PROCEEDINGS OF THE IRE

Absorption of Ultrasound by Tissues

and Biological Matter*H. P. SCHWANt, FELLOW, IRE

Summary-General principles which determine the frequencydependence of both absorption and velocity of ultrasound in matterare outlined and applied to cell suspensions and tissues. The mecha-nisms which are responsible in the biological case for the experimen-tally observed frequency dependence of ultrasonic properties are de-scribed. They relate predominantly to macromolecular components.Finally, the relationships which pertain to the propagation of ultra-sound in heterogeneous tissue complexes are discussed, and conse-quences for the medical application as a therapeutic tool are con-sidered.

B OTH electromagnetic radiation and ultrasoundhave found increasing use for therapeutic pur-poses after World War II. While the electrical

properties of body tissues anid pertinent applicationshave been summarized in another place, it is intenided inthis chapter to outline our present knowledge aibout ab-sorption of ultrasound in tissues and to see how suchknowledge pertains to medical applications.'

wTaX = aw + 2(aX)' 1

I + (coT)2

2 (wT)2c2 = Co2 + - (aX)'coc, - _ )2

(2)

(3)

where w is the anigular frequency 2irJ. The absorption isexpressed in terms of absorption per wavelength AX,a is inidicative of the possible presence of frequency inide-pendent absorption processes, not related to the exist-enice of a relaxation process, and (aX)' is the highestpossible value of aX. The inidices o and oo in the velocityterm c refer to very low or very high frequenicies, re-spectively. The corresponiding frequenicy dependenlce ofthe absorption per wavelenigth aX is illustrated in curvea of Fig. 1. For a broad spectrumii of time conistants, rep-

ABSORPTION AND VELOCITY OF ULTRASOUND INTISSUE AND BIOLOGICAL MATTER

The mode of propagation of sound in matter is com-pletely characterized by its coefficient of absorption andits velocity. The absorption coefficient is best defined by

I = Io exp (-,ux) (1)where Io stands for initial energy, I for energy at a dis-tance x from the initial site, and ,u is the absorption co-efficient. The equation assumes plane wave propagationi,i.e., considers only reduction of intensity due to trueabsorption processes and not due to spread of eniergycaused by divergenit characteristics of the beam. Theabsorption coefficienit is usually expressed either interms of neper per cm in accordance with (1) or indecibels per cm. Changes of velocity and absorptionwith frequenicy reflect the presence of processes of en-ergy tranisfer which require time. If such a process ischaracterized only by one relaxation time constant T,2both absorption and velocity follow the simple relationi-ships

* Original manuscript received by the IRE, September 1, 1959.This work was supported by the Office of Naval Research, ContractNo. 119-289.

t Electromedical Div., The Moore School of Elec. Engrg., Uni-versity of Pennsylvania, Philadelphia 4, Pa.

1 H. P. Schwan, "Alternating current spectroscopy of biologicalsubstances," this issue, p. 1841.

2 The time constant T can be defined, in general, as the time ne-cessary for the response to a step function cause to cover (1- Ile) ofthe difference between immediate and final response value.

100

Fig. 1-Sonic absorptioni per wavelength (aX) as a function of fre-quency f. Assumed are relaxation mechanisms, which are char-acterized by distribution functions of activation energies of coii-stant magnitude. (a) One time constant; (b) a moderate ralnge ofactivation energies; (c) a wide range of activationi energies. Bothordinate and abscissa are in arbitrary units.

reselntative of a uniform distribution of activation ener-gies ranginig from onle value to aniother, both velocityanid absorption coefficient appear less frequency de-pendent, as indicated by the curves b anid C.3 It is ap-parent that for a sufficiently broad distribution- func-

3 E. L. Carstensen anid H. P. Schwan, "Acoustic properties ofhemoglobin solutions," J. Acoust. Soc. Amer., vol. 31, pp. 305-311;March, 1959.

1 9591959

PROCEEDINGS OF TIHE IRE

tiOln of activation energies an almost linear frequenicydependence of the absorption coefficient can be ob-tained over a very wide range of frequencies.The frequency dependenice of the absorptioni coef-

ficient of most investigated tissues closely follows thisbehavior. It is characterized by a power functioni whoseexponent varies betweeni I and 1.3. Actual values ofabsorption have beeni reviewed by Goldman anid [lueter4atnd are sunmmarized in Table I for the three imajorclasses of tissues.

TABLE IABSORPTION COEFFICIENTS AND V1ELOCITWS FOR MAJOR CLASSFS

OF BODY TissUIs

1) Absorption coefficienit (eper petr cm) 1 Illc 2 me

Muscle (representative of all soft tissnieswith high wxater conitentt) 0.3 0.5

Fat 0.07 0.2Bone 0.6-2

4 mmmc

1

0.6

2) Velocity ._______

MAuiscle 1570 1 20 mi/SecFitt 1440Bonie 3360

The munscle data are represenitative of all soft tissuies withl highwxrater conitenit.

Application of (3) shows that the frequency de-pendenice of the velocity of sounid should be extremelysmall ini comiiparisoni with the velocity itself. TIhe valid-ity of this statement should nlot be impaired if a otne-time constatnt relationi of the type giveni inl (3) is re-

placed by a relationiship which iniclud(les maniy timiie coII-stants.3 Indeed, experimenital data support this poitit ofview: The velocity is indlependenit to a fraction of a percenit from frequenicy.3 Actual values are also givemi illTable I. For ac more detailed discussioni of velocity datain tissue we refer particularly to Frucht's work.5 Thedata in Table I demonistrate that the velocity of all softtissues is niear that of water. Differenices up to 10 percenit reflect the influence of the solid comnponienits in-volved in the structure of tissue. The similaritv of thevelocity values with those of water is due to the highwrater cotntent of most soft tissuLes.

MIECHANISMI OF ULTRASONIC ABSORPTION IN TissUIEAND SUSPENSIONS OF BIOLOGICAL CELLS

The statements formulated above, as related to thefrequency dependenice of absorptioli characteristics, ex-

plain observed data inl terms of a broad spectrum of dif-ferenit processes and related activationi energies. Theobserved frequelncy dependenice thus appears well ex-

4D. E. Goldman and T. F. Hueter, "Tabular data of the velocityand absorption of high-frequency sound in mammalian tissues,' J.Acoust. Soc. Amer., vol. 28, pp. 35-37; January, 1958. "Errata," vol.29, p. 655; May, 1957.

5 A. H. Frulcht, "Die Schallgeschwindigkeit in menschlichen undtierischen Gewebeni." Z. ges. exp. MYed., vol. 120, pp. 526-557; Max',1953.

plained and reasonable, considering the com-iplexity ofbiological structure. However, the advaniced mathe-matical argument does Inot say anything about theorigin of the related relaxation processes. Pertinienit workwill be summarized in this sectioni.The absorptioni of sound by blood has beeii inivesti-

gated throughout the frequeiicv range fromi 0.7 to 10mc extensively by Carsteniseii and Schwan.6-7 The re-sults of this investigationi demonstrate:

1) Most of the absorptioni of ultrasoniic waves inblood arises from the presence of the protein coni-tent of the blood. This could be verified by show-ing that the predominant part of the absorptioniis in proportion to the over-all protein conteint anidnot to the cellular concenitrationl.6

2) A small but nioticeable fraction of the sonic ab-sorption is due to the cellular organiization ofblood, i.e., due to the presenice of erythrocytes and,consequently, is niot of molecular origin. This ab-sorption contributioni is due to the relative move-menit of the cells against the surrouniditng fluidswhich result from differences of specific weight.Anl observed decrease of this absorptioni conitribu-tionI at high cellular conicenitrationi levels reflectsthe faclt that the possibility of relaltive Inovellmenltbecomiies inhibited in the iinlllediitte neighborhoodof other cells.

Further data concerning the mechanism of absorp-tioII were obtainied fromi anl inivestigationi of the acousticproperties of albumnin.8 The data obtained with albunlinand hemoglobini seem to support the concept of ani ab-sorption which is inidepenident of the particular imatcro-molecule ilnvolved, if expressed in ter-mlls of absorptionper gramii proteini miiatter in a givei1 volumine of water.The detailed hemnoglobini study miienitionied above' lenidsfurther support to the formulated mal<thematical analy-sis in term-is of the preseince of a broad spectrumn of tim-iieconistanlts. It was also possible to demolnstrate that thesmall but meeasurable change in velocity with frequencyagrees with values predicted froimi the absorption behav-ior of hemnoglobini on- the basis of a relaxation theorywhich assumies a broad spectrumn of timile constants.3On the other hland, it becamiie obvious that the blood

data alonie couldl llot explain the imiechaniismi of sonlic ab-sorptioni in tissues. Either aniother mechanism, otherthan the molecular onie, whiclh is niot very nioticeable inblood, cointributes strongly to the tissuie properties, orthe tissue proteinis must be assumed, specifically, to ab-sorb much imiore stronigly thami albumin anid hemnoglobinin order to accounit for observedI high tissue absorptioni

6 E. L. Carstensen and H. P. Schwvan, "Absorption of soLiuid aris-ing from the presence of intact cells in blood," J. Acoust. Soc. Amer.,vol. 31, pp. 185-189; February, 1959.

E. L. Carstensen, K. Li, and H. P. Schwan, "Determination ofthe acoustic properties of blood and its compotnenits," J. Acoust. Soc.Amer., vol. 25, pp. 286-289; March, 1953.

8 H. P. Schwan and E. L. Carsteniseni, "Advantages anid lin-iita-tions of ultrasoniics in medicinie, " J. A wner. lel.{ sc4ss., vol. 149, pp.121 125; May, 1952.

1960 Ntovember

Schwan: Absorption of Ultrasoutnd by Tissues and Biological Matter

values (Table 1). The latter conclusion found support instudies concerned with the absorption of cell nuclei insolutions.9 In this case, the absorption per weight per-centage solid compound (proteins and other nuclearmolecules) was found to be very much higher than in thecase of albumin and hemoglobin. A detailed study ofliver tissue substantiated this result.10 Liver tissue wassubjected to repeated fractionation so that, at first, arather coarse separation of the tissue into smaller cellcomplexes was accomplished. Then the division wasfurther carried down in progressive steps, so that,eventually, even subcellular components, such as mito-chondria and cell nuclei, were destroyed. Finally, aa solution of liver tissue proteins, which is free of allcellular or subcellular organization, was obtained.Throughout this process, ultrasonic absorption andvelocity were monitored under a variety of conditions.The following conclusions were reached:

1) At least 80 per cent of the total tissue absorptionis of molecular origin, i.e., remains unchanged asthe destruction of tissue structure is advancedstep by step. The small change of about 20 percent of the absorption takes place at the veryinitial step of tissue grinding and therefore is dueto the initial existence of relatively large struc-tures, such as pieces of connective tissue, etc.

2) Changes of the molecular constituents may be af-fected by variation in hydrogen ion concentration(pH). While the absorption coefficient responds tothese changes in a very pronounced way, thecharacteristic of the frequency dependence is notaffected. This indicates that the affected changesdo not alter the fact that a broad spectrum of ac-tivation energies participates in the absorptionmechanism. Other changes in the absolute valueof the absorptioni coefficient can be affected bythermal denaturation of the tissue proteins.

In summary, by far the largest part, of the ultrasonicabsorption of tissues arises on a macromolecular level.It is due to the existence of a broad spectrum of thus farunspecified transfer processes associated with the pres-ence of the macromolecules. While the specific absorp-tion per weight percentage macromolecule content issimilar for albumin and hemoglobin, it is much largerfor tissue proteins. It is also subject to considerablechange with the chemical environment of the proteinsand denaturation.

PROPAGATION OF SOUND IN HETEROGENEOUSTISSUE COMPLEXES

One of the foremost applications of ultrasound is inphysical medicine. It is utilized to affect heating andevoke consequent physiological responses well below

9 A. Smith and H. P. Schwan, "Ultrasonic absorption and veloc-ity of sound of cell nuclei," Proc. Natl. Biophysics Conf., Columbus,Ohio; March, 1957. (Abstracts, p. 66.)

10 H. Pauly, "Absorption of Ultrasound in Biological Media,'presented at the Internatl. Conf. on Ultrasonics in Medicine, LosAngeles, Calif.; September 6-7, 1957. (Abstract.)

the surface of the human body. This is found to bebenieficial in the treatment of a variety of rheumaticand arthritic conditions. The superiority of ultrasoundfor this purpose in comparison with other forms of dia-thermy i.e., ultrashort wave and microwave therapy,may be best illustrated by means of Fig. 2.11 In it the

,IC

dcm

us

10

t.OF

0.7-1 7 a

0.1 1.0

Acm (IN TISSUE)

MW-~~~~~~

I70-1.0 tO

71cm (IN TISSUE)

(a) (b)Fig. 2-Depth of penetration vs beam divergenice for ultrasoniic (US)

and microwave (MW). The data pertain to muscular tissue as themedium of propagation. A reflector diameter of 5 cm is asstlliedin both cases. (Reprinted by courtesy of the American Journal ofPhysical Medicine.)

penetration, which can be achieved with either of theseforms of energy, is plotted on the ordinate and the angleof divergence, which characterizes the beam of eitherform of radiation, on the abscissa. The divergence per-tains to the "distant field." It is only well defined suf-ficiently far from the source so that it is meaningful tocharacterize a monotonously declining field in termls ofits constant spreading characteristics.12 The data referto "piston" sources, i.e., are based on the assumptioni ofa plane source of radiation from whose individual partswavetrains originate all equal in intenisity and phase.It is assumed further, that the size (diameter) of thefield spread, i.e., the smaller angle of divergence, isachieved with larger diameter, or aperture, of thesource of radiation. The penetration data pertain tomuscular tissue as a representative for all tissues withhigh water content. Fig. 2 demonstrates that it is mucheasier to combine good penetration with practical beamdefin-ition with ultrasound than with electromagneticradiation.

Another major advantage of ultrasound results fromnthe aforementionied observation that the velocity ofsounid is nearly the same for all soft tissues. The char-acteristic impedance Z, which is determined by theratio of sound pressure and particle velocity, is predom-

11 H. P. Schwan, "Biophysics in diathermy," in "TherapeuticHeat," S. Licht., Ed., E. Licht, New Haven, Conn., vol. 2, pp. 55-115; 1958.

12 In the "distant" field the intensity decreases inversely with thesquare of the distance, duie to the constant spread of the beam. Inter-ference of different waves, originating from different parts of theradiant source, cause periodic fluctuations in the "near" field. Theseparation between near and distant field may be defined by the dis-tance D2/X where D is the diameter or the effective aperture of theradiaiit source, and X the wavelength of the radiation.

1959 1961

PROCEEDINGS OF THE IRE

inanitly determinied by the velocity and is onily to aminor extent dependent on the absorption coefficienit,for the values foutnd to be typical for tissues. Henice,aniy fractionial reflectionl of eniergy

Z1- 2

Z1 + Z2

which arises at the interface separatinig two differenittypes of soft tissue, will be a very minior onie for soutndpropagated into the human body." This, by nio meanis,holds for the case of electromagnietic radiationi, aspointed out in another place in this volume.' The dis-tribution of heat sources resulting from the applicationof a plane wave of ultrasoniic energy traveling throughvarious tissues, such as skin, subcutaneous fat aiidmuscle tissue, consequently, can be predicted imnmedi-ately from the absorptioni coefficients of these tissues.This is done simply by allowinig for the atteiluation ofthe sound wave which takes place in each tissue and re-alizinig that the differenitiated form of (1)

dI--- =IuIo exp (- /x)

dX (4)

is e(qual to the heat rate. Pertinent calculationis havebeeni carried out by Schwan, Carstensen and Li.'4 Fig. 3summmarizes some typical data which result from suchcalculationis and pertain to the ratio of the heat de-veloped in tissues benieath the subcutaneous fat layer tothe total heat made available from the radiant source

to the body, i.e., including the heat developed in thesubcutaneous fat layer. This ratio has been termed"depth efficiency"" since it characterizes to what extentthe desired goal of developinig as much energy as possi-ble in the "deep" tissues beneath the subcutaneous fat isrealized. The heatinig in the fat is considered unimpor-tant and undesirable since it canniot be utilized to evokephysiological responises, such as dilatation of blood ves-

sels to the saime extent possible in muscular tissues. Fig.3 demonstrates that an ultrasonic frequency of about 1

mc, as presently applied in clinical practice, has ani ex-

cellent depth efficiency, while the microwave therapyused presently, operating at 2450 mc, fares very poorlyin comparison.'

The application of physical forms of energy for heat-ing purposes in medicine demanids that the power indi-cated and produced by the generating equipment can

13 This does not apply to the boundary between soft and hardtissues such as bone. Indeed, strong reflections and selective botund-ary heating take place under such circumstances. They are also par-tially due to the transformation of normal and longitudinal soundwaves into rapidly absorbed transversal "shear" waves.

1' H. P. Schwan, E. L. Carstensen, and K. Li, "Heatinig of fat-muscle layers by electromagnetic and ultrasonic diathermy," AIEETrans. on Commun. & Electronics, pp. 483-488; September, 1953.

0.6 1 2 3FREQUENCY (Mc.)

Fig. 3 Depth efficienicy of ultrasound (ratio of energy which reachesdeeper situated tissues to the total energy absorbed by the body).The parameter inidicates the thickness of the subcutaneouis fatlayer in cm. (Reprinted by couirtesv of E. Licht, pLublisher of"Therapeutic Heat," S. Licht, Ed., Nfew Haven, Coini., 1958.)

be identified, or is, at least, simply related to the eniergyabsorbed by the patietnt. If this is Inot so, dlifficultiesarise in relatiing instrument inidicated and biologicaleffective power. Reproducibility of patienit dose anddose rate may then be seriously imnpaired, makinig it im-possible to operate under controlled coniditiotns. It hasbeeni shown that the amounit of electromiiagnietic radia-tion which is absorbed by the human body is, in a verycomplicated manner, related to the totally availablepower.'5 This is a consequence of the fact that, (lepelid-ing oni frequenicy and thickniess of such tissues ais skillanid subcutaineous fat, the inptut wA7ave imlpedanice of thehumani body canl vary between the wa-ve impedanice ofair and values which are differenit fromii this by as mIluChas one order of magnitude. Ultrasoinic eniergy, oni theother hanid, if properly applied, is completely trans-mitted to the human bodv,16 establishing another ad-vantage of ultrasounid in comiparison with microwvavetherapy.

15 H. P. Schwan and K. Li, "The mechanism of absorption ofultrahigh frequency electromagnietic energy in tissues, as related tothe problem of tolerance dosage," IRE TRANS. ON MEDICAL ELEC-TRONICS, no. PGME-4, pp. 45-49; February, 1956.

16 TIo achieve this, it is necessary to avoid having even very thinilayers of air present between the sound transducer and the body suir-face. The sonic impedance of air is very different from that of thetissues and would establish a major impedance discontinuiity and,thereby effectively hinder the transfer of sonic energy. The necessityof maintaining good mechanical contact throughout the applicationof sonic energy is a disadvantage of sonic therapy. For a more de-tailed comparison we refer to Schwan, op. cit., footniote 11. Also seeH. P. Schwan, "The biophysical basis of physical medicine," J. Amer.M4ed. Assoc., vol. 160, pp. 191-197; January, 1956.

1962 JNovJembey