensive cavitation as the leftventricular pressure rate increased 共Fig. 5兲, which is in concordance with other in vitro cavitation studies 关21,22兴. The imagesalso showed that the first type of cavitation which could be visualized as dp/dt increased was bubbles formed on the surface ofthe leaflets 共Fig. 3兲. This was observed for all the valves andindicates the onset of a ‘‘water hammer’’ type of cavitation.Higher levels of dp/dt produced ‘‘vortex’’ cavitation near theleaflet edge for the Björk-Shiley and CarboMedics valves.With the pressure transducer positioned near the potential cavitati
Penn State University, University Park, PA 16802 Hans Nygaard Department of Cardiothoracic and Vascular Surgery, Aarhus University Hospital Skejby Sygehus, 8200 Aarhus N., Denmark A New Method for Evaluation of Cavitation Near Mechanical Heart Valves Evaluation of cavitation in vivo
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