ime-resolved multidistance near-infrared spectroscopyf the adult head: intracerebral and extracerebralbsorption changes from moments of distributionf times of flight of photons
dam Liebert, Heidrun Wabnitz, Jens Steinbrink, Hellmuth Obrig, Michael Moller,ainer Macdonald, Arno Villringer, and Herbert Rinneberg
ear-infrared spectroscopy �NIRS� and imaging ofhe head offer the opportunity to provide clinicallyignificant data, e.g., brain tissue oxygenation, non-nvasively at the bedside. However, often suchIRS signals contain contributions from the brain asell as from the overlying tissue. Therefore im-roved instrumental approaches combined with ad-anced methods of data analysis must be applied toifferentiate intracerebral from extracerebral sig-als. There are two approaches based on diffuseeflectance for achieving such a differentiation: �i�easurements at various source–detector separa-
ions,1 �ii� time-resolved measurements.2 Photonsetected at greater distances from the source haveenetrated deeply into the tissue with a higher prob-bility than those detected at short distances. Anal-
A. Liebert �[email protected]�, H. Wabnitz, M. Moller, R.acdonald, and H. Rinneberg are with Physikalisch-Technischeundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany. J.teinbrink, H. Obrig, and A. Villringer are with the Department ofeurology, Charite, Humboldt University, Schumannstrasse 20-1, 10098 Berlin, Germany.Received 1 September 2003; revised manuscript received 19 De-
gously, photons detected after long times of flight onverage probe deeper tissue layers than early pho-ons. In this paper both approaches are combined.
The chance of retrieving useful information abouthe optical properties of the brain and overlying tis-ue from measured data depends on realisticallyodeling the light propagation in the head. For a
ather simple model—assuming a semi-infinite ho-ogeneous medium—steady-state as well as time-
nd frequency-dependent solutions of the diffusionquation are available3,4 and have been frequentlysed. However, it has been shown that the overly-
ng tissues of unknown optical properties contributeemarkably to the results of optical measurements onhe adult head.1,5,6 A two-layer model is a better, yetar from realistic, approximation of the adult head.olutions of the diffusion equation for a two-layerodel are derived for determining the optical prop-
rties of both layers.7–10 More realistically, the tis-ue interrogated by photons should be considered as
multilayered structure consisting of scalp, scull,erebrospinal fluid, and gray and white matter.11
In functional stimulation experiments, changes inbsorption may be of interest even when absolutehanges cannot be assessed. In such a case model-ng is much more straightforward. Recently, we re-orted on an approach to analyzing small changes inhe absorption coefficient in a multilayered tissue
odel by using measured distributions of times ofight of photons �DTOF�.2 This method relies onime-dependent mean partial path lengths calculatedy Monte Carlo simulations with assumed back-round optical properties of the tissue layers. Inhis analysis deconvolution of the measured DTOF byhe measured instrumental response function is re-uired. Such deconvolutions are difficult,12 in par-icular because of the limited signal-to-noise ratio ofhe measured DTOFs.
In the present study we propose a new method forstimating absorption changes at various depths bynalyzing the changes in moments of the DTOFs ofhotons recorded at various source–detector separa-ions, i.e., integral, mean time of flight, and variance.n contrast to DTOFs of photons, their moments caneadily be corrected for the instrumental response.he sensitivity factors that relate absorption changes
n different layers to observed changes in the mo-ents were calculated by Monte Carlo simulationsith assumed background optical properties for thearious head layers. Our method was validated bynalyzing simulated DTOFs.We applied our method to deduce changes in the
bsorption coefficient in various layers of the head ofealthy volunteers following intravenous adminis-ration of indocyanine green �ICG�, an absorbing con-rast agent. Previously several authors performedptical measurements on the head after intravenousnjection of ICG, showing that the washout of the dyean be monitored by optical techniques. The kinet-cs of inflow and washout of the dye may be used tossess the perfusion of brain tissue. NIRS of theead following ICG boli injected into the internal andxternal carotid arteries showed that a certain frac-ion of the recorded signal originated from the brainissue and that the sensitivity toward intracerebralbsorption changes increases with increasing in-eroptode distance.13 Cerebral blood flow can be as-essed with NIRS from the initial slope of thencreasing dye concentration in brain tissue following
bolus of ICG.14 This method of analysis was ap-lied to data obtained by NIRS on piglets,14,15 neo-ates,16 and adults.17 A similar approach wasested for estimating blood flow in muscles.18 Fur-hermore Hopton et al.19 derived cerebral blood vol-me by performing NIRS of the head followingpplication of a bolus of ICG and additionally moni-oring ICG concentration in the peripheral blood.
In neonates the influence of extracerebral tissuean be neglected because of its small contribution tohe overall changes measured. However, in adultshe measured NIRS signals originate from both in-racerebral as well as extracerebral compartments.revious studies were performed by using continuous
ight at single source–detector separation; hence dif-erentiation of intracranial and extracranial changesf absorption was impossible. Based on frequency-omain measurements on healthy volunteers, Kohl-areis et al.20 were able to determine absorptionhanges separately in two layers following an ICGolus. However, for data analysis the thickness of
he upper layer had to be assumed. In the presentaper we exploit additional information from time-esolved measurements to determine intracerebralnd extracerebral absorption changes without suchssumptions.
. Theory
e consider the propagation of photons through aemi-infinite, diffusely scattering, multilayered me-ium taken as a tissue model �Fig. 1�. There are
max � 1 homogeneous layers of equal thickness cov-ring the lowest, infinitely thick layer jmax. The re-uced scattering coefficient �s, j� and absorptionoefficient �a, j refer to layer j, and nj is the refractivendex that determines the speed of light cj in thatayer. Bundles of photons are launched into the tis-ue at the top layer � j � 1� and exit this layer at aocation separated from the site of entry by theource–detector distance r. The survival weight Wif each photon bundle is reduced along its travelhrough the tissue according to
Wi � W0,i exp���j
lij�a, j� , (1)
here lij is the total path length of the ith bundle inhe jth layer and W0,i its survival weight when onlyeflection and refraction at boundaries are taken intoccount.The mean partial path length MPPj of photons in
ayer j is defined as21
MPPj�r� � �lj�r� �
�i
lijWi
�i
Wi
. (2)
he mean partial path lengths may be used to derivemall absorption changes that occur in various layersrom changes A of attenuation measured at severalource–detector separations r:
A�r� � �logNtot*�r�
Ntot�r�� �
jMPPj�r��a, j. (3)
tot�r� denotes the total number of photons �integral�xiting the top layer at distance r from the launchingite, and Ntot* is the same quantity measured after ahange �a, j in the absorption coefficient of layer jccurred. Mean partial path lengths MPPj�r� can bealculated by Monte Carlo simulations for the as-umed background optical properties of the layerededium. They represent a matrix of sensitivity fac-
ors that transforms changes �a, j in absorption intohanges A�r� in attenuation.
For comparison we refer to an alternative method,ntroduced by Steinbrink et al.,2 to deduce changes inhe absorption coefficients �a, j from changes in therofile of the DTOF measured at a single source–etector separation r. To outline this method inrief, consider the corresponding distribution of
tt
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imes of flight of photons diffusely reflected from theissue. Each photon bundle with time of flight
ti � �j
lij�cj
s sorted into the time channel indexed by k, providedk � ti � tk�1. The time-dependent mean partialath length TMPPj,k traveling in layer j by photons ofime channel k is given by
TMPPj,k � �ljk �
�@i�tk�ti�tk�1�
lijWi
�@i�tk�ti�tk�1�
Wi
. (4)
n Eq. �4� the summation is restricted to those pho-ons that exit the top layer at time t within the time
ig. 1. �a� Head model consisting of nine homogeneous layersindexed by j� of the same thickness �2 mm�, located at a depth of� 2� j � 1� mm, covering a semi-infinite homogeneous bottom
ompartment � j � 10�. Also shown are the schematic trajectoriesf three photon bundles �indexed by i� leaving the top layer at theame location separated from the source by r �source–detectoreparation�. �b� Corresponding distribution of the times of flightf photons with Nk being the number of photon counts in the kthime channel tk � t � tk�1. The times of flight of the three photonundles considered are indicated.
i
nterval tk, tk�1�. From measured attenuationhanges Ak the changes �a, j in the absorption co-fficient of the various layers of the tissue model cane inferred from solving the system of linear equa-ions:
Ak � �logNk*Nk
� �j
TMPPj,k�a, j. (5)
k denotes the number of detected photons in the kthime channel and Nk* is the same quantity measuredfter a change �a, j in the absorption coefficient ofayer j occurred. Such an analysis of the full DTOFrofile can be extended in a straightforward mannero a multidistance method, i.e., considering a set ofifferent source–detector separations r.Apart from total photon counts Ntot�r�, we can ex-
loit higher moments of measured DTOFs to deducehanges in absorption occurring in various layers.t has been suggested2,22 that changes in the meanime of flight of photons �t measured at severalource–detector separations r can be used to deducemall absorption changes �a, j according to
�t�r� � �t*�r� � �t�r� � �j
MTSFj�r��a, j, (6)
here
�t�r� �
�i
tiWi
�i
Wi
(7)
enotes the mean time of flight of photons detected atistance r from the launching site and �t*�r� is theame quantity measured after the absorption coeffi-ient of layer j was changed by �a, j. The mean-ime-of-flight sensitivity factor MTSFj of layer jepends on the source–detector separation r and isiven by
MTSFj�r� � ��m
�ljlm�r�
cm� �lj�r��t�r�, (8)
here the cross term can be expressed as
�ljlm�r� �
�i
lijlimWi
�i
Wi
. (9)
oth changes in attenuation and mean time of flightave been successfully exploited to derive changes inbsorption by employing a two-layer head model20
ith a known thickness of the upper tissue layer. Inef. 20 attenuation and phase shifts were deduced
rom single-distance frequency-domain measure-ents carried out at a single modulation frequency.In the present paper we extend the analysis to the
ariance V�r� of distributions of times of flights ofhotons measured at several source–detector sepa-ations r to deduce changes �a, j in the absorptionoefficient of various layers. For this purpose we
ntroduce the variance sensitivity factor VSFj forach layer j according to
V�r� � V*�r� � V�r� � �j
VSFj�r��a, j, (10)
here
V�r� �
�i
ti2Wi
�i
Wi
� �t2�r� (11)
enotes the variance of the distribution of times ofight of photons detected at the source–detector dis-ance r and V*�r� is the same quantity measured afterchange �a, j of the absorption coefficient in layer j
ccurred. VSFj is defined as
VSFj�r� � ��m
�n
�ljlm ln�r�
cm cn� 2�t�r� �
m
�ljlm�r�
cm
� �lj�r� �t2�r� � 2�t2�r��, (12)
here the first cross term is given by
�ljlm ln�r� �
�i
lijlimlinWi
�i
Wi
. (13)
quations �3�, �5�, �6�, and �10�, expressing changes ofoments by changes in the absorption coefficients of
he various layers, represent linear approximations,ssuming that the changes in absorption are suffi-iently small, i.e., that
�j
��lj�a, j���1
olds true. For identical absorption changes in allayers, �a, j � �a and cj � c �homogeneous medi-m�, Eqs. �8� and �12� simplify to MTSF�r� � �cV�r�Ref. 23� and VSF�r� � �c��t � �t�3�r�, the last termeing the third centralized moment of the DTOF ofhotons.As mentioned above, Monte Carlo simulations inhich assumed background optical properties aresed allow one to calculate the various sensitivityactors according to Eqs. �2�, �4�, �8�, and �12�. Tonalyze how the sensitivity factors depend on depthnd source–detector separation, we performed suchimulations �for details see Section 3� for a simpli-ed 10-layer tissue model, assuming the same op-ical properties for all layers ��a � 0.01 mm�1, �s�
1 mm�1, n � 1.4�. For each layer we plottedFig. 2� sensitivity factors MPP, MTSF, and VSFbtained in this way versus source–detector sepa-ation r. For comparison Fig. 2 includes a plot ofhe TMPP versus total time of flight of photons.PP, MTSF, and VSF depend in different ways on
ource–detector separation r, a fact that can bexploited to deduce absorption changes occurring inifferent layers. For this purpose the informationontained in Fig. 2 is presented in a different way in
ig. 3. For selected values of r, sensitivity factorsPP, MTSF, and VSF, each normalized to its max-
mum, are plotted versus depth z associated withach layer. As can be seen, at a fixed source–etector separation the maxima of MPP, MTSF,nd VSF occur at increasingly larger depth z, i.e.,he variance is more sensitive to changes occurringn deeper layers whereas attenuation is most sen-itive to absorption changes in superficial layers.enerally the maxima of MPP, MTSF, and VSF
ig. 2. Sensitivity factors of the layer j of the head model �Fig. 1�ersus source–detector separation r: *, j � 1; E, j � 3; �, j � 5;, j � 7; ‚, j � 9. �a� Mean partial path length MPPj Eq. �2��; �b�
ime-dependent mean partial path length TMPPj Eq. �4�� versusotal time of flight tk at source–detector separation r � 20 mm �foromparison with MPPj�; �c� mean-time-of-flight sensitivity factorTSFj Eq. �8��; �d� variance sensitivity factor VSFj Eq. �12��.
ensitivity factors are calculated by Monte Carlo simulations forssumed homogeneous background optical properties �a, j � 0.01m�1, ��s,j � 1 mm�1.
ig. 3. Sensitivity factors versus depth z � 2� j � 1� mm of the topine layers at selected source–detector separations: *, MPPj; E,TSFj; �, VSFj. �a� r � 14 mm, �b� r � 26 mm, �c� r � 38 mm,
d� r � 50 mm. Data are taken from the same simulation ashown in Fig. 2. Each curve is normalized to its maximum value;urves are drawn to guide the eye.
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B
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hift toward larger values of z when the source–etector separation r is increased.Our method for deriving changes �a, j from
hanges of moments of measured DTOFs offers thedditional advantage that the instrumental re-ponse can be readily taken into account. In con-rast to the method proposed by Steinbrink et al.,here changes in the profile of the DTOF werenalyzed by using TMPPs, no deconvolution of theTOF by the �measured� instrumental response
unction is needed in our approach. Rather, theoments calculated from the measured DTOFs can
e corrected for the instrumental response simplyy subtracting the corresponding moments of thenstrumental response function to obtain the true
oments. However, since changes of moments areonsidered rather than the moments themselves, noorrections have to be made, provided the instru-ental response does not change during the course
f the experiment.
. Validation by Monte Carlo Simulations
. Monte Carlo Code
ur method of deriving absorption changes �a, jrom corresponding changes of moments was testedn calculated DTOFs obtained from Monte Carloimulations. The Monte Carlo code used2 is basedn the variance-reduction technique.21 Our tissueodel consisted of nine layers each 2 mm thick on
op of a semi-infinite bottom layer �Fig. 1�. Calcu-ations were carried out for a total of 5 � 108 pho-ons detected at source–detector separationsetween 5 and 62 mm. The distributions of timesf flight of photons were calculated simultaneouslyor a whole set of 19 concentric, consecutive, ring-haped detectors, each 3 mm wide, together withhe mean partial path lengths and the cross termsefined in Eqs. �2�, �4�, �9�, and �13�. The sameefractive index of nj � n � 1.4 was assumed for allayers, and the Fresnel reflections at the top surfacef our layered tissue model were neglected.
. Changes of Moments
irst, the validity of Eqs. �3�, �6�, and �10�, in par-icular that of the underlying linear approximation,as checked by forward calculations carried out for
hree different tissue models, i.e., one homogeneousodel and two inhomogeneous models. In the ho-ogeneous case �Case 0� the background optical
roperties were set to �a0,j � �a0 � 0.01 mm�1 and�s0, j � ��s0 � 1 mm�1. In the inhomogeneous cases
he absorption coefficient was increased by 5% eithern the top �Case I, Fig. 4� or bottom �Case II, Fig. 5�ve layers. In all cases the DTOFs were calculatedy Monte Carlo simulations as described above andsed to derive the changes of the moments appearingn the left-hand sides of Eqs. �3�, �6�, and �10�. Inigs. 4�a�–4�c� �Case I� and Figs. 5�a�–5�c� �Case II�he changes �open symbols� of attenuation, meanime of flight, and variance obtained in this way arelotted versus source–detector separation. On the
ther hand, the sensitivity factors are evaluated fornchanged �background� optical properties onlyCase 0� and, together with the known values of �a, j,sed to evaluate the right-hand sides of Eqs. �3�, �6�,nd �10� for both inhomogeneous models �Cases I andI� solid lines, Figs. 4�a�–4�c� and 5�a�–5�c��. Foromparison we applied the same procedure to the time-ependent changes in attenuation see Figs. 4�d� and�d�� according to Eq. �5� by using the time-dependentensitivity factors Eq. �4�� evaluated with backgroundptical properties.As can be seen from Figs. 4�a�–4�d� and 5�a�–5�d�
hanges in moments calculated by using sensitivityactors �solid lines� quantitatively agree with thoseerived directly from simulated DTOFs �open sym-ols� by integration over times of flight. The differ-nces observed are mainly caused by the limitedntegration ranges used, causing errors in the calcu-ated moments. Furthermore, in Monte Carlo sim-lations the number of detected photons is very lowt large source–detector separations �r � 30 mm�,ausing a pronounced scattering of the moments de-uced from simulated DTOFs. On the other hand,n both cases �I and II� the linear approximation stillolds true at large source–detector separations.he sum
�j
��lj�a, j�
as calculated to be smaller than 0.12 at the largestource–detector separation considered, i.e.,
�j
��lj�a, j� �� 1.
. Statistical Uncertainty of Moments
he moments of DTOFs offer another advantage;.e., their uncertainty due to photon noise can beasily estimated. In two situations analytical ex-ressions for the standard deviation of momentsan be derived: �i� Moments calculated from DT-Fs measured by time-correlated single-photon
ounting. In this case Poisson statistics can bessumed for each time channel, and expressions forhe uncertainty of the moments derived can be eas-ly obtained.24 �ii� Moments calculated from DT-Fs obtained by Monte Carlo simulations based on
he variance-reduction technique. In this caseoninteger weights of photon bundles are accumu-
ated in the time channels, and, according to Eq. �1�,hese weights depend on the individual pathengths in each layer for each photon bundle. Inhe homogeneous case ��a, j � �a and cj � c�, how-ver, all photon bundles with a given total time ofight ti�tk � ti � tk�1� corresponding to the path
ength ctk experience the same absorption regard-ess of their individual trajectory in the medium,eading to the same weight exp���actk�. With thisssumption the following analytical expressions are
btained for the standard deviation of changes ofoments:
�A�r� � � 2N0tot
�1�2
, (14)
�Ak� � 2
N0k�1�2
, (15)
��t�r� �
��k
2N0k tk � �t�r��2 exp��2�a ctk��1�2
Ntot,
(16)
V�r�
�
��k
2N0k� tk � �t�r��2 � V�r��2 exp��2�a ctk��Ntot
.
(17)
ere N0tot �N0k� is the total number of photons �theumber of photons in the kth time channel� of DTOFsbtained by Monte Carlo simulations, neglecting ab-orption. In this case all photon bundles carry theame weight, i.e., Wi � W0,i � 1, and Poisson statis-ics apply. On the other hand, N is the total num-
ig. 4. Changes in moments �open symbols� versus source–etector separation r derived from simulated distributions of timesf flight calculated after absorption is increased by 5% in the top 5ayers of the head model with homogeneous background opticalroperties, �a0 � 0.01 mm�1 and ��s0 � 1 mm�1: �a� change inttenuation A�r� Eq. �3��; �b� change in mean time of flight �t�r�Eq. �6��; �c� change in variance V�r� Eq. �10��; �d� change inime-dependent attenuation Ak Eq. �5�� versus total time of flightk at source–detector separation r � 20 mm. Solid curves, calcu-ated by using corresponding sensitivity factors and an assumedncrease in absorption ��a, j � 0.0005 mm�1, j � 1, . . ., 5�; verticalars, standard deviations calculated according to Eqs. �14�–�17�.e� Change in absorption coefficient �a, j versus depth of layer z �� j � 1� mm, reconstructed from *, A�r�; �, Ak; �, �t�r�; �,V�r�, and a combination of E, A�r�, �t�r�, V�r�. Solid line,ssumed change in the absorption coefficient.
er of photons contained in the DTOFs calculated,ith absorption taken into account.The standard deviations of the changes of moments
hown in Figs. 4 and 5 as vertical bars are calculatedccording to Eqs. �14�–�17�.
. Solution of the Inverse Problem
o solve the systems of linear equations Eqs. �3�, �5�,6�, and �10��, we used singular value decompositionSVD�, in particular the algorithm provided by Mat-ab 6.5 �MathWorks Inc.� and sensitivity factors asalculated in Section 2. The SVD was truncated tohree singular values. Using changes in either at-enuation, mean time of flight, or variance at 12ource–detector separations �5 mm � r � 38 mm inteps of 3 mm, where r is the inner radius of theing-shaped detector�, we can derive changes in thebsorption coefficient for 10 different layers. Alter-atively, the combination of all moments �intensity,ean time of flight, and variance� determined at only
our source–detector separations �14, 20, 26, and 29m� corresponds to 12 known parameters, providing
ufficient information to resolve changes in absorp-ion, again in 10 layers. Figures 4�e� and 5�e� illus-rate the accuracy at which changes in the absorptionoefficient in various layers can be derived by theseifferent methods of analysis, i.e., reconstructed fromA�r�, Ak, �t�r�, V�r�, and a combination of A�r�,�t�r�, V�r�. The results are compared with thenown �steplike� change in �a. We can see that allethods tested reproduce the trend in absorption
hanges correctly. The accuracy of various methodsepends on the number of singular values used andn the distribution of absorption changes over theifferent tissue compartments. The rather broadransition range in the vicinity of the step revealshat the spatial �depth� resolution in these specificonditions is of the order of 1 cm.
What combination of moments, measured at whichource–detector separations, is best suited to derive
ig. 5. Same as Fig. 4 but for an assumed increase in absorption�a, j � 0.0005 mm�1, j � 6, . . . , 10� of the five bottom layers.
am
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FflS
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bsorption changes in selected layers of the headodel remains to be explored.
. Experiment and Data Analysis
. Four-Channel Time-of-Flight Instrument
e developed a four-detection-channel time-of-flightnstrument as in Fig. 6. Three semiconductor lasers� � 687, 803, 826 nm� provided light pulses with aulse duration of �100 ps at a repetition rate of 20Hz �PDL-800, PicoQuant GmbH, Germany�. The
utput pulse trains of the three diode lasers wereultiplexed in time, i.e., delayed in such a way that
ulses corresponding to different wavelengths wereeparated by 15 ns with respect to one another. Theutput of each laser head was coupled into a separatetep-index fiber core diameter, 630 �m, numericalperture, 0.38; length, 1.5 m�, and the three fibersere arranged to form a bundle.At each wavelength the mean power of the laser
adiation impinging on the tissue was �0.5 mW.he tips of the fibers were positioned 2 mm above the
issue, and the illuminated area was �2 mm2. Theight diffusely reflected from the head was collected
ig. 7. Details of the detector box �one channel�. The angularosition of the rotary attenuator and the distance between thehotocathode �PMT� and the output face of the fiber bundle aredjusted manually.
y four fiber bundles �Loptek GlasfasertechnikmbH and Co. KG, Berlin, Germany� each with aumerical aperture of 0.54, a diameter of 4 mm, andlength of 1.5 m. The four detecting fiber bundlesere positioned at distances of 1.5, 2, 2.5, and 3 cm
rom the source fibers. Since the power of the lightollected by the fiber bundles decreases dramaticallyith increasing interoptode separation, the outputf each fiber bundle was attenuated by adjusting aotating attenuator to achieve similar count rates inll detection channels �Fig. 7�. In this way the fullynamic range of all detectors could be exploited.s attenuators we used thin transparencies with a
andom pattern of black spots rather than conven-ional neutral-density filters, since for these filtersttenuation depends on the angle of incidence and onavelength. The light collected by each fiber bundleas transmitted onto the photocathodes of four sep-rate photomultiplier tubes �PMT, R7400U-02amamatsu Photonics, Japan�, each operating at a
oltage of 900 V.The effective numerical aperture of each fiber bun-
le could be reduced by increasing the distance be-ween its tip and the photocathode of theorresponding detector �Fig. 7�. The width of thenstrumental response could be improved in thisay25 as illustrated in Fig. 8, albeit at the expense of
he collection efficiency of the particular detectionhannel. At small source–detector separations aarrow temporal response is particularly important.owever, since sufficient count rates are available at
mall interoptode distances, a trade-off between suf-cient time resolution and uncertainty due to photonoise could be easily made. By adjusting the dis-ance between the tip of each fiber bundle and thehotocathode facing it and by rotating the corre-ponding attenuator, one can vary the overall atten-ation of each detection channel by �6 orders ofagnitude. This range of attenuation was sufficient
o adjust the count rates of the four detection chan-els when one is measuring on adult heads with in-eroptode distances ranging from 1 to 4 cm.
ig. 6. Schematic of the three-wavelength �687-, 803-, 826-nm�our-detection-channel time-domain NIRS instrument �DL, diodeaser; PDL800, driver of diode lasers; PMT, photomultiplier tube;PC134, TCSPC electronics; HV, high-voltage power supply�.
ig. 8. Full width at half-maximum of the instrumental responseunction, ■ , versus the distance between the photocathode and theutput face of the fiber bundle. Decrease in the overall photonollection efficiency, E, expressed by the total number of photons Nf the measured instrumental response normalized to the value N0
The output of each detector was amplified by aeparate preamplifier �Becker & Hickl GmbH, Ger-any� and fed into a separate time-correlated single-
hoton counting �TCSPC� PC board �SPC-134,ecker & Hickl GmbH�. Since the laser pulses cor-esponding to the three wavelengths were multi-lexed in time, three corresponding DTOFs wereecorded simultaneously and stored in 1024 timehannels corresponding to a time-to-amplitude con-erter range of 50 ns. The measurements were per-ormed at count rates of �1 MHz�detection channel.hotons were accumulated during 60 ms, and all col-
ected DTOFs were stored every 100 ms. Data ac-uisition was controlled by a software packageeveloped in LabView 6i �National Instruments�.The instrumental response was measured by posi-
ioning the emitting fibers at a distance of 6 cm inront of all receiving fiber bundles, the faces of whichad been covered by a sheet of paper to fill all trans-ersal modes of the bundles. The laser-light inten-ity was adjusted by neutral-density filters. Asllustrated in Fig. 8 the distance between the tip ofhe detection fiber bundle and the photocathode of theetector facing it influences the instrumental re-ponse. Therefore the instrumental response waseasured after the setting of the detection optics was
hanged. The overall response of the instrumentanged between 200 and 600 ps, depending on detec-ion channel, wavelength, and distance between theutput face of the detecting bundle and the detector.
. Indocyanine Green Bolus
ndocyanine green is a dye with an absorption max-mum at �800 nm.26 It is used in ophthalmology as
contrast agent and for assessment of hepatic func-ion. There are no reports of severe adverse eventsfter administration of ICG. In our experiments 5g of ICG �Pulsion Medical Systems AG, Germany�
n 3 ml of saline were administered intravenously tohealthy volunteer. We rapidly �1–2 s� injected a
olus every 5 min into the cubital vein of the volun-eer who was comfortable in a supine position. Fouronsecutive injections were performed. The optodeolder carrying the source fibers and the four detect-
ng fiber bundles was positioned approximately abovehe motor cortex area on the left hemisphere of theolunteer and fixed by a bandage. The subject gavenformed consent, and the procedure was approvedy the local ethics committee.
. Signal Processing
he moments, i.e., integral, mean time of flight, andariance, of the measured distributions of times ofights of photons were calculated after subtractingackground and correcting for the differential non-inearity of the TCSPC electronics. This procedureas carried out for all DTOFs of photons acquired at
our source–detector separations at a wavelength of03 nm. Singular value decomposition was appliedo solve the system of 12 linear equations Eqs. �3�,6�, and �10�� with changes in attenuation A,hanges in mean time of flight �t, and changes in
ariance V measured at four source–detector sepa-ations. The SVD was truncated to three singularalues. By analysis of changes in attenuation Ak ofhe kth time channel by using TMPP sensitivity fac-ors, it was previously shown23 that at most threeingular values were significant.The sensitivity factors MPP, MTSF, and VSF en-
ering the system of linear equations Eqs. �3�, �6�,nd �10�� were calculated by Monte Carlo simulationsith homogeneous optical properties and assuming
he refractive index of tissue to be n � 1.4. Theensitivity factors were calculated at source–detectoreparations of 1.5, 2.0, 2.5, and 3.0 cm, which corre-pond to the interoptode distances used in our exper-ments. To estimate the background opticalroperties, the analytical expression for time-esolved diffuse reflectance of a semi-infinite medi-m3 was fitted to a DTOF averaged over a time
nterval of 20 s before injection of ICG. In doing so,he background absorption and reduced scatteringoefficients were determined to be �a0 � 0.07 mm�1
nd �s0� � 1.5 mm�1, respectively. Although theseackground optical properties do not represent theeal in vivo situation because of the assumption of aemi-infinite medium, these estimations are the bestvailable at the moment. The sensitivity factorsay be improved in principle by a more realisticodel of the head based on individual anatomical
nformation �obtained, for example, from magneticesonance imaging� and published optical propertiesf the various layers of the head �for a review see Ref.3�.The SVD analysis described above was performed
ndependently for each set of DTOFs acquired at fourource–detector separations during one collectionime period. In this way we were able to follow theynamics of absorption changes in various layers ofhe head at a sampling rate of 10 Hz. All calcula-ions were carried out with the aid of Matlab 6.5.
ig. 9. Changes in integral Ntot normalized by the initial valuetot�t � 0�� of the mean time of flight �t and of the variance V
f the distributions of times of flight of photons versus time beforend after injection of a bolus of ICG at t � 20 s. The DTOFs wereeasured on the head of a healthy volunteer at � � 803 nm and atsource–detector separation of 3 cm. The moments are averaged
ver four consecutive injections: black curve, Ntot; gray curve,�t; light gray curve, V.
5
F�tcastdiudanotsoasnbtpesfs
fldcfeitr
mstbdht
cciidcfilw
Ftcucurve, Ntot; gray curve, �t; light gray curve, V.
Faarvseparations r � 1.5, 2.0, 2.5, and 3.0 cm �Fig. 10�.
Fscc
. Results
igure 9 illustrates the dynamics of moments �Ntot,t, and V� following the injection of a bolus of ICG at� 20 s. The moments derived from DTOFs re-
orded at the source–detector separation of 3 cm andt 803 nm �close to the maximum of the absorptionpectrum of ICG� were averaged over four consecu-ive ICG injections. As is clearly visible in Fig. 9 theelay between the injection of the bolus and the drops the shortest for variance and the longest for atten-ation. In addition, both variance and, to a lesseregree, the mean time of flight rapidly rise againfter reaching their minimum values. This resulticely matches the fact that the inflow and washoutf ICG is faster in the intracerebral compartmenthan in the overlying tissues since, at a selectedource–detector separation �e.g., 3 cm�, the maximaf the sensitivity factors MPP, MTSF, and VSF occurt progressively deeper layers �Fig. 3�. Note that theignals do not return to their initial level. This phe-omenon is caused by the retention time of ICG in theody, which is determined mainly by metabolism inhe liver. In our investigations the injections wereerformed at time intervals of 5 min, which was longnough to assure that the shape of the boli was notignificantly influenced by the residual absorptionrom the previous bolus. The initial levels of theignal for different boli varied by not more than 10%.In Fig. 10 the dynamics of integral, mean time of
ight, and variance are shown for various source–etector separations. For easy comparison thehanges of moments were scaled to cover the rangerom zero to one by subtracting the minimum value ofach moment and normalizing the resulting curve byts maximum value. The differences between theime courses of the three moments, in particular theapid return of the variance after reaching its mini-
um, are most pronounced at large source–detectoreparations. They tend to disappear at short in-eroptode distances. This behavior can be explainedy the different penetration depths of the photonsetected at various source–detector separations andence by the different contributions of intracerebralissue to the volume interrogated.
With our head model �nine layers, each 2 mm thick,overing a semi-infinite lower compartment� thehanges in the absorption coefficient occurring at var-ous depths are calculated by SVD and are presentedn Fig. 11. The faster washout kinetics of ICG ineeper layers compared with superficial layers arelearly seen. The initial change in �a in the super-cial layer is delayed and washout takes considerably
onger compared with deeper layers exhibiting rapidashin and washout of ICG. The transition be-
ig. 12. Same as Fig. 11 but averaging the changes in the ab-orption coefficient �a over the top four layers �extracerebralompartment� and the remaining six bottom layers �intracerebralompartment�.
ig. 10. Same as Fig. 9 but at various source–detector separa-ions r: �a� r � 1.5 cm, �b� r � 2.0 cm, �c� r � 2.5 cm, �d� r � 3.0m. The moments are rescaled by subtracting the minimum val-es and normalizing the resulting curves by their maxima: black
ig. 11. Changes �gray scale� of the absorption coefficient �a inll �10� layers of the head model �Fig. 1� versus time before andfter injection of a ICG bolus at t � 20 s. The �a, j values wereeconstructed from moments �attenuation, mean time of flight,ariance� of DTOFs measured at � � 803 nm and source–detector
ween both patterns occurs at a depth of �8 mm.ote that, because of the strong scattering of light in
issue, only low spatial frequencies are contained inhe diffusely reflected light. It follows that the truepatial �depth� resolution �Fig. 11� is worse than thehickness �2 mm� of the each layer of our model.
Keeping the rather low spatial resolution in mind,e divided the head model into two compartments
epresenting intracerebral and extracerebral tissue.onsistent with the observed transition in the dy-amics of absorption changes, we assumed that thextracerebral compartment consisted of the four topayers. Anatomically this thickness of 8 mm seemseasonable for the skin and skull. Figure 12 dis-lays the dynamics of absorption changes in the in-racerebral and extracerebral compartments,btained by averaging the absorption changes amonghe layers of each compartment. As expected thentracerebral compartment exhibits a shorter delayn the rise in absorption to its maximum, followed by
rapid decrease. Again, this result can be ex-lained by the fast washin and washout kinetics ofCG in brain tissue. In contrast the extracerebralissue experiences a later rise in absorption anduch slower washout kinetics.
. Conclusions
time-resolved NIRS instrument with four paralleletection channels has been developed, allowing theiffuse reflectance to be measured simultaneously atour locations on the head of a healthy volunteer.he instrument was used to record distributions ofimes of flight of photons at source–detector separa-ions of 1.5, 2, 2.5, and 3 cm before and after appli-ation of a bolus of indocyanine green �ICG�. Weave analyzed changes in the zeroth, first, and second
centralized� moments, calculated from the measuredistributions of times of flight, to derive changes inhe absorption coefficient occurring at various depthsf a head model consisting of nine homogeneous lay-rs of the same thickness �2 mm� above a semi-nfinite homogeneous medium. Following injectionf the ICG bolus, the six lower layers showed thehange in the absorption coefficient rapidly increas-ng to a maximum, followed by a fast drop. Theynamics of the upper four layers were slower; i.e., annitial rise in the change in the absorption coefficientccurred at a later time followed by a slow washouteriod. The different dynamics observed were inter-reted to be characteristic of intracerebral and extra-erebral compartments. A similar dynamics ofignal changes is known from magnetic resonancemaging studies following application of a bolus ofd-DTPA �gadolinium diethylene triamine pentaace-
ic acid� and, in addition, from ICG studies employingrequency-domain near-IR spectroscopy.20
We have extended the method to derive changes inhe absorption coefficient from changes in the atten-ation and mean time of flight,20,23 previously pub-
ished in the literature, by including the secondentralized moment �variance� of distributions ofimes of flight of photons. Within a linear approxi-
ation, we obtained changes in the absorption coef-cient of various layers from changes in attenuation,ean time of flight, and variance by using theethod of singular value decomposition togetherith the mean partial path length MPP, the mean
ime of flight sensitivity factor MTSF, and the vari-nce sensitivity factor VSF calculated by Monte Carloimulations. Our method of analysis was tested onimulated distributions of times of flight of photons.ur theoretical as well as experimental results re-ealed that variance is more sensitive to intracerebralhanges than attenuation and mean time of flight.urthermore, compared with previous approaches
single-distance, time-, or frequency-domain tech-iques, multidistance cw or frequency-domain meth-ds�, the multidistance time-domain method appliedn this paper provides more information and hencellows investigation of more layers with improvedobustness in the results.
Our results from the dynamics of absorptionhanges following application of a bolus of ICG sug-est that cerebral blood flow in adults can be moni-ored more reliably compared with NIRS whenontinuous light is used. This implies that ourethod may help to introduce NIRS into the clinicalonitoring of stroke patients and patients with other
ascular diseases.
A Liebert is on leave from the Institute of Biocy-ernetics and Biomedical Engineering, Trojdena 4,2-109 Warsaw, Poland. He was partially sup-orted by a Marie-Curie Fellowship from the Euro-ean Commission �Quality of Life Programmeontract QLGA-CT-2000-52128�.
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