Acoustical Properties Of The Human Skull

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Acoustical properties of the human skullF.J. erfor AdvancedResearch,Indianapolis.Indiana46202J. E. BargerBolt Beranekand eceivedI January 19771revised4 November 1977)The nd soundspeedwere measuredon a seriesoffreshand tswere madein the frequencyrangefrom 0.95 to 6 MHz. Most studieswere restrictedto an upper frequencylimit of 2.2 MHz. Anaxisymmetricfocusedbeam configurationwas usedas the soundsourcefor the measurementsand thereceiverswere small disk-type(3-mm-diam)piezoelectricceramics.The geometricand temporalcharacterof the focusedbeamwasstudiedas a consequenceof passagethroughthe skull sections.Someskullsweresoctionedso that their individuallayexcomponentscouldbe studied.A simplethree-layeranalyticalmodelseemsto explainthe major aspectsof insertionand reflectionloss.The dominantfeaturein determininghuman adult skull lossesis the middlelayer (diploe)of cancellousbone.This studycorroboratespreviouswork on insertionlossas a functionof frequencyfor compositeskull. The studyprovidesnew quantitativeinformationon the acousticscatteringpropertiesof diploe,scoundvelocity,and dispersionin compositeskull and its components,attenuationcoefficientsin skull componentsand sound-beamdistortionandshifts after transmissionthrough compositeskull. We concludethat with selectionof appropriatefrequencies(0.5-1.0 MHz) and beam configurationit will be possibleto perform clinicallysignificanttranskulldiagnosticimagingand interrogationin the adult human brain.PACS numbers: 43.80.Cs, 43.80.EvINTRODUCTIONreflection loss, and insertion phase shift through skullsRelativelylarge sections(typically5 x 5 cm2) ofhuman adult, child, and infant skulls were studied todetermine their acoustical properties in the frequencyrange from 250 kHz to 2.2 MHz. In addition, theacoustical properties of some skulls and skull components were studied at frequencies up to 6 MHz. Mostskulls were studied at times staxting from three tofour hours after patient death through several weeksbefore immersion in buffered formalin, after whichtime they were studied for many additional months.Specific skulls were sectioned into individual layerscomprising the outer ivory table, the diploe, and theinner ivory table. These layers were studied singlyand in reconstructed composites to determine the contribution of the various skull layers to the overall acousticalcharacteristics.This. study was conductedprimarily to provide sufficient quantitative information on the acoustical properties of human skull bone so that the potential fortranskuLl visualization, interrogation, and possibletherapy of intracranialcontents by ultrasonic meanscoukl be thoroughlyevaluated. An important objectiveof the work was to evaluate critically the idea that anaxisymmetric focused beam will provide controlledlateral resolution when transmitted through an area ofskull laxge enoughto smooth out distortions due tosmall-scale skull inhomogeneities.We have proposed an analytical model that explainsthe acousticalcharacteristicsof skull in a mannerwejudge appropriate for either experimental or commercial instrumentation design considerations.Our principal measurements were of insertion loss,1576J. Acoust.Soc.Am.63(5),May1978and their component layers. In a few cases, we variedthe angle of incidence of the focused beam from 0 ø(normalincidence)to aboutõ0ø. The patchsize throughwhich soundwas transmitted was varied systematicallyin some of the measurements.Forsome of the thickerskulls, we measured the broadening of the transmittedbeam.Phase speed in the samples was computed from thefrequency depeadenceof the phase angle of transmittedsound. This method reveals the frequency dependenceof phasespeed(dispersion),informationthat is nearlyimpossible to obtain from transit-timemeasurementswhich measure directly the group speed. Nevertheless,some transittime measurementswere made to showhow dispersion causes the higher-value group speeddata that axe usually reported in the literature. Massdensity and thickness were measured for the individuallayers of some skull samples. A series of measurement,,were made to show quantitatively the effects of skullirregularities,which must not mask the effects causedby true irregularitiesof the intracranialcontents to bevisualized.The fluctuations of acoustical properties of skull sec-tions were measured as functions of lateral translation,angularion, and separation of the skull relative to thetransducer. The deflection and broadening of both oneway and two-way focused beams were measured also.I.A.MATERIALSANDMETHODSInstrumentationThe instrumentationto obtainourand 80areillustratedapparatus usedschemati- 1978AcousticalSocietyof America1576

1577F.J. FryandJ. E. Barger:Acousticalpropertiesof thehumanskullI GENERATORFUNCT'ONIITRIGGERIKROHN-HITEI RFIII I cDEcDL-I1CI I 1DATA !COUPLER IINPU'rOSCILLOSCOPEI I UNIBUSARENBERGIII IPG-6o-cOUIII !õ INCH15771 ¾3 ff?;3INPUT95 MODELaI00I' 0" YITRIGGERINVERTI IN MALOU INPUTIN T [ INPUTTUNINGINDUCTORAMPLIFIER// (!,B.,N \ ATTENUATOP OdBFIG.1.Schematic illustrationof measure-ment apparabas.l:SdBSAMPLE . 8-].POSITIONINGTSTAGEMICROMETERPOSITIONINGSTAGEI I -- POSITIONING FOCUSEDTRANSDUCER-- GLASS-WALL- TANKRECEIVE2:: : /P BE"B'. SAMPLEWATER' REGION.oa,SKULLtally on Fig. 1. This apparatus can generate ultra-The sound pressure on the transducer axis as a func-sonic pulses that have limiting frequencies as low astionof distancefromthe transducerfaceshowsthat250 kHz andas high as 6.0 MHz, time-bandwidthprod-the maximum pressure occurs at about 18 cm, with aucts as high as 1000, and peak pressures as large asdepthof focus (definedat 3-dB downpoints) of 10 cm.eight bars at the focus.The magnitudes of the Fourier coefficients of a pulsewavelorm measured at the focus are shown on Fig. 2.Two probe channels are avail-able; the reference channel has 48 dB of dynamicrange and the receive channelhas 120 dB of dynamicrange.The waveformsreceivedon the two channelsare superimposed and sampled 2048 times.The wave-form samplesaxe read by a PDP 11/40 computerforedi[ing disk filing, and subsequentanalysis.Impulses are generated by setting the amplifier gatedwell interval at the inverse of the desired pulse bandwidth, with the ampIifier input open circuited. Coher-ent waveform pulses having time-bandwidth productslarger than unity are generated by the function generatot, which is triggered by the gate-openingpulse.Pulses are shapedby the amplifier output stage andthe [uning inductor, which is connected across the transducer. The transducer is an electrostrictive sphericalcap with an aperture of 49 mm a focal length of 190ram, and a highly damped resonance frequency at 1.7MHz.J. Acoust. Soc. Am., Vol. 63, No. 5, May 1978Thiswaveformhas a useablebandwidthof fromabout250 kHz to abou,:2.0 MHz, for over this range theFourier coefficients are at least 60 dB larger than thosefor background noise.The ultrasonic probes are 3-mm-diameterand 0.01-in. -thick disks of Keramos, Inc. (Lizton, Indiana),Kezite K-15 pie:.,oelectric ceramic.Receiving sensitiv-ities of these probes are within I dB of - 133 dB/V/ barover the frequency range extending from below 100 kHzto about 5 MHz. The probes are symmetrical in termsof their output with respect to their front and b ck face(i.e., a 180ø ro :ationin a given plane-wave field willyield the same voltage output). With the disk faceperpendiculax to the direction of propagation the 6-dBdownpoints correspondto a probe rotation of ß 13ø.This directivity aspect has posed no problem in our experimentalarrm gementsince in all measurementsthe

1578F. ,I. FWandJ. E. Barger:Acousticalpropertiesof thehumanskull1.001578B. Data analysisBy observing the. physical configuration of Fig. 1 thesequence of recorded waveforms can be foRowed.0.jprobe (A). This pulseis designatedx waveformin theZ Thetransient recorder is triggered by the electrical pulsethat drives the transducer. Sampling of probe outputsbegins a/ter a delay set in the recorder, chosen tocatch the incident pulse just as it passes the referencedata analysis algorithms. The reference probe is pesitioned close enough to the skull sample so that it willcatch the reflected pulse next. This reflected pulse isdesignated z waveform in the data analysis algorithms.The output level from the pulse amplifier is adjustedso that the peak voltage from the reference probe willfall just short of the peak voltage capacity of the recorder. The next waveform is measured by the receiveLUprobe (B) as it records passageof the pulse that hasRREQLIENCY(MHz)FIG. 2. Relative magnifydes of Fourier coefficients of transducer pulse waveform measured at its focus.traveled through the skull sample. This pulse is designated y waveform in the data analysis algorithms. Attenuators in the receive probe circuit are also adjustedso that the peak voltage from the receive probe fallsjust short of the peak voltage capacity of the recorder.The recorded voltage waveforms x, y, and z are re-lated to the soundpressures p,, /),, and p, by the sensitivitiesg t of the reference channel and g2 of the receivesignal output on the probe was maximized by rotatingthe probe about its own axis.Calibrated attenuatorsbefore and after the receive-probe amplifier allow thereceived signal to be adjusted to within 1 dB of the reference signal The transient waveforms captured bythe recorder are viewed on an oscilloscope before theyare transmitted through the data coupler to the computer.channels; i.e.,incidentpressurewaveformp x/gt ,reflectedpressurewaveformp, z/g ,(1)transmittedpressurewaveformp Y/gz ßThe attenuations in the two channels At and A 2 are defined by Ai - 20 loggi ßExperimental skull samples were positioned in thepulsed ultrasonic beam from a stage that can be movedloss, reflection loss, and the phase angles of the twoalongthree perpendic.ularcoordinatesand rotated aboutloss functions.the vertical coordinate. The receive probe was mountedon a stage that can be positioned anywhere along thebeam axis and can be moved accurately in the horizontaland vertical directions by means of micrometer adjustment. The reference probe is attached to the transducer, and this combination can be positioned in boththe horizontal and vertical directions by micrometeradjustment. Transducer, probes, and sample wereall immersed in water contained in a 25 x 25 x 45-cm sglass-walled tank.surement of the ratio of the Fourier coefficients P Insertionloss as a function of time and formalinfix-ation was obtained on skull samples starting as soonafter death as the autopsy procedure would permit (usu-ally within four hours)andfor as longas six nswere immediately placed in buffered mammalianRinger's solution, and the insertion loss of these sec-Four functionsof the data were calculated:insertionInsertion loss (IL) is the decibel mea-andP where the waveformp is measuredat the sameplaceas p butwith no skullpresent,andwherecapitalletters represent the Fourier coefficients of the waveforms represented by lower-case letters.Insertionphaseshift (I ) is the difference betweenthe phaseangles of the two Fourier coefficientsIL--20ioglr,I/Ir; I: 201ogl7' I/171 A(2)I - argP - argP : argY - argY'Because we require only differences in the attenuationin the probe channel B, calibration of the probe is notnecessary.Reflectionloss is the decibelmeasureof the ratiotwo Fouriercoefficientstions was determined as a function of frequency.Anumber of subsequent measurements were made duringthe timewhilethe skullsectionswerestoredunderre-frigeration in Ringer's solution. They were withdrawnand broughtto 37 øC for the measurements. Within afew weeks, the skulls were placed in buffered formalin,and the acousticmeasurementscontinued for six months.J. Acoust oc. Am., Vol. 63, No. 5, May 1978ofthe Fourier coefficients P, and/ . Reflection phaseshift is the difference between the phase angles of theRqb argP - argP, argZ - argX .Since the reference probe channel A is used to makeboth pressure measurements in the ratio, its calibration is not required.

1579F.J. Fry andJ. E. Barget:Acousticalpropertiesof the humanskullTABLE I.1579Skull density and thickness b70.960.900.982.84ßßßbßßß - -. 1.73912. b. bßßßb0.74111.939. 1.022.221.684.921.8791. 7381.914. 1012 (infantskull)Average withoutskull No. 12SAverageof five positionsmeasuredalonglinear cut passingthroughregionof central ray passage. Nodata, notapplicable,or notobtained. 360f(li/c t - l /c o) .The four functions of the data are calculated by thePDP 11/45 computerusingtwo differentprograms.The first prograni is the data editing and file-makingprogram.This program first causes the transfer ofthe 2048 data words from the recorder memory intocomputer core memory. The operator then designatesthe beginning and ending addresses of each of the threewaveforms x, y, and z. These addresses are estimatedfrom the oscilloscope display of the recorder memory.Datafliescoreonto a diskaremadeforeach waveformand writtenfromfile.The second program assesses'the data files and computes the data functions according to Eqs. (2) and (3).A 1028-point FFT algorithm is used to computetheFouriercoefficientsfromthe data files.AccurateThe lengthof t[avel in the skull layer is l h/cosO ,and the effective length of travel in displaced water isl o I l cos(80- 8.), whichis the travel lengthin skullprojected onto the direction of the incident beam, adistinction necessary in our measurements because weare using a plane receiver that is perpendicular to thereceived sound rays.When Snell's law is substituted in Eq, (4) togetherwith the travel lengths l a and l , a quadratic equation isobtainedfor the normalizedsoundspeedx cl/c a. Thephaseangle-frequencyratio is q)' ø/Hz, andwe definethe dimensionless parexacter m astimem: cos8o ('Mco/360h)registrations for the y and z waveforms is obtained bysubtracting from their addresses the address of theleading edge of their x waveform. In this way, all timesare referenced to the time the incident waveform passesthe reference probe. The transmit pulse waveformonly starts the transient record?r; it is not the timereference. By this technique, the phase accuracy isnever worse than the error caused by the interval uncertainty of one sample.The data are sampled at intervals of 0. 05 ts, and theFFT program analyzes 1024 samples. This procedureresults in a frequency resolution of 19 kHz. Theacoustical properties that are reported as functions offrequency in this paper have a resolution of 19 kHz,except as otherwise noted.(4) (1/x - x sin2 o)(1- x2sinZ8o)-'/ z .(5)The solution of Eq. (5) for the soundspeedin the skulllayer isc : c0( a stnaO0)' /aC.(6)Normal incidence transmission and reflectionlosses(analytical mode0We seek an aralytical representation for humanskullsof the transmissionand reflectionof near-normalincidence ultrasound. This analytical model was firstused, together with values of skull parameters that arereported in the literature, to obtain an estimate of theacoustical properties of the skull samples that wereto be measu.red. These calculationstold us how muchThe phase speed is found from the insertion-lossphaseangle versus frequency data. Consider a layer ofthicknessh and soundspeed c immersed in water havingsound speed co.Let the angle of incidence in water be8o and the off-normal angle in the skull layer be 8 .The phase angle in degrees of the insertion loss isthe difference between the increase in phase of soundtraveling throughthe skull and the increase in phaseof soundtraveling through water displaced by the skull.J. Aco at. Soc. Am., Vol. 63, No. 5, May 1978dynamic range and frequency resolution would be required of the measurement apparatus. After the measurements were completed we used the model to calculate the acoustical properties of three of our skullsamples, using our own measured skull parameters.The parameters used in this calculation are listed inTable II and the calculations themselves are plottedtogether with the measured properties that correspondto them.

ofthehumanskullII.Parameters1580D. Scattering and absorptionlossesin diploe-analyticalof four model skulls.considerationsInnerOuterThe diptoe layer usually found in adult skull is cancellous bone, having a blood and fat-filled porous 9x1050.010.12 (l Fa) e0.011.706.002.00model 41.702.502.00model 120.600.000.10Density(g/cm3) ture.Sound speed(cm/s)bLoss factorThickness--model6The dimensionsof the blood and fat-filledinclu-sions are random, and an average thickness in the directionnormalto the surfaceforsomeskullsis about0.6 mm (for normally dense diploe skull types), whiletheir average width in the direction parallel to the surface is somewhat larger.Inclusions for various diseaseeF is frequencyin MHz. (SeeEq. 14.)states may become larger on the average, giving the entire diploe a spongy consistency, and the solid ivorytables may erode down to the diploe. The wavelengthcorresponding to a typical diagnostic ultrasound frequency of 1 5 MHzis 1.0 mminwater,so that for thisfrequency the dimensions of the inclusions are equal toThere is negligible conversionto shear waves in thelayers of skull whenthe incidenceangle is within about20ø of normal, (measurementsmade by us in the courseof this studybut not includedbecauseof spacelimita-p and bulk modulus B of blood differ greatly from thedensity and bulk modulus of cancellous bone, diagnosticultrasound will be severely scattered by these inclusionsScattered sound energy would be effectively lost fromthe transmitted beam, thereby causing insertion loss.(mm)aValues taken from Table I. Values estimated from Tables III and IV.or smaller than a wavelength.tions) so we will model only longitudinal waves. Skullsare generally constitutedof three relatively homogeneous layers: the outer and inner tables of solid ivorybone, andthe central layer of diploe of cancellousbone. The outer and inner tables have only slightlyScattered sound power is proportional to the squaredrelative difference of the mechanical properties of theinclusions from the mechanical properties of the matrixin the frequency range where the wavelength is morethan threedifferent specific acousticimpedanceand relativelylow soundattenuationcompared to diploe. The diploelayer has a lower specific acousticimpedance,andalarge and highly frequency-dependentattenuation. Thetransition regions are undulatingand variable.The impedanceequivalent network of three paralleland plane layers, where each layer has different acoustical properties, is shownon Fig. 3. Each of the threeances for jth layer are(7)where b is the complexsoundspeedof the jth layerandh is its thickness. Absorptionis accountedfor byan imaginary factor of the bulk modulusB, as shownin Eq. (8), where c is the magnitudeof soundspeed.The commonly measured pressure attenuationfactora is relatedto the factor , as shownalsoin Eq. (8),b --B/p c (l i ;) ,o f /c .(8)sure, namely, twice the incident soundpressure PlacoThe sum of the incident and reflected pressures at theouter surface of the outer table appears across theterminals Of the T network that represents the outerThe transmittedsound pressure appears acrossthe T network that represents the inner table. Theequivalent network is terminated at both ends by a re-sisrive impedanceequal to the specific acoustic impedance of water, in which the skull samples are immersed.J. Acoust.Soc.Am., Vol. 63, No. 5, May 1978of the inclusion.Forthe(, p/p)2:(1 - pi/p,,,)2:0. 169 ,(9)wherePtis thedensityofincludedbloodandfat (1.03g/cm3) andPmis the densityof the bone-bloodmatrix(1.75 g/cm3 computedfrom dataof TableI). For thebulk modulus, this squared difference is(AB/B)z (1- BJBm)z 0.589 ,(10)whereBeis thebulkmodulusofincludedblood(Bt pic from data of Tables I and IV).to the differenceThe scattered power dueof bulk modulus is 3.5 times greaterthan that due to the difference of density. Therefore,we will consider only scattering due to difference ofbulkmodulus.The intensity abroption coefficient that representsscattering losses due to bulk modulusdifference onlyhas beenworkedout by MasonandMcSkimin. Theirresultis 4 ' f x- (&B/B) ,The network is excited by the blocked acoustic pres-table.the diameter 2.54 10 øgbar)z andB . is the bulkmodulusof theblood-bonematrix (B. p cZ 1.09 10tt / bar computedZ ipyb tan( fh/by) ,Z ip b csc(2 fh/b ) ,timesdensity, this squared difference isseries-connected T networks models a layer with twoseries Z andoneshuntZ' impedance.t Theseimped-Since both the density(11)

1581F.J. Fry andJ. E. Barget:Acousticalpropertiesof the humanskull1581IOO0900800/-x?'.,'/,,,1-7oo 'rFIG./ X .-'/ . /500INSERTIONLOSSZX4.Measuredacousticalproperties of s U - amp[e No. 6,compared with calculated properties of model No. I.n-- 500 ,/Z4OO2.42 5I0.5It.O3001.52.0FREQUENCY (MHz)whereXis thesoundwavelengthand is theaverageinclusionvolume.The normalizedvariancein decibels per unit length of travel in diploe becomesof inclusionIL/I 11.5F dB/cm, F F ovolumes is fl.(12)The factor /] in Eq. (11) is a necessarygeneralizationof Mason and McSkimin's result, because they assumedsuch a narrow distribution of inclusion volume (distribu-tion in diploeis clearly not narrow.) We assumea Rayleigh distribution so that 4/ .The insertion loss across a layer of thickness I isrelaled to the intensity absorptioncoefficient byIL - 10loge- ' 4.34 ml 8.68 al.(13) 11.5J F dB/cm, F Fo ,(14)whereFo (c/3 l)x 10s MHz.E. Physicaldescriptionof skull samplesThe mass density and thickness were measured onsome of the human skull samples to provide data necessary for compw:ation of the acoustical properties ofskulls within the francework of the proposed three-element transmission-line model Where possible, thesemeasurementsweremadeon the individualskulllayers (outer ard inner ivory tables and diploe). ThickNumericalvaluesfor the insertionlosscan be obtainedby substitutingEqs. (10) and (11) into Eq. (13), togetherness measurements were made using a linear-scalecomparator with markings spaced 0.1 mm apart thatwith the following experimentally determined parameters:allowed estimating dimensions to within ñ 0. 02 min. ,6 (0.06)s 1.13x10- cm ,X c/f Z. SxlO /.f .The result is I.L/I 11.5 dB/cm, where F is the frequency in MHz.that recorded in the literature. The two diploe mea.surements which are at the high side of other re-porteddata, were for the very denselayers, We didThe scattering loss is based on Rayleigh scatteringtheory, which is valid for frequencies low enough sothat the inclusionThe average density of the outer table shown in TableI is similar to those recorded in the literature; ourinner table average density is somewhat higher thandiameteris less than about one-thirdwavelength of sound. The upper frequency f' of thisvalid region for inclusions with average diameter d 0.6mm in a matrix with soundspeed2.5x10 cm/s is[ --c/not compute densities for skull components that werenot intensively .,.tudied(randomlyselectedfrom thoseskullsin which:tufficientthicknessexistedto obtainsamples that could be handled)for their acousticproperties.II.RESULTSA.Measured reflection3d 1.3 MHz. Therefore, the calculated loss per unitdistance can be expected to increase as the fourth powerof frequency only at frequencies lower than 1.3 MHz.At higher frequencies, the scattering loss saturates,and the loss per unit distance will increase as the sec-The measured and computed acoustical propertiesare shown on Fig. 4 for skull No. 6, which is repre-ondpowerof frequency. The theoretical scatteringlosssentative of aduR parietal bone since it is almost 1 cmJ, Acoust. Soc. Am., Vol. 63, No. 5, May 1978and transmissionlosses

humanskull7Oi306OIREFLECTIONLOSS15821200I 2.57.105cm/sec)lOOOX/I -MEASUREDCALCULATED s of skull sample No. 4,compared with calculated proper-400ties of modelNo.II.20020-z\\10----, oMEASUREDI I0.5 .o .5-2oo2.0FREQUENCY (MMz}thick and has a 6-mm-thicktion the transmission-linediplee layer.For computa-model was used with mea-quite linear, and the phase speed of the composite skullsured parameters that are summarizedin Table II.The insertionloss oscillatesThe measured sound phase shift caused by insertionof the skull is also plotted on Fig. 4. The data areabout a value of 6 dB atfrequencies lower than about 0.5 MHz, where reflectionof soundis the principal cause of insertion loss. Atsampleis calculatedfrom Eq. (6)to be 2.42x10s cm/s.Departures from phase linearfry with frequency thatindicate dispersion are small over the frequency rangefrequencies between about 0.6 and 0.9 MHz, the absorption loss in the diplee layer begins to limit soundtransmission, so the oscillations are damped out and theinsertion loss increases linearly with frequency. Atabout 0.9 MHz, the scattering loss in the diplee layerbegins to limit soundtransmission, so the insertion lossbegins to increase as the fourth power of frequency.At frequencies greater than about 1.3 MHz the wavelength of sound in the diplee becomes less than threetimes the characteristic diameter of the inclusions,fromcausing the scattering-lossquencies below about 1.3 MHz, suggesting once morethat the value used in calculation for absorption lossmay have been too low.mechanism to saturate.Thereafter, the insertion loss increases only as thesecond power of frequency. The calculated values of insertion loss are lower than the measured values by about3 dB, suggesting that the values of absorption loss usedin the calculation may be too low; otherwise the twocurves are quite similar.Thedg.reflectionlossvariesAt low frequencies,fromabout3 to about15the resonances are closelyspaced in frequency, because the full skull thicknessparticipates in the reflection process. At frequenciesabove about 0. 7 MHz, where diplee losses dominatesound transmission, resonances are seen only in theouter table. These resonance peaks are widely separated because thinner skull sections are participatingin the reflection process. The calculated and measuredreflection-loss plots are qualitatively similar, althoughtheir high-frequency oscillations occur prugressivelymore out of phase. Evidently, the outer table thicknesswas not accurately measured at the point of sound transmission.J. Acoust Soc. Am., Vol. 63, No. 5, May 19780.5to 1.4MHz.The measured acoustical properties axe shown on Fig.5 for skull No. 4, which is representative of adult temporal bone since it is about 6 mm thick and has a 2.5-mm-thick diplee layer.Insertion losses are similarto those for the thicker skull at frequencies below about0.7 MHz, but the sharp increase due to scattering lossin diplee is nearly absent. Again, the calculated lossesare about 3 dB smallerThereflectionlossthan the measuredvariesfromaboutlossesat fre-20 to about4dB. The lower internal losses due to thinner dipleeallow closely spaced resonance peaks to appear at higherfrequencies than for the thicker sample. Again, themeasured and calculated reflectionlosses are in quali-tative agreement, but the spacing of resonance peaks issomewhat different. This result suggests that the layerthicknesseswherethe sound was transmittedaredif-ferent from where they were measured.The measured sound phase shift caused by insertionof No. 4 skull is also plotted in Fig. 5. We see that theskull is almost completely nondispersive over the frequency range extending from 0.3 to 2.0 MHz. Theplmsevelocityin this frequencyrangeis 2.57x 10s cm/s.The measured acoustical properties are shown on Fig.6 for skull No. 12, which is representativeof infantbone and is only 0.74 mm thick and has no diploe

1583F.J. Fry andJ, E. Barger:Acousticalpropertiesof the humanskull15837O'OFI/IREFLECTIONLOSSI --- CALCULAT[O20//' / /--MEASURED 7ooq600// /soo FIG.6.Measuredacousticalproperties of skull sample No. 12,compared with calculated properties of model No. IV.PHIS[SmFT o2.26105cm/ c) 0.5 CALCULATEDj -i.o1.5;2.0FREQUENCY (MHzllayer. Insertion loss is very low over the entire frequency range, reaching a maximum value of only 4 dBin the neighborhood of 1.0 MHZo The calculated insertion losses agree with the measured losses to withinabout 1 dB. The absence of diploe completely eliminatesthe large increase in loss with increasing frequency.The measured reflection losses vary from about 3 toabout 20 dB. These losses are lowest at about 1.0 MHz,where the transmission losses are greatest. The firstthicknessresonance,andthe onlyonelyingwithinthemeasurement frequency band, is seen at 1.9 1V[Hz.Measured and calculated values agree within about 2dB overthe entiremeasurementband.The measured sound phase shift caused by insertionof the skull is also plotted on Fig. 6. The data arelinear, indicating nondispersive transmission acrossthe measurement band. The phase speed for this sampie is lower than those for the adnlt skull sampies,are shownon Fig. 7, where they axe compared withtwice the one.way loss data. The data for the one-wayinsertion loss is the average of four separate measurements. AveragLngremoves the smaJl-scale fluctuationswith frequency. The measured two-way loss differsfrom twice the s.verageone-wayloss only in small-scalefluctuations.C. Experimentallconfirmation of dipole scatteringWe have hypothesized that sound in a collimated beampassing through

human adult skull losses is the middle layer (diploe) of cancellous bone. This study corroborates previous work on insertion loss as a function of frequency for composite skull. The study provides new quantitative information on the acoustic scattering properties of diploe, scound velocity, and dispersion in composite

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