ISSN 0006�3509, Biophysics, 2014, Vol. 59, No. 3, pp. 447–452. © Pleiades Publishing, Inc., 2014.Original Russian Text © A.A. Anosov, I.S. Balashov, R.V. Beljaev, V.A. Vilkov, R.V. Garskov, A.S. Kazanskij, A.D. Mansfel’d, M.I. Shcherbakov, 2014, published in Biofizika, 2014,Vol. 59, No. 3, pp. 545–551.

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A change in the temperature of brain regions comesto be an important diagnostic parameter [1]. For mea�surement of deep temperature, noninvasive methodsare developed: magnetic resonance (MR) thermome�try [2] and ultrahigh�frequency (UHF) thermometry[3, 4]. Ideally, MR thermometry will allow completelysolving the problem of reconstructing the spatial dis�tribution of deep temperature of the brain, but thismethod requires expensive equipment, trained per�sonnel and specially prepared facilities. UHF ther�mometers are substantially cheaper, they can be usedby medical personnel, but they require specialshielded rooms. However, equipment designers [5]assert that the high noise immunity of their deviceallows using it in rooms without shielding. They do notdisclose their secrets: possibly, the device uses a fre�quency range in which radio signals are not transmit�ted. We propose to use, for measuring the deep braintemperature, acoustic thermometry. This method isbased on registering the own thermal acoustic radia�tion of the human body in the megahertz range [6, 7].Registration of acoustic signals does not require spe�cial rooms, the measurement accuracy (in a timeabout 20 s) makes tenths of a degree, while the milli�meter range of acoustic wave lengths provides a betterspatial resolution than the one that can be obtainedwith UHF thermometry. Note that registration of theown thermal fields of the human organism, withoutany kind of external impact, is perfectly safe forpatients. A shortcoming of the proposed method in

measuring the deep brain temperature is that theacoustic signals are strongly attenuated in passingthrough the skull bones. Together with the BurdenkoInstitute of Neurosurgery, we have performed exami�nations of intensive care patients who partly lackedthe skull bones. For independent temperature mea�surements we used infrared (IR) thermometry. Bythis method it is possible to register the surface tem�perature of skin at millimeter spatial resolution withaccuracy of hundredths of a degree [8].

The task posed in the work consisted in using thedeep (acoustic) and surface (IR) measurements toreconstruct the temperature profile in the brain depth.

Thermal acoustic radiation arises as a result ofthermal motion of atoms and molecules of matter. Thepressure created by such acoustic waves comes to be anoise signal with zero mean. In order to obtain mean�ingful information, they measure the mean squared

pressure By the Rayleigh–Jeans law, the magni�

tude of thermal acoustic radiation emitted by anacoustic black body of temperature T in frequencyrange Δf equals

(1)

where k – Boltzmann constant, c – sound velocity,ρ – density of medium and f – radiation frequency.The mean squared pressure of thermal acoustic radia�

p2⟨ ⟩ .

p2⟨ ⟩

p2⟨ ⟩ 4πkTρf2

c�����������������= Δf,

Acoustic Thermometry of the Patient Brain with Traumatic Brain Injury

A. A. Anosova,b, I. S. Balashovb, R. V. Beljaevc, V. A. Vilkovc, R. V. Garskovd, A. S. Kazanskija, A. D. Mansfel’dc, and M. I. Shcherbakova,d

aKotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, 125009 Russiae�mail: anosov@hotmail.ru

bSechenov First Moscow State Medical University, Moscow, 119992 RussiacInstitute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia

d“IRTIS” Ltd., Moscow, 105120 RussiaReceived April 22, 2013; in final form, January 14, 2014

Abstract—Non�invasive deep brain acoustic thermometry is carried out for two patients at Burdenko Neu�rosurgery Institute. This method is based on the measurements of the own thermal acoustic radiation of theinvestigated object. These two patients have got the brain injury. Some of their skull bones are absent. Infraredthermometry was also used to measure the surface temperature of the forehead skin. On the basis of the exper�imental data the temperatures deep within the brain were reconstructed. The values for the two patients areequal to 37.3 ± 0.7 and 37.0 ± 0.3°C.

Keywords: brain temperature, thermal acoustic radiation, temperature reconstruction, acoustic thermometry

DOI: 10.1134/S0006350914030026

COMPLEX SYSTEMS BIOPHYSICS

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tion received by a round sensor in homogeneousmedium is set by a formula [6]:

(2)

where S is sensor area. At a temperature of 300 K fortypical parameters of an acoustic thermometer (S =

1 cm2, Δf = 1 MHz) the square root of makesabout 5 ⋅ 10–3 Pa.

For measurements of thermal acoustic radiation weused a multichannel acoustic thermograph [9–12]developed in IAP RAS (transmission band 1.2–2.7 MHz, threshold sensitivity at an integration timeof 10 s, 0.3 K). In acoustic measurements, low�viscos�ity sonographic gel (OOO Gel’�Medika, Russia) wasapplied onto skin. The received acoustic signals wereconverted into electric one, which were amplified,passed though a quadratic detector and averaged witha time constant of 30 ms. From the thermograph out�put the signals were fed to a 14�bit multichannel ADCE14�140 (ZAO L�Card, Russia, www.lcard.ru) at adiscretization frequency of 1 kHz per channel and intoa computer. An ad hoc program performed furtherdata averaging.

The surface temperature was measured with a por�table computer thermograph IRTIS�2000 (OOO Irtis,www.irtis.ru) with a temperature drop sensitivity of0.05 K (at the 30°C level), which picked up thermalelectromagnetic radiation in the 3–5 μm [13]. To add,use was made of an IR ear thermometer.

In reconstruction of the distribution of deep braintemperature, use was made of the equation of heatconductance with account of blood flow, proposed byPennes [14] for human body:

(3)

where t is time, x – axis directed into the head (x = 0 –body surface coordinate), T(x) – temperature profile,Td – deep temperature (temperature of inflowingblood), η – specific blood flow, a2 – temperature con�ductivity coefficient. Therewith the temperature dis�

tribution was held to be stationary: Bound�

ary conditions were defined by the head surface tem�perature T(0) = Ts, which could be different atdifferent points, and deep temperature T(∞) = Td. Theuse of such boundary condition is connected with thefact that thermal acoustic radiation coming from thedeep regions of the brain is practically completelydamped (see below). Under such conditions a solutionof equation (3) will be the temperature distribution:

(4)

p2⟨ ⟩ kTcρs

�����������Δf,=

p2⟨ ⟩

∂T∂t����� a2∂2T

∂x2������� η T Td–( ),–=

∂T∂t����� 0.=

T x( ) Tsxd��–⎝ ⎠

⎛ ⎞ Td 1 xd��–⎝ ⎠

⎛ ⎞exp– ,+exp=

where quantity

(5)

can be regarded as the characteristic depth of temper�ature distribution.

To calculate the acoustic�brightness temperature(quantity proportional to the mean squared pressure ofthermal acoustic radiation) we used the known expres�sion [15]:

(6)

where γ is ultrasound absorption coefficient (inten�sity). For simplicity let us take that this value does notchange in space. If we take the literature data for brain(see below) at a frequency of 2 MHz [16], the contri�bution of temperature at a depth of 20 cm (character�istic size of head) into acoustic�brightness tempera�ture makes 0.1%, which allows writing the upperboundary of integration as ∞ (see above). Usingexpressions (4) and (6), we can calculate the acoustic�brightness temperature:

(7)

The surface temperature of the head is non�uni�form. We supposed that the variation in surface tem�perature is connected with that the heated deep regionis closer to (or farther from) the surface. For tworegions with surface temperatures Ts1 and Ts2, the fol�lowing proportion is valid:

(8)

That is, the lower the surface temperature and thelarger the difference between deep and surface tem�peratures, the greater is the characteristic depth of thetemperature distribution.

In the work we examined two head zones with dif�ferent surface temperatures: Ts1 and Ts2. For acousticmeasurements, these surfaces were covered with gel ofambient temperature. The surface temperaturedecreased but in 5–10 min the situation was stabilized.The acoustic measurements yielded two acoustic�brightness temperatures TA1 and TA2. Therewith the Tsof the surface with gel was the same in either zone. Theuse of expressions (8) and (7) for TA1 and TA2 providesa set of three equations, solving which we can find Td,d1 and d2:

(9)

In two patients—A (woman of 25 years) and B(man of 30 years)—we measured the acoustic�bright�

d a

�����=

TA γT x( ) γx–( )exp x,d

0

∞

∫=

TA Ts– Td Ts–( )/ 1 γd+( ).=

Td Ts1–( )/d1 Td Ts2–( )/d2= .

Td Ts1–( )/d1 Td Ts2–( )/d2,=

TA1 Ts– Td Ts–( )/ 1 γ1d1+( ),=

TA2 Ts– Td Ts–( )/ 1 γ2d2+( ).=⎩⎪⎨⎪⎧

BIOPHYSICS Vol. 59 No. 3 2014

ACOUSTIC THERMOMETRY OF PATIENT BRAIN 449

ness temperature of the brain in the area where skullbones were absent. The patients had suffered cranio�cerebral trauma long ago, and the injured regions havebeen completely overgrown with skin. With the IRthermograph, we measured the surface temperature ofthe skin over the injured regions. Also, for comparisonwe measured the acoustic�brightness and surface tem�perature of an undamaged area of the forehead. Mea�surements of the forehead temperature were also per�formed in three examinees. In patients and examineesalike we measured the temperature in the externalauditory duct with the IR thermometer.

In Fig. 1 we present the thermograms of patient Aand patient B. In the patient�A thermogram on theforehead (under hair) we can see a region heated to35.3°C, which corresponded to the loss of frontalbone. It was at this site (where the brain was immedi�ately under the skin) that we performed the acousticmeasurements. In the patient B thermogram, in theupper right part of the head we can see a region heatedto 35.8°C, which corresponded to the region where apart of parietal bone was lacking. At this site (wherethe brain was immediately under the skin) we per�formed the acoustic measurements of the brain tem�perature.

24

28

32

28

34

37

31

36

25

40°C°C(a) (b)

Fig. 1. Thermograms of patients A and B made with an IRTIS�2000 IR thermograph. Patients were lying on trolleys, accessedfrom the head. White circles mark the sites of acoustic measurements.

40

35

30

25

20

152001000 15050

Time, s

(a)40

35

30

25

20

152001000 15050

Time, s

(b)

Forehead

Aco

usti

c�br

igh

tnes

s te

mpe

ratu

re, °

C

Aco

usti

c�br

igh

tnes

s te

mpe

ratu

re, °

CBrain

Brain

Forehead

Fig. 2. Time dependences of acoustic�brightness temperatures of the forehead and brain of patients A and B. Brain and foreheadmeasurements on patient A were in duplicate; on patient B the brain measurements were run four times and the forehead mea�surements, six times. Averaging, 5 s.

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ANOSOV et al.

The results of acoustic measurements are shown inFig. 2: the acoustic�brightness temperatures of thebrain and forehead in patients A and B. The measure�ment scenario was as follows: preliminarily, the sensorwas in a thermostat at room temperature, measure�ments lasted 50 s (from 80th to 130th second) duringwhich the sensor through the gel contacted thepatient’s skin, after which the sensor was placed backinto the thermostat. We can see the expected result:acoustic�brightness temperature of the brain (36.4 ±0.2°C in patient A and 36.8 ± 0.2°C in patient B) ishigher than the forehead temperature (30.0 ± 0.2°C inpatient A and 31.9 ± 0.2°C in patient B).

In Fig. 3 we show the results of measurements onall participants of the study; along with patients, pre�sented are data on the forehead temperature in threeexaminees C, D, E (men aged 19, 25, and 48). It is evi�dent that the acoustic�brightness temperature of thebrain in patients is on average 6.6 ± 0.3°C higher thanthe forehead temperature. The skin temperature in thearea lacking skull bones is 1.5 ± 0.1°C higher than theforehead skin temperature. No significant distinctionsare observed in either acoustic�brightness or surfacetemperatures of the forehead in patients and healthyexaminees. Note that the acoustic�brightness temper�ature of the forehead is lower that the skin surface tem�perature of the forehead. This is caused by that acous�tic measurements involved application of gel at ambi�ent temperature, which was then warmed. The

established temperature of the surface of skin with gel(29.0 ± 0.1°C in patient A, 30.0 ± 0.1°C in patient B;during measurements in patient B, the temperature inthe ward was higher) was lower than the skin tempera�ture. The acoustic�brightness temperature, accordingto (6), is determined by the temperature of both thenear�surface tissues and of deeper�lying ones. There�with, the greater is the absorption the stronger is thecontribution from near�surface tissues. Therefore,cooling of the skin by the gel has led to that the acous�tic�brightness temperature of the forehead was lowerthan the surface temperature of skin to which no gelwas applied, while the acoustic�brightness tempera�ture of the brain was higher than the skin surface tem�perature in the area devoid of skull bone. This is due togreater decay of ultrasound in the skull bones than inthe brain tissues.

To determine the deep temperature of the brain, itis necessary to know the absorption of ultrasound inthe brain and in the skull bones. We have used datapresented in the literature [16]: at a frequency of2 MHz the ultrasound (intensity) damping factors are0.34 cm–1 in brain and 12 cm–1 in skull bone. Damp�ing in the thin layer of skin was neglected. We alsoassumed that the main contribution to ultrasounddamping is made by its absorption. The measured dataand the results of reconstruction of the deep tempera�ture of the brain of patients are presented in the table.First of all, of interest are the reconstructed values ofdeep brain temperature, 37.3 ± 0.7 and 37.0 ± 0.3°C.It appears that such values can be deemed as normaltemperature of the brain. For comparison we mea�sured the temperatures of the external auditory ductwith a standard IR thermometer. This has also yieldedvalues that are not extremal: mean temperature (rightand left ear) in patient A was 35.9 ± 0.1°C, in patientB 36.2 ± 0.1°C, in examinee D 35.4 ± 0.1°C.

Of the two reconstructed characteristic depths ofthe temperature distribution, of most interest is the d2,determining the temperature profile in the regiondevoid of skull bone: for patient A it is 4 ± 3 mm, forpatient B, 1.0 ± 0.3 mm. The value obtained forpatient B appears underestimated. This can be con�firmed by calculating with (5) the blood flow rate(temperature conductivity coefficient in soft tissues isheld to be constant: a2 = 0.0012 cm2/s [17]). Theresults of calculating the brain blood flow rate were0.6 ± 0.6 min–1 for patient A and 7 ± 6 min–1 forpatient B. According to literature data [17], the brainblood flow rate ranges 0.5–1.0 min–1, which corre�

37

36

35

34

33

32

31

30

29363533 34

Forehead ABrain A

Aco

usti

c te

mpe

ratu

re, °

C

IR�temperature, °C

Forehead BBrain BForehead CForehead DForehead E

Fig. 3. Acoustic�brightness and IR temperatures ofpatients (A, B) and examinees (C, D, E).

Reconstruction of the deep temperature profile

Patient Ts, °CForehead Brain Reconstruction

Ts1, °C TA1, °C Ts2, °C TA2, °C Td, °C d1, mm d2, mm η, min–1

A 29.0 ± 0.1 33.9 ± 0.1 30.0 ± 0.2 35.3 ± 0.1 36.4 ± 0.2 37.3 ± 0.7 6 ± 3 4 ± 3 0.6 ± 0.6

B 30.0 ± 0.1 34.3 ± 0.1 31.9 ± 0.2 35.8 ± 0.1 36.8 ± 0.2 37.0 ± 0.3 2.3 ± 0.5 1.0 ± 0.3 7 ± 6

BIOPHYSICS Vol. 59 No. 3 2014

ACOUSTIC THERMOMETRY OF PATIENT BRAIN 451

sponds to the data for patient A. For patient B, theflow rate obtained by reconstruction is greater than thedata presented in the literature; this is caused byunderestimating the characteristic depth of tempera�ture distribution.

The errors in temperature measurements presentedin the table (columns 2–6) are standard errors. Theinaccuracies of reconstruction have been obtained bymodel calculations. Therewith as initial data we usednot the measured temperatures but random valuesnormally distributed with the means equaling themeasured values and rms deviations equaling the stan�dard errors of measurement. Instead of literature datafor damping factors we used random values normallydistributed with the means equaling the presented lit�erature data and rms deviations making 10% of themeans. Using 1000 realizations, we modeled a situa�tion of having not one but 1000 measurements. Calcu�lated by the data of this sample, the rms deviations arepresented in the table (columns 7–10) as reconstruc�tion errors. Therewith the distribution of deep temper�ature obeyed the normal law, the distribution of bloodflow was close to exponential, and the distributions ofcharacteristic depths were close to an Erlang distribu�tion.

In discussing the results, let us consider in moredetail the following question: Are the obtained tem�peratures (about 37°C) due to the consequences oftrauma in patients, or are such values generally char�acteristic of the human brain? By the data of protonMR spectroscopy [18] the average brain temperaturein five volunteers made 37.1 ± 0.41°C (a result gener�ally coincident with ours). This suggests that the tem�peratures we have measured in the brain of patients aremost probably not connected with earlier traumas butcome to be typical of the human brain. Indirectly thisconclusion is favored by the data of Fig. 3: the surfaceand the acoustic�brightness temperatures of the fore�head in patients and in healthy examinees do not differsignificantly.

Also demanding explanation is the obtained ten�fold difference in the patients' blood flow rate (0.6 and7.0 min–1), considering that the reconstructed deeptemperature practically coincide. In our opinion, the7 min–1 value is an overestimate (which is confirmedby literature data, see above) caused by limitations ofthe proposed model. The solution of set (9) for braintemperature Td and characteristic depth d2 of braintemperature distribution can be presented in the form:

(10)

where ΔTeff and deff are some effective values of theincrement of temperature (several degrees) and tem�perature distribution depth (several millimeters)respectively. These effective parameters are deter�

Td TA2γ1

γ2

���ΔTeff, d2+γ2

γ1

���deff,= =

mined by quantities that enter set (9). The

term comes to be a small parameter. In this way, thedeep brain temperature in the main is determined byits measured acoustic�brightness temperature plussome small addition, an error in determining whichdoes not entail substantial changes of the deep tem�perature. The characteristic depth of temperature dis�tribution is determined by the small parameter andupon random experimental errors may become extre�mally low (which does not tell on the accuracy ofdetermining the deep temperature). The blood flow

rate is proportional to and at an extremally

low d2 may assume too high values (which has hap�pened in reconstructing the temperature in patient B).Thus, the proposed model is not suitable for correctlyassessing the blood flow. Among the reconstructedparameters, significant is the deep temperature, andthe accuracy of its reconstruction is acceptable formedical purposes. The other characteristics are givenfor illustration, and the error of their measurementcomes as a reference parameter.

Let us note that deep acoustothermometry of thebrain in patients partly lacking the skull bones hasbeen performed for the first time. Along with that, weused surface IR thermometry. In essence, to recon�struct the deep temperature profile, we measured thesurface and the integral deep temperature. These datawere insufficient for finding the temperature distribu�tion. Therefore, the model included an assumptionthat the greater the difference in deep and surface tem�peratures, the larger the characteristic depth of thetemperature distribution. This requirement can belifted by using a multifrequency receiver of thermalacoustic radiation. Such a sensor is being designed inIAP RAS [19].

ACKNOWLEDGMENTS

The authors are grateful to I.A. Savin andG.A. Shchekut’ev for their help in organizing thestudy.

The work was supported by the Russian Founda�tion for Basic Research (13�02�00239) and the RFGovernment (11.G34.31.0066).

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γ2

γ1

��� 0.03=

η 1

d22

����∼ ,

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