Analysis of near-infrared spectroscopy and indocyanine green dye dilution with Monte Carlo simulation of light propagation in the adult brain

. Near-infrared spectroscopy (cid:1) NIRS (cid:2) combined with indocyanine green (cid:1) ICG (cid:2) dilution is applied externally on the head to determine the cerebral hemodynamics of neurointensive care patients. We applied Monte Carlo simulation for the analysis of a number of prob-lems associated with this method. First, the contamination of the optical density (cid:1) OD (cid:2) signal due to the extracerebral tissue was assessed. Second, the measured OD signal depends essentially on the relative blood content (cid:1) with respect to its absorption (cid:2) in the various transillu-minated tissues. To take this into account, we weighted the calculated densities of the photon distribution under baseline conditions within the different tissues with the changes and aberration of the relative blood volumes that are typically observed under healthy and patho-logic conditions. Third, in case of NIRS ICG dye dilution, an ICG bolus replaces part of the blood such that a transient change of absorption in the brain tissues occurs that can be recorded in the OD signal. Our results indicate that for an exchange fraction of (cid:1) =30% of the relative blood volume within the intracerebral tissue, the OD signal is determined from 64 to 74% by the gray matter and between 8 to 16% by the white matter maximally for a distance of d =4.5 cm .


Introduction
In 1977, near-infrared spectroscopy ͑NIRS͒ was used for the first time as a noninvasive measurement method to detect changes in the cerebral hemoglobin oxygenation ͑oxy-Hb, Deoxy-Hb͒. 1 More recently, NIRS has been applied to estimate cerebral oxygenation under routine clinical conditions. 2,3 Furthermore, for an improved monitoring of cerebral hemodynamics in neurointensive care, NIRS has been combined with indocyanine green ͑ICG͒ dye bolus injection, 4 whereby ICG is a highly absorbing tracer substance in the IR region. This procedure allows us to determine the mean transit time of ICG ͑mtt ICG ͒, the cerebral blood volume ͑CBV͒, and the cerebral blood flow ͑CBF͒ of adult patients at the bedside. 5,6 The technique has recently been validated in healthy volunteers. 6 Early detection and treatment of cerebral ischemia to prevent further neurological damage in patients with severe brain injury and stroke is one of the most important issues in neurocritical care. Patients in the neurointensive care unit are mostly in a critical, unstable condition. Stable xenonenhanced computed tomography, positron emission tomography, single-photon emission computed tomography, or mag-netic resonance spectroscopy are powerful research tools, 7-10 but they require the patient to be transported and thus involve a potentially high risk. The established methods for bedside measurement of CBF with inert tracers such as the nitrous oxide dilution method 11 or the 133Xenon dilution technique 12 are difficult to perform clinically and are time-consuming. Additionally, 133Xenon dilution detected with multiple collimators measures regional cortical perfusion, which may not be representative when cortical electrical depression is present. 13 The NIRS method does not involve spectroscopy in the strict sense, but is restricted to an intensity measurement of the transmitted light at different wavelengths; whereby for each wavelength, the transmitted light has the same wavelength as the incident light. A distinction thereby has to be made between a baseline signal, which for all practical purposes is constant in time and depends, among other things, strongly on the relative blood content of the involved tissues, and a time-dependent signal, which is caused by a number of effects, such as a variation of the blood oxygenation, the passage of a tracer, or a short-term change of the relative blood volume contained in the blood vessels in the various tissues involved in the photon paths. Because the baseline is usually not of interest clinically, the time varying signal is extracted with the aid of a difference procedure such that the baseline drops out. This signal is normalized and denoted as the optical density ͑OD͒ signal. Along with the baseline, however, the OD signal depends largely on the relative tissue blood content because the time dependency is due mostly to variations taking place in the intravascular space.
A problem associated with the NIRS ICG dye dilution method used for CBF measurement is due to the fact that the OD signal from the brain tissue is contaminated by contributions from the extracerebral bone and scalp tissue. From a clinical point of view, the spatial photon density distribution, that is, the spatial sensitivity profile that characterizes the volume interrogated by NIRS between emitter and receiver, 14 should be concentrated in the brain tissues of interest with minimal contamination by other structures. Accordingly, several theoretical and experimental approaches were made to analyze the influence of these contaminations on the measured OD signal. [15][16][17][18][19] Among others, these investigations supported the finding that the cerebrospinal fluid ͑CSF͒ in the subarachnoid acts as a light guide. 20 One method to subtract the extracerebral contamination from the detected OD signal is based on spatially resolved spectroscopy ͑SRS͒. 21 The localization of the origin of the various contributions to the measured OD signal is thereby derived from consecutive NIRS measurements with different emitter-detector spacings. However, interindividual variability of anatomy restricts the applicability of SRS, mostly because individual verification and calibration is unsuitable for rapid noninvasive CBF measurements at the bedside, in particular in the neurointensive care unit. Other methods are based on time-resolved spectroscopy ͑TRS͒ 22,23 or high frequency modulated 24 measurements.
As Monte Carlo ͑MC͒ methods lend themselves for the analysis of light propagation in biological tissues, a number of studies relating to the application of NIRS in the brain have been presented. [25][26][27][28] Most simulations were thereby performed on homogeneous geometrical structures 14,29 not taking into account the different tissues the light has to pass through nor the folded surface structure of the brain. Such approaches suffer in reality, because they do not reflect the scattering differences in the various tissues and geometries. Other approaches were based on two-dimensional ͑2D͒ magnetic resonance images ͑MRI͒ to separate the different tissues, such as the scalp, skull, and CSF layer. 30,31 Recently, also threedimensional ͑3D͒ head models derived from MRI data were used to simulate the light propagation in the head. 32,33 In this paper, results from MC simulations are presented where light propagation, more precisely, the propagation of photons, was simulated between an emitter and a detector externally attached to the adult head. For these simulations, a 3D anatomical brain model was obtained from MRI data of a healthy, 30-year-old male volunteer. The implementation of the MC code followed the theoretical description of Prahl, 34 a significant difference being the application of a fixed sufficiently small step-size for the photon propagation such that anatomical details could be taken into account. From the simulation, the contribution of the various tissues to the total absorption is obtained which in all cases considered allowed us to assess the extracerebral contamination.
A first aspect of interest of our study was directed toward an assessment of the influence of the CSF by comparing simulations performed on a brain area comprising sulci filled with CSF ͑see Fig. 1͒ with simulations on another area with a small volume of CSF. A second major focus was related to the influence of the relative blood content in the various transilluminated tissues, because the first place the OD signal is obtained from is the intravascular space where the change of the blood content over time is highest. With respect to the clinical application of NIRS ICG dye dilution, the dependency of the baseline signal on the blood volumina within the different tissues of the head is a key characteristic because ICG is confined to intravascular spaces. Although the baseline signal measurement is not of further clinical use, this dependency can be used to estimate how large the time-varying, useful OD signal will be when an injected ICG bolus replaces blood partially. The resulting blood-ICG intermix causes a transient change of absorption within the tissues of the observed optical segment. This follows from the assumption that the probability for an interaction of a photon with the blood-ICG intermix to occur increases with increasing relative blood volume ͑rel. BV͒ of the involved tissues. The rel. BV for each tissue was given per 100 cm 3 of tissue and assumed to vary between the tissue types according to published data.
Apart from arterial pulsation, which is the major origin of the OD signal, the rel. BV may furthermore change markedly within time intervals relevant for measurements ͑sometimes within seconds͒. A change in rel. BV yields a baseline shift in a typical NIRS measurement. If the change is sufficiently rapid ͑seconds͒, it is amenable to an evaluation. Wolf et al., 35 for example used the finding that the OD signal varies synchronously with ventilation to determine venous oxygenation in neonates.
In this study, the rel. BV was understood as a mean value, averaged over arterial pulsations of blood contained within a unit volume of tissue. In the literature, the rel. BV of the gray and white matter is often denoted as CBV. The CBV within the brain tissues includes the arterial, capillary, and venous blood components of the cerebral vessel system 36,37 whereby 70 to 80% of the CBV is contained within the venous vessels. 38 In earlier days, no direct attempts were made to quantify the CBV, although the CBV was estimated to change in a power-law relationship: CBV= 0.8ϫ CBF 0.38 with the CBF, as found by Grubb. 39 More recently, the CBV, respectively its changes, were determined directly using various methods. The work of Ito 40 documented the overall change of CBV, while his newer studies 37 focused on the change in the arterial component of the CBV during hypercapnia and hypocapnia, using positron emission tomography ͑PET͒ with H͑2͒͑15͒O and ͑11͒CO. Other PET studies 41 showed an increase of the CBV in relation to sodium nitroprusside in an anesthetized baboon. In another approach, the regional cerebrovascular response, including arterial and venous change of CBV, to sympathoexcitatory reflexes was evaluated with contrast-enhanced computer tomography ͑CT͒. 36 Additionally, a functional MRI was used to measure the change in CBV with high temporal resolution in relation to visual stimulation 42 with a ⌬CBV of 27± 4%.
For the MC simulations absorption and scattering properties of the various tissues of interest here were taken from the literature. Because published values are mostly based on measurements performed on excised tissue, however, it is to be assumed that the ͑unknown͒ blood content associated with these values is generally low. It is not unreasonable to hypothesize that the enormous spread of the published data can at least partially be attributed to differences in blood content. Accordingly, a comparison of the baseline results obtained with selected tissues assumed hypothetically to have a low and homogeneously distributed blood content with three different cases of higher blood content was made ͑"standard" case, furthermore, "below average," and "best" case͒. These simulations served to estimate the highest possible baseline and subsequently the highest possible OD signal that can be expected to originate from each tissue. The passage of the blood-ICG intermix increases the effect further according to the rel. BV.

Anatomical Model and Material Matrix
MRI scans were performed on a Philip's Intera 3T wholebody unit equipped with a transmit-receive body coil and a commercial eight-element head coil array ͑MRI Devices Corporation, Waukesha, Wisconsin͒. T2-weighted anatomical images were obtained with a turbo spin echo sequence ͑TE/ TR= 80/ 4000 ms͒ from 155 slices covering the whole brain as shown in the sagittal section in Fig. 2 with a spatial resolution of 0.8ϫ 0.8ϫ 0.8 mm. T1-weighted anatomical images were acquired with a 3D T1-weighted gradient echo sequence ͑TE/ TR= 2.3/ 20 ms͒ with the same positioning and geometry. Enhancement of brain vascular structures was achieved with a 3D inflow-weighted gradient echo sequence with TE/ TR= 1.88/ 21 ms and maximum intensity projection reconstruction. The MRI results of the three complete scans were stored in three separate 3D matrices with each having a resolution of 2 16 gray scales.
We processed the MRI data of the three T1/T2 value matrices with a feature and structure matching algorithm to eliminate artifacts due to movements of the healthy volunteer, a 30-year-old male, during the three 20-min measurement times. The perceived matching accuracy of the three MRI data matrices was at 0.5 mm within the range of the image resolution. The result was stored in one 3D data set of 512 ϫ 512ϫ 100= 26 214 400 voxels. Next, we selected one slice of the 3D MRI data set ͑Fig. 3͒ and defined thresholds dependent on the MRI histogram. These thresholds were used to segment the MRI data set into the different tissue types, namely the scalp, the skull, the CSF, and the gray and the white matter. We also included the air around the head of the healthy volunteer. The result of this segmentation process for the white matter is shown for the selected MRI slice in Fig.  3͑b͒ in comparison with the unsegmented MRI of the same slice ͓Fig. 3͑a͔͒.
Finally, we obtained a 3D matrix ͑hereafter called material matrix͒ having the size of 512ϫ 512ϫ 100 voxels containing the identification numbers of the different tissues of the brain. The identification was used to assign tissue-specific absorption and scattering coefficients ͑scalp, skull, CSF, gray and white matter͒ to each voxel.
We intended in particular to analyze the spatial sensitivity profile, which is defined by the density distribution of those emitted photons that reach the receiver, in the case where the examined human forebrain region contained a deep sulcus near the temple ͑Fig. 1͒ filled with a high volume of CSF. These results were then compared with the photon density distribution within a region 1.5 cm further to the sagittal line of the head, which contained only a small sulcus filled with  less CSF. To this end, the CSF volumina were calculated from the segmented MRI data. For both configurations that were simulated, a region of interest was defined containing 10 slices and covering the area spanned by the largest emitterdetector distance under consideration, which was d 3 = 4.5 cm. For both configurations, the number of pixels representing CSF were counted. The region with the high volume of CSF ͑slice 6 in Fig. 1͒ contained approximately CSF = 1.7 ml, while the region with the small amount of CSF ͑slice 8 in Fig.  1͒ included approximately CSF = 0.7 ml. The CSF volume ratio between the region with a high amount of CSF to the one with a small amount was thus 2.4. The simulations were carried out for emitter-detector distances of d 1 =2 cm, d 2 =3 cm, and d 3 = 4.5 cm, respectively.

MC Simulation
The NIRS measurement corresponds to the measurement of the time-varying intensity of a stream of photons, assumed to propagate in a stochastic fashion in the tissue. When a photon is scattered elastically in an optically dense material where the scattering centers are large compared to the wavelength, such as is the case in biological tissue, the scattering is of the Mie type. Elastic scattering is characterized by the fact that the photon energy does not change; in the case of Mie elastic scattering, furthermore, the scattering is highly oriented in a forward direction. Accordingly, an anisotropic scattering scheme was used for the simulations.
For the MC procedure, based on the anisotropic modeling approach of Prahl, 34 we simulated the path of individual photons whereby each photon started at the emitter and was allowed to interact with the different tissues. This interaction included elastic scattering and redirection ͑Sec. 2.2.1͒ or absorption ͑Sec. 2.2.2͒ of a photon. At boundaries, furthermore, internal reflection may occur according to the optical densities ͑Sec. 2.2.3͒. Those photons that reached the detector were considered to be as "successful" and were sampled.
During the propagation, we let each photon travel a given distance ⌬l while it was checked at each step whether the photon had passed the border between two materials or if the photon had been scattered or absorbed. The step-size ⌬l was chosen to be 0.01 mm, which was sufficiently small to ascer-tain that a photon could not pass through different materials without taking into account the associated changes in the absorption and scattering coefficients.

Scattering
Within the framework of anisotropic scattering, the scattering coefficient s is used to describe the statistical nature of the scattering process. The unit is given as 1/mm, and the probability for the occurrence of a scattering process over the distance ds is given by In a dense medium, the values of s are often found to be quite high such that they are difficult to measure. Instead, the reduced or transport scattering coefficient, s Ј, is usually documented in the literature because it is less critical to determine and because it is derived from the diffusion approximation. The relationship between the scatter coefficient s and the reduced scatter coefficient s Ј is given by s Ј= s ͓1 − g͔͑͒. 43 Thereby, the anisotropy factor g͑͒ = ͑cos ͒ describes the mean scattering-induced deviation from the forward direction, while it is independent from the azimuthal orientation ͑transverse anisotropy͒. It depends in general on the wavelength, which is constant in our case. A typical value for biological tissue is g = 0.9 as can be seen in Table 1. This implies that the light is scattered mainly in a forward direction with a small diversion.
The scattering angle was assumed to change with the material. According to Henyey and Greenstein, 44 the probability distribution for the interaction between biological tissue and near-infrared light 45 can be given as follows: The anisotropy factors used in our MC simulation are given for the different tissues in Table 2 ͑see Sec. 2.2.3͒. In the actual implementation, the stochastic nature of the propagation was taken into account by choosing for each photon the scattering angle from a random number , where ͓0,1͒.
is then given as follows: 34 In agreement with transverse anisotropy, azimuthal scattering was assumed to be isotropic, such that the probability distribution for was considered uniform such that =2 with the random number ͓0,1͒.

Absorption
The probability of absorption along a path of length ds is calculated as If a photon is absorbed, it is discarded from the simulation. Because probabilities are smaller than 1, care was taken that the incremental pathlength was sufficiently small ͑in addition to geometrical constraints given by the anatomical details͒ that the sum of the scattering and absorption probability did not violate this condition.

Optical coefficients and internal reflection
The optical attributes of each voxel were given by a pair of values for a and s = s Ј1/͓1−g͔͑͒, which were derived from the literature. It is found that the published values for both coefficients a and s Ј differ widely, which can be attributed in part to difficulties in isolating the relevant tissue within the living organism. When the measurements were performed under excised conditions, furthermore, the results show changes in the optical attributes with increasing duration from the time of excision. Of particular importance for our work is the circumstance that the blood content of the tissue at the time of measurement is not known ͑or not reported͒; yet this parameter influences the optical properties of a biological tissue decisively. Table 1 contains a collection of literature values and documents the variations that were found between the different materials. Apart from the absorption coefficients and the scattering coefficients, the table also contains the values of the anisotropy factor g.
We performed our simulations using the set of optical properties a , s , g and the refractive index for the different tissues of the adult head as listed in Table 2, provided by van der Zee 43 and Okada 26 and also used by Fukui. 31 Internal reflection was taken into account by applying Fresnel's equation and Snell's law whenever a photon crossed the borderline from one tissue to another and having a different index of refraction.

The Implementation of the MC Simulation
The incremental step-size was chosen as 0.01 mm, such that the passage of a photon through more than one material boundary in one step was avoided. This value was a compromise in that the limitation given by the maximal reciprocal values of a and s , which are in the range of 0.002 to 0.2 mm had to be observed in addition ͑Table 2͒, while the time necessary for the computation was kept as small as possible. For the rest, the general procedure followed the one published by Prahl. 34 The lifetime of a photon includes the three phases "birth," the repeated decision process, and "death."

Birth
The random generator created a photon at the surface of the emitter optode. The photon obtained an initial direction of flight within the defined angle of the light beam of the optode.

Decision process
When a photon had moved a step of length ⌬l in its initial direction, a decision was made with respect to the further motion of the photon. The current coordinates of the photon were related to the material matrix to determine the probability of absorption using a from the lookup table. If absorption had not occurred, the probability for scattering was evaluated and a new direction of the photon was determined based on the random numbers and according to Eqs. ͑3͒ and ͑4͒ to

Death
The stepwise procedure was repeated until the photon was detected successfully or it "died." A photon was considered successful when it crossed the defined detector plane in the distance of d 1 =2 cm, d 2 =3 cm, and d 3 = 4.5 cm, respectively, with an entry angle that was within the range of the defined angle of acceptance ͑␤ = 90 deg͒ of the optode. The photon was registered and the path was stored. In turn, death occurred whenever a photon was absorbed ͑Sec. 2.3.2͒, exceeded a specified distance from the detector surface, or moved outside the head into air ͑reentry could be excluded because of the convex shape of the head͒. The paths of dead photons were discarded.

Evaluation
First, two series of MC simulations were performed, one modeling a configuration with a low CSF volume in the tissue and a second set highlighting a situation with a higher CSF volume ͑see Table 3͒. Each series comprised the emitterdetector distances d 1 =2 cm, d 2 =3 cm, and d 3 = 4.5 cm, respectively, and every simulation was done with 30ϫ 10 6 photons in total, subdivided into three portions of 10ϫ 10 6 photons each. After each run, the number of successful paths as well as the differential pathlength factor ͑DPF͒ value along with the photon density distribution within the different tissue types were recorded. Care was taken that the standard deviation was less than 3% in all cases. For simplicity and completeness, the simulations included the absorption processes, although approaches have been presented where the photon trajectories are determined in the absence of absorption and then reweighted. 46 For short distances, d 1 =2 cm, the processing time was short enough to accept the waste of absorbed photons. For the longer emitterdetector distances, we included a reduction factor to minimize the effect of absorption. However, the chosen reduction factor k for a influences the result of the MC simulation in that for 0 Ͻ k Ͻ 1, paths with a short pathlength s * are favored. In the case k =0, no absorption takes place. For such a case, the successful paths have to be reweighted as described in other implementations. 46 The associated procedure was as follows: This lowered the number of successful paths between the emitter and the detector according to the effect of absorption.
Another side effect of reducing a by a factor k consisted of allowing photons to stay alive even when they had moved away so far that they never would reach the detector surface any more. As a consequence, processing time increased. To minimize this problem, we ignored photons that had traveled a total path length that was longer than a specified distance from the detector surface ͑50 times the emitter-detector dis-tance͒.
For the compilation of the photon density distribution, each successful photon path was scrutinized stepwise according to the tissue that had been passed. This distribution was assumed to represent a direct measure for the baseline and the OD signal to be expected under equivalent condition. To this end, the number of path segments in each tissue was related to the total number of segments to yield a relative fraction ͑%͒. Both baseline and OD signal were assumed to exhibit the same dependence on the local photon density.

Influence of Tissue Blood Content
In the presented approach, the 3D anatomical structure of the brain region was taken into account in detail, while the primary blood content within the different tissues was not considered. At this time, it is not possible to visualize all small blood vessels within the cerebral tissue and simulate the dynamics of the blood flow within the cerebral vessels. As will be mentioned later in this section, blood and blood-ICG inter- Table 3 Calculated photon density distribution of the different brain tissues for d 1 = 2 cm, d 2 = 3 cm, and d 3 = 4.5 cm at brain regions with high ͑1.7-ml CSF͒ and low volumes of CSF ͑0.7-ml CSF͒ in the surrounding. +: The rel. BV content of the sample probes with which the optical parameters were determined are assumed to be very low and set to one ͑normalized unit͒ for later weighting purposes for all tissues except for the CSF. CSF of a healthy person does not contain blood at all. mix have different passage velocities in the intracerebral and extracerebral tissues, whereby ICG does not pass the capillary walls.
The MC simulations described so far included optical characteristics of the different tissues as reported in the literature ͑baseline conditions͒. As the associated values were determined by using tissue samples where the blood content was not specified or unknown, it was only possible to make hypothetical assumptions with respect to the effects on the OD signal associated with changes in the blood content of the various tissues. The simulations outlined in the following were nevertheless considered useful, because they allowed us to assess the clinical significance of the NIRS ICG dye dilution measurement method.
Three theoretical cases with different sets of rel. BV contents were considered: a "standard," a "below average," and a "best" case scenario ͑Tables 4-6͒. The respective rel. BV values were chosen according to literature data. ICG dye was at first not taken into account in these simulations. In a further step, the case of NIRS in combination with ICG dye dilution was approximated. After bolus injection, the rel. BV in the tissues will rapidly be replaced with the blood-ICG dye intermix causing a large jump of the OD signal due to the high absorption of ICG. Yet, the measured slope of this signal cannot be attributed to a specific tissue in a straightforward manner because the ICG reaches all tissues involved in the measurement but the mean transit times mtt ICG are different. Accordingly, the possible effect of the first passage of the blood-ICG dye passage within the observed optical segment was assessed by consideration of different exchange fractions ⌬ of the rel. BV ͑Table 7͒ containing the blood-ICG intermix.
Yet another aspect is of interest. Baseline conditions associated with a given rel. BV cannot be quantified as long as these conditions are strictly constant. Under certain clinical circumstances, however, such as in neurointensive care, rela-   Table 3 are weighted with the rel. BV within the tissue for d 1 = 2 cm, d 2 =3 cm, and d 3 = 4.5 cm at brain regions with high and low volumes of CSF in the surrounding areas. For the below average case, the rel. BV values, given in Table  4, were reduced by 5% for the extracerebral tissues of scalp and skull ͑ࡗ͒, while the rel. BV for the cerebral tissue of gray and white matter ͑छ͒ were reduced by 15%. ଁ: For healthy volunteers, CSF does not contain blood and therefore it does not contribute to changes in the baseline of the OD signal. tively slow ͑in comparison to the heart beat͒ and small changes of the baseline conditions themselves, given by the primary rel. BV are observed. Likewise, a signal that varies synchronously with the breathing cycle can be isolated ͑e.g., Fig. 4͒. As such changes may be significant and important clinically, an analysis of the dependence of the measured values of the rel. BV of the various tissues involved is of relevance.
As a positive circumstance in view of clinical applications, the rel. BV for gray and white matter is higher than for the scalp and skull. Leenders 47 estimated the CBV, here used as the rel. BV and measured in ml/ 100 g, for gray matter to be 5.2 and for white matter to be 2.7, respectively. The rel. BV factors for scalp and skull, in turn, were calculated from values of the CBF values published by Xu Zhu,48,49 where the CBF is given with 50.2 for the brain, 0 ͑Ref. 48͒ or 1.8 ͑Ref.
49͒ for the bone and 2.0 for the scalp, measured in ml/ min ϫ 100 g. These values have been considered as the standard case in the following.
Based on these findings, the assumptions made for the below average and the best cases were based on the following further considerations: First, the change of rel. BV for the brain tissue is related to the change in CBV, which has been estimated to vary in a power-law relationship with the CBF ͑CBV= 0.8ϫ CBF 0.38 , Grubb 39 ͒, implying that 15 to 20% of the relative blood content is exchanged per unit of time. Functional MRI studies with high temporal resolution in relation to visual stimulation, 42 yielded a ⌬CBV of 27± 4%. Other groups reported a CBV increase of 10± 13% for optic flicker simulation with 2-Hz and 21± 5% for 8-Hz stimulation frequencies. 50 Average CBV increases for humans have been Table 6 Best case scenario: Calculated photon density distributions of Table 3 weighted with the change in the relative blood volume within the tissue for d 1 = 2 cm, d 2 =3 cm, and d 3 = 4.5 cm at brain regions with high and low volumes of CSF in the surrounding. For the best case, the rel. BV values, given in Table  4, were increased by 5% for the extracerebral tissues of scalp and skull ͑ࡗ͒, while the rel. BV for the cerebral tissue of gray and white matter ͑छ͒ were enlarged by 15%. ଁ: For healthy volunteers, CSF does not contain blood and therefore it does not contribute to changes in the baseline of the OD signal.  Table 7 Influence of the exchange fraction ⌬ of the rel. BV content, while NIRS ICG dye dilution is performed and a blood-ICG intermix passes the optical segment: Calculated photon density distributions of Table 3 were weighted with the exchange fraction ⌬ of the rel. BV within the tissue for d 1 = 2 cm, d 2 = 3 cm, and d 3 = 4.5 cm at brain regions with high and low volumes of CSF in the surrounding. The values for the rel. BV are taken from measured in the range of 32± 10%, 51 10.9± 2.5%, 52 23.5± 14.6%, 53 and 28± 7% 54 in bolus tracking MRI experiments. Based on these reported data, we assumed a change in the rel. BV for gray and white matter of 30% as representative to estimate the influence on the monitored OD signals during NIRS with ICG dye dilution. That the change in the rel. BV can be monitored with NIRS accompanied by ICG dye dilution is shown in the following case ͑Fig. 4͒, where a patient was mechanically ventilated with an inspiratory pressure of 25 mbar and an expiratory pressure of 10 mbar. From our unpublished results for NIRS ICG dye dilution measurements, we perceived transit times of ICG ͑mtt ICG ͒ in the range 5 to 12 sec for the brain tissue. The mtt ICG for the scalp was measured to be approximately 20 sec on a patient with a brain herniation, where the interruption of the CBF circulation could be documented with a transcranial Doppler measurement. Based on the relationship CBF = CBV / mtt, we estimated as representative factors the ones presented in Tables 5 and 6. The change in rel. BV in the extracerebral tissue was assumed to be smaller than in the cerebral tissue, due to the fact that the blood flow is smaller and slower. The change of rel. BV in extracerebral tissue was therefore estimated to be on the order of 10%. In healthy persons, the CSF does not contain blood, and based on this circumstance, it was not assumed to cause changes in the OD signals.
To analyze the influence of the rel. BV content on the baseline signals, the above mentioned changes in rel. BV values ͑30% corresponding to ±15% and 10% corresponding to ±5%, respectively͒ were used to reweight the MC simulation results of the spatial photon density distribution within the different tissues.
In the below average scenario, we hypothesized that the results of the primary simulations could be weighted with the rel. BV contents as mentioned above: A reduction of 5% for scalp and skull and of 15% for gray and white matter was assumed. In turn, for the best case scenario, the rel. BV contents were increased by 5% for scalp and skull and by 15% for the gray and white matter. The results of these weightings are given in Tables 5 and 6.
In order to model the passage of an ICG bolus through the observed optical segment hypothetically, the exchange frac-tions of the rel. BV, ⌬ ͑exchange of intravascular volume per unit of time due to blood flow͒ were assumed as 10% ͑relatively slow blood perfusion͒ for scalp and skull, while those for gray and white matter were set to 30% ͑high blood perfu-sion͒. Only in this scenario, which involves the application of ICG, can the maximal possible change in the absorption be monitored: As long as no ICG dye is present, the exchange ⌬ of the rel. BV does not manifest itself because there is no change in the absorption coefficient, under the assumption that the blood content itself is constant.
Finally, the DPF was determined from the step-size ⌬l and the number of steps n the photon needed to pass from the emitter to the detector according to Because the ICG concentration is strongly changing between the time of injection ͑bolus͒ and the first and second passage of the optically observed brain segment and further decreases according to the clearance rate of the liver, which under normal conditions, causes ICG to disappear within 15 to 20 min after injection, the change of the DPF due to altered paths of the photons was not considered.

Result
A first simulation series was devoted to three different emitter-detector distances applied to the human forebrain, whereby the region of interest was near the temple ͑near slice 8 in Fig. 1͒, an area that includes a deep sulcus with a high amount of CSF. Further simulations were performed 1.5 cm closer to the sagittal line of the head ͑approximately slice 6 in Fig. 1͒. This region contains less CSF ͑volume͒. The MC simulations for the smallest emitter-detector distance of d 1 =2 cm were made with no reduction factor ͑i.e., k =1͒ in order to verify the influence of the absorption factor a . For the arrangement with an interoptode distance of d 2 =3 cm, the reduction factor for the absorption was set to k = 0.1. In case of the distance of d 3 = 4.5 cm, a reduction factor of k = 0.01 was used. For all simulations, the opening angle of the light beam of the emitter optode was specified to be ␣ = 45 deg.
The results of the simulations pertaining to the region with a low CSF volume are shown in Fig. 5, while those relating to the region with a deep sulcus filled with a large volume of CSF are shown in Fig. 6.

Photon Density Distribution within the Tissues
The successful paths of the photons were analyzed to extract information with respect to the tissues that were traversed and to the spatial photon density distribution in each material. In Table 3, the relative photon density distributions are listed for the tissues of the scalp, skull, CSF, gray matter and white matter. A distinction was thereby made between the emitterdetector pair at positions with high and low CSF volume in the optically observed areas, respectively.
There is a relatively small difference in the overall photon density distribution between the three examined emitterdetector pair positions. With a emitter-detector spacing d 1 =2 cm, however, simulated photons travel almost entirely through the scalp and skull only, while for d 2 =3 cm, 6 to 10% and for d 3 = 4.5 cm approximately 16 to 22% of the photons also pervade the brain. As expected, with increasing emitter-detector distance, the photon density in the gray and white matter increase. Yet, the simulated photon density distributions are still low, which implies that even in the best case, only 22% of the OD signal is obtained from gray and white matter, while the rest of the signal is dominated by extracerebral contamination.
These results ͑Table 3, baseline conditions͒ describe the situation where the observed optical segment is associated with unknown, presumably very low rel. BV content within the different tissues. The weighted results, taking the blood content for standard, below average, and best case scenarios into account are given in Tables 4-6, respectively.
The weighted simulation results for the sampled optical segments with a low volume of CSF show that for the average case 5 to 51% and for the best case 7 to 58% of the photon density distribution can be expected to derive from the gray matter, depending on the chosen emitter-detector distance. Furthermore, 3 to 10%, or 3 to 11%, respectively, of the photon density distribution is postulated to be located in the white matter for an emitter-detector spacing between d 2 =3 cm to d 3 = 4.5 cm. For the distance of d 1 =2 cm, the white matter is hardly traversed. This allows us to conclude that the probability that a photon passes through the brain tissue is given by 0 to 10% for a distance of d 1 =2 cm for the below average or best case of rel. BV content and up to 53 to 68% for a distance of d 3 = 4.5 cm for below average or best case, respectively.
The following results focus on the time point of NIRS extended with ICG dye dilution technique, when the injected ICG dye passes the monitored brain segment. In order to assess the effects of the first passage of the blood-ICG dye intermix in the observed optical segment on the expected change in absorption, the results were weighted with the exchange fraction ⌬ of the rel. BV ͑Table 7͒. The exchange fraction ⌬ of the rel. BV is, on the one hand, dependent on the rel. BV content itself and, on the other, also larger for the intracerebral tissue than for the extracerebral tissue. The assumption thereby made was that the blood-ICG dye intermix is dominated by ICG ͑ICG bolus injection͒, which due to the high absorption coefficient of ICG becomes apparent.
The weighted results indicate that for the first passage of blood-ICG dye intermix, at best, between 64 to 74% of the OD signal is determined by the gray matter of the cerebral cortex for an emitter-detector distance of d 3 = 4.5 cm. Although these results are still strongly dependent on the rel. BV within the tissues and on the exchange fraction ⌬ of the rel. BV, they allow us to conclude that NIRS together with ICG dye dilution technique can produce useful CBF measurements within neurointensive care monitoring due to the fact that there is a more than 50% possibility that the light is interacting with the ICG dye in the blood vessels of the gray and white matter than with other tissues. Nevertheless, corresponding corrections for the extracerebral contamination still have to be included. The significance of this conclusion has to be relativized insofar as the baseline conditions, in particular the rel. BV at the beginning of the measurement, are not known. Only short-term changes of rel. BV, yet possibly clinically important, can be recorded.

Differential Path Length Factor
We evaluated the DPF on the basis of the simulations of the various configurations. The calculated values, given in Table  8, are compared with DPFs from Okada. 26 As can be seen, our results with a DPF varying between 6.15 and 7.6 depending on the volume of surrounding CSF are similar to those published by Okada, 26 where the DPF is calculated to be 5.9. The value 43 of 5.9 has also been obtained by Okada using MC simulations. Furthermore, Okada examined the change of the DPF in relation to the distance between emitter and detector optodes. He showed that the DPF will decrease when the distance between the optodes is greater than 4.5 cm, while for narrower optode separations, the DPF remains almost constant at 7.5. 26 The explanation he proposed for this effect was that the CSF has an increasing influence on the DPF with increasing distance between the optodes.
Our simulations show that for the low CSF volume case, the DPFs for the emitter-detector distances of d 1 =2 cm and d 2 =3 cm were approximately equal. For d 3 = 4.5 cm, the DPF was in turn higher. In contrast, for the simulations with a high volume of CSF in a deep sulcus, the DPF values for d 1 =2 cm and d 2 =3 cm were also of the same size, while the DPF for d 3 = 4.5 cm decreased by more than can be explained by the different anatomical structure. Therefore, we note that these results are due to the strong influence of the CSF on the surrounding.

Conclusion and Discussion
New neuroprotective treatment options such as hypothermia applied for brain protection after cardiac arrest, severe stroke, or brain injury made it essential to develop new bedside monitoring techniques to detect cerebral ischemic thresholds and to control the effects of treatment. Therefore, the measurement of electrophysiological data, such as electroencephalography or somatosensory, evoked potential, as did the monitoring of cerebral hemodynamics and oxygenation, which are some of the most important issues in neurocritical care. 55 Since 1993, NIRS ICG dye dilutions 4 has been used for a improved monitoring of cerebral hemodynamics in neuroin-tensive care. However, from the first application of the NIRS ICG dye dilution, one of the caveats which has been subjected to discussion is related to the contribution of the extracerebral tissue. A further important aspect is associated with the blood content of the various tissues involved, which may vary considerably ͑and is unknown in the excised tissues which were used in the published optical data͒, therefore various scenarios were subjected to a theoretical analysis.
On the basis of MC simulations, the light propagation of NIRS in an anatomical head model was modeled and the statistical photon density distribution in the tissues were estimated. Based on the results, we assume that for a emitterdetector distance of d 3 = 4.5 cm, the contributions from the white and gray matter to the OD signal vary between 16 and 22% ͑Table 3͒, that is, the calculated photon density distributions were relatively low with 11 to 17% for the gray matter and 5% for the white matter. We interpret these results as being representative of a scenario with an unknown, but presumably low rel. BV content in the different tissues, in particular in the tissues of clinical interest. Simulation of a brain region containing a low volume of CSF. In all three subfigures, the scalp, skull, gray matter, white matter, and CSF are shown in single MRI image. The emitter and detector optode are marked with black arrows on white rectangulars. The arrows mark the direction of the light into the head ͑emitter͒ and out of the brain ͑detector͒. The successful paths of the MC simulation between emitter and detector are shown overlayed in dark gray. ͑a͒ MC simulation result, optode distance d 1 = 2 cm. ͑b͒ MC simulation result, optode distance d 2 = 3 cm. ͑c͒ MC simulation result, optode distance d 3 = 4.5 cm. In order to obtain insight into the influence of the blood content within the different tissues on the baseline signal, standard, below average, or best case conditions with respect to the rel. BV were defined. Accordingly, the calculated photon density distributions were weighted with these rel. BV contents of the tissues, yielding the results of Tables 4-6, respectively. The weighted results for a distance d 3 = 4.5 cm show a range of the baseline signal component obtained from gray and white matter for a low CSF volume of 52 to 57% and for a high volume of CSF of 59 to 67%. This can be summarized in the statement that approximately 50 to 60% of the baseline signal is contributed by the rel. BV contained within the gray and white matter. The weighted results of the three discussed cases of rel. BV in the tissue document that 42 to 58% of the baseline signal is determined by the blood content in the brain vessels in the gray matter for d 3 = 4.5 cm, while 8 to 11% is determined by blood content in the brain vessels in the white matter. It has to be noted, however, that this conclusion is based on a number of hypotheses regarding the rel. BV of the various tissues involved including its influence on the baseline signal. As was explained earlier, the baseline signal is not of interest. For the OD signal, however, it can be assumed that the same dependence on the rel. BV prevails because the OD signal is essentially created in the intravascular space. The same percentages given above also apply approximately for the OD signal.
Additionally, the scenario of NIRS extended with ICG dye dilution has been taken into account. An assumption was made with respect to the influence of the blood-ICG intermix passage, causing a strong change in absorption, for an exchange fraction of ⌬ = 30% of the rel. BV content within the intracerebral tissue. One finds that the OD signal is determined under these conditions to an extent of 64 to 74% by the gray matter and between 8 and 16% by the white matter maximally ͑Table 7͒. It should be noted, however, that this component of the OD signal is strongly dependent on the baseline of the rel. BV content in the tissues and the exchange fraction. For high rel. BV, the OD signal will be strongly influenced by the blood content in the brain vessels of the white and gray matter, and the exchange fraction will be higher in these tissues and have a stronger contribution to the OD signal when blood-ICG intermix passes the observed optical segment. We therefore conclude that the NIRS measurements in combination with the ICG dye dilution technique through the skull with optodes placed on the scalp contains a significant contribution from brain vessels within the gray and white matter such that mtt ICG , and CBV as well as CBF can be estimated. Yet, under all conditions investigated in the simulation pre-sented in this paper, the extracerebral contamination of the OD signal must still be evaluated and, if necessary, compensated, because even under the most favorable condition, 15% of the OD signal may be derived from extracerebral tissues. This fraction may increase to over 50% under less favorable circumstances.
It was found that the CSF has a significant effect on the OD signals. The reason for this effect derives from the low values of the material coefficients a and s as well as from the index of refraction for CSF. Consequently, the CSF in the interspace between brain and skull functions as a light guide. 20 This light guiding effect can also explain the increase in the photon density distribution through the gray matter with increasing CSF volume. This conclusion is further supported by the calculated DPF values.
The DPF values derived from our simulations for the assumed emitter-detector distances d 1 =2 cm and d 2 =3 cm as well as for low and high CSF compartments correspond largely to the DPF values in the literature. We derived a DPF of 6.15 for the case of a high CSF volume over the emitterdetector distance of d 3 = 4.5 cm under baseline conditions ͑Table 8͒. This corresponds essentially to the results of MC simulations reported by Okada. 26 In turn, we obtained a DPF of 7.6 for the case of less CSF over the distance of d 3 = 4.5 cm. Okada argued that the DPF is influenced by the CSF and the CSF causes a reduction of the DPF. In the absence of CSF, furthermore, the DPF is the same as for shorter emitter-detector distances. Our results support this argument, even if the DPF of 7.6 is slightly higher compared to the value obtained for shorter distances, but this can be explained by the differences in the anatomical structures, which in our approach are taken into account.