1.

Introduction

Both morphology (depth, location, and shape) and the wavelength-dependent optical properties of the underlying tissue affect the observed signals of diffuse optics (DO).^1,2 These are often modeled to be homogeneous or as simplified layered signals when fitting them with a theoretical model to obtain the quantities of interest.^3–8 This is done not because the researchers do not appreciate the complex relationship between the two, but rather because the details of that relationship are too complex to know and utilize for practical measurements. Nevertheless, some more advanced methods utilizing a large number of source–detector pairs to reconstruct tomographic images use the underlying tissue morphology derived from brain scans as a priori information.^9–11 This comes at the cost of being less practical.

The availability of a complex model is not the only issue. Some of the atypical, heterogeneous tissues reduce the signal-to-noise ratio (SNR) to levels that would require unpractical solutions with the current technologies to obtain a reliable number of photons for data processing. This consequence is not a surprise because the physics of the photon propagation is well understood,^3,5,12,13 and it is important to note that these heterogeneities also affect other modalities.

The lack of a universal agreement over the analysis methods and a reliable assessment of the limitations of the technology led to the failures of several clinical trials^14–17 using commercial near-infrared spectroscopy (NIRS) oximeters for neuro-monitoring. This has been particularly impactful in the neurocritical care of conditions such as traumatic brain injury (TBI) and led the clinical community to debate over the utility of NIRS due to the observed limitations in reproducibility, reliability, and accuracy which has been reflected in both the literature^18–22 and elsewhere (e.g., in various discussions in congresses and forums). Many early adopters were discouraged by these results and abandoned NIRS-based cerebral oximetry. It can be argued that this could have been addressed better by the manufacturers through a careful study of the relationship between the tissue morphology and the optical signals and with more advanced online quality control measures. As expected, similar problems arose in studies emerging from research groups that are the developers of the technology and were addressed on an ad hoc basis during the data analysis, mainly by discarding unreliable data.^18–22 Detailed studies of this relationship were also carried out using simulations and with limited in vivo data.^23–32

In this article, an analysis of the data obtained by time-resolved spectroscopy (TRS)³³ and diffuse correlation spectroscopy (DCS)³ over several years using the patient brain scans as the guiding data is reported. We opted not to use this information to build a complex model (would have been unstable due to the limited number of measurements) but rather to use them as a set of case studies. It will be argued here that this is an important contributor to a controversial issue in the field. Our goal is to provide anecdotal examples and speculate on different actions that could be taken to minimize the impact of these complexities on both the clinical science and also the clinical trial levels.

From our presentation, it will be evident that this population is very heterogeneous, and each case should be inspected with respect to the quality of the optical signals as well as the potential ability to probe the brain through overlaying, complex tissue structures. The open question is whether these instructions or suggestions on how to improve the measurements and to develop indicators as to when to trust the results and/or to discard them could lead to a more successful future for near-infrared spectroscopic methods. Our goal is to offer an illustrated guide to assist end-users—such as developers of emerging commercial technologies, young researchers, and clinical collaborators—in applying diffuse optical methods for neuromonitoring in patients with critical care pathologies.

2.

Materials and Methods

2.3.

Subject Inclusion Criteria and Study Protocols

Three different groups of patients present in the intensive care unit (ICU) of the VHUH were selected for enrollment in this study: a cohort of malignant middle cerebral artery (MCA) infarction patients, a cohort of subjects with different severity of TBI and with subarachnoid hemorrhage (SAH).

All cohorts obtained clearance from the local ethical committee within VHUH (ACU-AT-203/2012-3531) and conducted according to the Declaration of Helsinki.³⁸ Informed consent was collected prior to the measurements and signed by either the patients or their legal representative.

In the case of the malignant MCA infarction cohort, patients with large hemispheric infarction were recruited for a prospective interventional study. The inclusion criteria were (1) the presence of malignant MCA infarction and a hypodense lesion involving at least 50% of the middle cerebral artery territory with or without decompressive craniotomy and (2) age between 18 and 65 years.

For the SAH cohort, patients were included in case of ischemic lesions related to subarachnoid hemorrhage and/or conditions following SAH [i.e., aneurysmal rupture with low Glasgow Coma Scale (GCS) score, bleeding, vasospasm, mild ischemia, and ischemic infarction]. These patients, aged more than 18 years, were included in a prospective interventional study.

In the TBI cohort, the inclusion criteria were the same as reported in Ref. 34. In summary, patients over 16 years old with a TBI, GCS score of 3 to 15 upon admission, who required ICP monitoring, and mechanical ventilation from onset or after clinical decline were enrolled. The eligibility criteria included normocapnia [partial pressure of arterial carbon dioxide (${\mathrm{PaCO}}_2$) of 35 to 40 mmHg] and stable hemodynamics allowing for a short hypocapnic challenge, with informed consent from a legal representative. The exclusion criteria were patients with contraindications for invasive neuromonitoring (e.g., anticoagulant use, scalp infection, and bleeding disorders) and clinical signs of brain death.

Despite the populations being different, the study protocol has been uniform: it consisted of $\sim 5\min$ of steady-state acquisition on selected positions on the head (Fig. 1).

Fig. 1

(a) Pictures during hand-held measurements. (b) Illustration of the placement of the optical probes and the recording of the placement in terms of angle and radial distance. The radial distance is measured from the nasion to the mark where the TRS bundle tip was leaning on. The angle was calculated considering the line that passes through the nasion and the eyebrows, perpendicular to the line of the nose, and the line used to calculate the radial distance (this figure was created by modifying images from Servier Medical Art,³⁹ part of Laboratoires Servier, licensed under a Creative Commons Attribution 3.0 Unported License).

The choice of the position for the measurements was made in collaboration with the expert medical staff who identified the different areas of interest according to the CT scans available prior to each measurement. Up to four positions were chosen on the same subject, and few subjects were measured multiple times during different acquisition sessions.

After the acquisition, the position of the probes on the head was recorded. First, the location of the TRS detection fiber tip was marked with a sterile surgical staple, which was fixed on the intact skin by standard transparent medical tape. Subsequently, the radial distance between the nasion and the staple was measured, as well as the angle spanning between this radial distance and the straight line passing through the nasion and the eye line, as visible in Fig. 2a. It was decided to use the TRS tip to represent the whole probe for convenience. To measure the radial distance and the angle, a flexible measuring tape and a protractor were used. Figure 1(b) shows an illustration to better understand these parameters. In cases where CT scans were taken after measurement, the staple position was then captured and visible in CT scans for post-processing reference, as shown in Fig. 2.

Fig. 2

Examples of three-dimensional reconstruction of CT scans with fiducial references of the probes’ placements for two different subjects and measurements. (a) The distances calculated according to the procedure explained in the text are shown. However, it should be considered that these distances are actually shorter than reality, due to the fact that the software did not provide a way to follow the curvature on the skin, whereas it calculates the straight distance between points. (b) The very first trial for recording the positioning of the probes is presented. Two positions were marked by staples, whereas D vitamin capsules were used in the other two. Higher contrast was found for the staples, without producing huge artifacts on tissue and were therefore chosen for the study.

Additional demographic and clinical information such as presence of injury, presence of decompressive craniectomy, sedation state, presence of hematoma, gender, presence of bone, and age were also collected.

2.4.

Data Evaluation

The optical data were analyzed following the physical models and procedures described in Refs. 13, 36, 40, and 41 by making use of MATLAB (Release 2018b, MathWorks, Natick, Massachusetts, United States). Once the optical data were fitted by the appropriate model, ${\mu }_a$, ${\mu }_s^{\prime }$ at both 687 and 830 nm were estimated by TRS, and ${\mathrm{StO}}_2$ was derived. Similarly, from DCS, a BFI was derived.

For the purposes of this work, a “baseline,” i.e., a period of constant hemodynamics, was assumed, and the mean values were calculated for all the variables at each measurement position on the head.

The CT scans were utilized in a more qualitative fashion to define regions of interest (ROIs) in correspondence with each probe position as detailed in Appendix A. We chose to consider an ROI as a circular area of 15-mm radius ($\sim 700{\mathrm{mm}}^2$) because the interrogated region below the probe is dominated by photons that have reached approximately this depth due to the interfiber distances.

As for the qualitative evaluation, the tissue composition below the probe was assessed by experienced clinicians and categorized. The following tissue types were selected and identified with an acronym: subcutaneous tissue (ST), cranial bone (CB), normal brain (NB), swollen subcutaneous tissue (SST), air (A), cerebrospinal fluid (CSF), SAH, extracerebral hematoma (EH), intracerebral hematoma (ICH), ischemic tissue (IT), and brain contusion. The combination of all tissue types going from the most external to the most internal in the head was listed per each ROI, providing a composition of different tissue types. The basic categories that were utilized are summarized in Fig. 3, and one example is provided. The skin was disregarded because it was common to all measurements. In Appendix B, we provide an example of swollen subcutaneous tissue compared with a regular one.

Fig. 3

(a) List of tissue types for the qualitative description of the regions of interest below the optical probe position. (b) Example of tissue composition where a hemorrhage is present (this figure was created by modifying images from Servier Medical Art,³⁹ part of Laboratoires Servier, licensed under a Creative Commons Attribution 3.0 Unported License).

A database was created gathering all the measured variables from optical data, CT scans, clinical information, and the different categories of tissue properties.

2.6.

Data Analysis

The bulk of the results are demonstrated as case examples by investigating the measured optical signals and their detailed structure to compare them with the clinical and radiological findings. Moreover, we used the results from a healthy volunteer to provide a fairly representative scenario for comparison against the data from pathological or abnormal cases.

Each case example is elucidated by the same set of information, whenever possible, as exemplified by Fig. 4. Both optical reconstructions and essential evaluated parameters are also reported as descriptors of the probed region.

Fig. 4

Scheme that allows one to appreciate the salient figures of the curves related to the DCS and TRS methods and to relate their shape with the characteristics of the tissue under scrutiny of the optical probe. The position of the latter is shown on the CT scan by a red circle. Furthermore, indicative ranges and values for the tissue of a healthy adult human head are provided in tables for the different modalities. This scheme will be the same one used to elucidate the clinical cases chosen in the following section. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

From the left, the corresponding slice of the CT scan of the patient is shown with the marked ROI on it. Below, the age and sex of the subject are reported.

Then, DCS results are presented as the normalized electric field autocorrelation function [$g_1(\tau )$, with $\tau$ as the delay time] derived from the normalized intensity autocorrelation function.³ For each probe position, $g_1(\tau )$ curves were averaged over a hundred consecutive as well as over the different detection channels. Therefore, only one autocorrelation curve is represented for the selected ROI, as in Fig. 4. Afterward, the fitting procedure was performed on this curve to retrieve BFI. The obtained fit is superimposed to the averaged $g_1(\tau )$ curve in this figure to appreciate how much the data are represented by the ideal model. In the same graph, the $g_1(\tau )$ curve obtained in the same way from the healthy volunteer is plotted in orange as a reference. In addition to $g_1(\tau )$, for each averaged curve, we have reported the information about the instrument $\beta$ parameter, count rate (intensity), and fitted BFI value in a table that can be compared with the ideal ones. The details about the typical behavior of the measurement and the range of values can be found in Appendix C.

Similarly, for each probe position, a hundred consecutive measurements were averaged for TRS DTOFs. Afterward, the fitting procedure was carried out, and the physiological and optical parameters were obtained.^33,42 To represent the raw data as normalized, the maximum of the DTOF is used for normalization (by simple division).^43,44 Apart from a visual inspection, TRS curves were described in terms of their overall shape (qualitative), amount of broadening with respect to the instrument response function (IRF), and the dynamic range.^33,45,46 Furthermore, we have quantitatively characterized the data by some descriptive parameters, such as relative full-width at half-maximum (rFWHM) of DTOF with respect to the IRF, difference of FWHM between DTOF and IRF ($\mathrm{\Delta }\mathrm{FWHM}$), SNR, ${\mu }_a$, ${\mu }_s^{\prime }$, and ${\mathrm{StO}}_2$. The values for each case example are reported in a table divided per light wavelength, either 687 or 830 nm. The rFWHM was calculated as the ratio between the FWHM of the DTOF and the FWHM of the IRF, although more complex equations do exist for a more precise estimation, taking into account for example the laser power.⁴⁷ The $\mathrm{\Delta }\mathrm{FWHM}$, instead, was calculated as the difference between the FWHM of the DTOF and the FWHM of the IRF. The SNR was computed as the ratio between the maximum of the TRS DTOF curve divided by the standard deviation over a portion of the background signal (the noise) present before the light pulse itself. Again, details about the typical curve behavior and values range can be found in Appendix C.

As a side note, general backscattered light shapes and indicative optical values are valid when the diffusion approximation is valid, as well as the approximation to have greater reduced scattering coefficient over the absorption one (weakly absorbing and highly scattering media).^40,48 On the contrary, other methods should be used to describe the diffused curve shape.⁴⁸ Similarly, other approximations used to solve the diffusion models for DCS and TRS may not hold true (i.e., homogeneous model, slow temporal changes in the fluence rate, and random walk approximation).⁴² For this reason, both qualitative and quantitative analyses are helpful in the quality assessment of the results.

3.

Results

3.2.

Case Examples

A table summarizing the following pathologic examples is provided in Appendix E. We suggest the readers to make this table available at the bedside to facilitate their reading and the comparison of cases.

3.2.1.

Healthy case H0

This case illustrates the data from a healthy 25-year-old female subject (see Fig. 5) where both TRS and DCS curves possess the typical shape following their respective theoretical models.

Fig. 5

Typical curves for TRS and DCS measured on a healthy volunteer (healthy case H0). The DTOF curves and their fit are shown. The fitting region of the DTOF curves is indicated in light blue dashed lines. It is important to point out that in the DTOF graphs, the 0 ns on the time axis was arbitrarily set and does not coincide with the peak of the IRF curve to be able to show the entire curve and its initial background. The typical distance between the IRF curves and their diffuse DTOFs can be appreciated, as well as the slower linear decay of the tail of the DTOF for both wavelengths. The latter also presents almost a decade of higher background before the curve, with a consequently decreased dynamic range for the DTOF. The fit follows very closely the curves of raw data points. The autocorrelation curve also presents a typical behavior as described in the text.

In this case, the decay for DCS $g_1(\tau )$ is roughly exponential. Due to the normalization, the curve starts near one and approaches zero at $\sim {10}^{-4}$ s. The intensity rate is high, above 90 kHz, with a $\beta =0.49$ and very close to ideal. The BFI value is within the normal range.

The TRS curves from both wavelengths show the expected behavior: the peak of the DTOF is shifted to later times with respect to the IRF peak, and the curve is broader with the FWHM of the DTOF, much larger than that of the IRF. DTOF plots are attenuated in amplitude than the IRF, with a long linearly decaying tail. The maximum signal level is acceptable, almost three decades above the noise background. The two wavelengths behaved similarly, and their shape looks alike.

The obtained ${\mu }_a=0.14{\mathrm{cm}}^{-1}$, ${\mu }_s^{\prime }=10-12{\mathrm{cm}}^{-1}$, and ${\mathrm{StO}}_2$ around 67% are not far from the indicated ideal values.

Additional similar examples are provided in Appendix D.

3.2.2.

Case 1

In this patient (male, 29 years), the probe was placed above a region that underwent decompressive craniectomy after malignant MCA infarction. The tissue composition was ST + EH + IT. The qualitative evaluation is based on Fig. 6. As seen in the figure, the results from 687 nm were not reported because there were very few detected photons. This is most likely due to the presence of highly deoxygenated blood in the infarct zone which absorbs differentially higher in this wavelength. This is coupled with the fact that the missing skull implied that the probe was resting on the brain/muscle directly, which absorbs more light than the typical scenario. Given the performance of this study’s device, the number of photons detected by the TRS for 830 nm was very minimal presumably due to the same reasons as above. The minimal DTOF curve that was observed could not be reliably analyzed with a photon diffusion model because it did not indicate a scenario where scattering dominated over absorption. Therefore, no optical properties are reported.

Fig. 6

Case example 1: acquisition on an infarcted area after hemi-craniectomy. DTOF at 830 nm and autocorrelation curves for the red circled placement on the CT scan are displayed. The latter is marked by a slow decay and the former by very poor SNR. The DTOF at 687 nm is missing due to even poorer data quality. The figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

DCS results also showed an atypical behavior that is often observed on dead tissue or on regions with minimal red blood cell movement.³ Unexpectedly, the intensity level was quite high, but the $\beta$ parameter was low and the decay time ($\tau$) was quite long lasting longer than ${10}^{-3}\mathrm{s}$, implying very low BFI. This may be expected because infarcted tissue is expected to have lower blood flow. On the other hand, the model did not fit the curve well and the quantitative results cannot be trusted. Note that once the fitted BFI is lower than $3\times {10}^{-10}\mathrm{cm}/{\mathrm{s}}^2$, the fits may be unreliable because the ergodicity of the measurement may no longer be sufficient due to very low blood flow.

In a case scenario like this, few considerations can be made to yield some guidelines. As for TRS, because the SNR is low, summing up more curves than a hundred could be a method to improve the DTOF or a longer acquisition time. Of course, higher injected source power and/or a larger detection area would also help. However, even with these improvements, it may not be sufficient to obtain a good fit by the diffusion model unless a device with a much narrower IRF is utilized, and the data are fitted by a more complex model (higher order approximations to the radiation transport equation or a Monte Carlo method^30,31). For DCS, the current practice is to report this type of curve as being indicative of blood flow less than one percent of the normal without a specific value.

As a consequence, quantitative results cannot be obtained by diffuse optical methods, but the nature of the data, especially the DCS data, reveals minimal blood flow in the region. Unfortunately, it is hard to predict how this type of tissue would reveal itself to a multi-distance CW NIRS device.

3.2.3.

Case 2

The ROI delineated in this case shows an area of the brain where extracerebral muscle tissue was swollen following a craniotomy, where the bone was repositioned in the head after surgery to treat a lesion (tissue composition: SST + CSF + CB/A). The patient (male, 18 years, initial GCS = 5) presented a diffuse axonal injury with epidural hematoma in the left cerebral hemisphere and cranial fractures due to a car accident and had undergone a decompressive craniectomy on the injured hemisphere.

The raw data and the clinical conditions are showcased in Fig. 7. For the depicted ROI, there is a high probability that the brain was not actually reached by the diffuse optical light path.

Fig. 7

CT scan with the ROI marked in red for case example 2, with the acquisition on a swollen muscle. DTOF curves and autocorrelation curve are compared with the respective ones from case H0, in orange. Lower intensity for all methods and greater/faster diffusion can be seen. The figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

DTOF curves qualitatively appear similar for the two wavelengths: their dynamic range looks similar to the one expected from a healthy tissue, and the DTOF appears broader than the IRF and with a slower linear decay. The DCS curve, instead, had a faster decay toward 0 intensity than the given healthy example, implying a faster BFI, although the curve shape is similar to a healthy-like one and its fitting looks reliable. In quantitative terms, the DCS detected a low light intensity rate, whereas the autocorrelation function had a comparable $\beta$ coefficient and a higher BFI with respect to the healthy example. ${\mu }_a$ coefficient was high for both DTOF curves, which is expected due to the faster linear decay, whereas ${\mu }_s^{\prime }$ was quite low. On one hand, the latter may be due to an amount of direct light, which could appear during hand-held measurements, where the adherence of the probe to the skin depends on the person who holds the probe. It could be remedied with the use of common load sensors, for example. On the other hand, swollen muscle tissue is characterized by accumulated liquid, which is mostly transparent/translucent and scatters less.

If these results are evaluated without care, they could be interpreted as representing true cerebral hemodynamics. However, from the CT scan, it appears evident that the probed area had a low probability to have intersected the brain cortex: the atypical increased thickness of the upper layers implies that the bulk of the photons did not reach the brain. In light of this, these data have to be interpreted as invalid for measuring the brain. Rather, they reflect the properties of the swollen muscle and, partially, the bone, which could be relevant for other reasons or studies.

From the perspective of the TRS, it is possible that a better setup, with a higher laser power and tighter FWHM of the IRF could allow us to time gate the photons and retrieve the information from the deeper layers. This would also require a more complex analysis method, e.g., using layers or anatomical priors, which are known to be unstable.^29–31

3.2.4.

Case 3

Figure 8 shows the findings from case 3, which is a common, yet very difficult case to interpret. The data were acquired above a swollen muscle with large edema and after a craniectomy procedure (tissue composition = SST + CSF + NB, male patient, 56 years). The etiology was a fall (initial GCS =13, later reduced to 8 at intubation) that produced subdural hematoma and subarachnoid hemorrhage requiring a decompressive craniectomy procedure on the left cerebral hemisphere.

Fig. 8

CT scan with the ROI marked in red, DTOF curves, and autocorrelation curve for case example 3: acquisition on a swollen muscle after a craniectomy. All figures of merit are tabulated. The decay for the autocorrelation curve is slower than in a healthy condition, whereas the DTOFs’ diffusion is lower, due to the lack of skull-related scattering events. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

At the TRS level, the DTOF curves detected for both wavelengths are analogous: sufficient dynamic range in amplitude, shorter photon path lengths compared with a typical brain, and fast linear decay of the backscattered light pulse tail in line with a higher absorption value which is due to the lack of the skull. Numerically, the values found display an absorption coefficient higher than usual, comparable to the previous case 2, whereas the ${\mu }_s^{\prime }$ is intermediate between case 2 and a normal expected value. DCS shows a slower decay and comparable shape to the normal case. Quantitatively, the DCS intensity of the acquired curves was acceptable, $\sim 24\mathrm{kHz}$ averaged over four channels, whereas $\beta$ was comparable to a healthy-like case. Finally, the obtained BFI is lower than for an intact head condition.

Referring to the CT, the photons have a low probability to have crossed their path with the cerebral gray matter, due to the thickness of the outer inflated tissue. Therefore, similar conclusions and suggestions to case 2 could be made here with a main difference: the absence of skull, which may account for the differences in the scattering properties and lower BFI.

This is another case of data appearing “normal” while possibly not reflecting the cerebral hemodynamics. The CT scans should be considered when evaluating these results.

3.2.5.

Case 4

In this case example, the probe was lying upon a region that underwent a decompressive craniectomy with an accumulation of cerebrospinal fluid between a thin layer of muscle and the brain, as visible in Fig. 9. The patient (male, 53 years) had an ischemic lesion on the right capsule–thalamic region and a hemorrhagic frontoparietal contamination on the left cerebral hemisphere after a fall (GCS = 11). He was treated with a decompressive craniectomy on the right hemisphere. Despite what is shown in the figure, the skull fragment had been replaced to its original position at the time of the measurement, and therefore, the tissue composition beneath the probe was SST + CB + CSF + NB.

Fig. 9

CT scan with the ROI marked in red, DTOF curves, and autocorrelation curve for case example 4: acquisition on a CSF accumulation after a craniectomy. The presence of inflamed tissue, CSF, and cerebral cortex has the combined effect of reducing at minimum the intensity rate of the autocorrelation function, not allowing for a reliable fit, and of the 687 nm DTOF, with just one decade of dynamic range. It is difficult to interpret the 830-nm DTOF curve as extraneous. The available figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

Qualitatively, DTOF curves reveal that overall, there were fewer detected photons but with comparable light diffusion to the healthy tissue. The 687-nm backscattered light pulse is more affected than the 830 nm one, which presumably is due to highly deoxygenated hemoglobin presence (which absorbs more at 687 nm). The data could not be fitted to the model with the current set-up and acquisition conditions.

DCS was unable to detect a usable intensity. Even after a long integration time, the curves shown in Fig. 9 are quite suspect, likely reflecting structures of noise (e.g., after-pulsing).

CSF is mostly translucent and low scattering could lead to a lower number of photons being scattered back to the detector. Furthermore, this measurement was taken over a region where the hair was shaved but hair follicles remained in place. This complicates the data acquisition greatly. In this case, the effects are quite visible and even without the CT scans one could notice the poor quality of the measurements. This may or may not be true for multi-distance CW measurements—stressing one more time the importance of the consideration of the underlying anatomy.

3.2.6.

Case 5

As highlighted in Fig. 10, this case offers an example that features a partial intersection of an intracerebral hemorrhage, which is the large, oval bright area in the CT scan enclosed in the red oval. Most likely, the measurements mainly reflect the skull and gray matter but could be influenced by the hemorrhage and its surroundings to some degree. The tissue composition assigned to this probe location is ST + CB + ICH/NB. The patient (female, 28 years) suffered a TBI and SAH (diffuse lesion type III) along with a complete spinal lesion at the C3 level. A decompressive craniectomy was performed on her left cerebral hemisphere.

Fig. 10

CT scan with the ROI marked in red, DTOF curves of TRS, and DCS autocorrelation curve for case example 5: acquisition partially intersecting a hemorrhage. Both DTOF curves and values resemble the healthy example of case H0, making it hard to distinguish them apart from the decay, which appears slower for all methods. The figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

By inspecting the DTOF curves, at a qualitative level, both wavelengths possess the same features: wide dynamic range and dispersion of the curve that is comparable to a normal tissue-like, slower linear decay which should mean lower absorption properties. DCS autocorrelation function, instead, has a damped shape, flat in the initial part, which does not appear to reflect a single exponential and has a slower decay.

On the quantitative side, the TRS figures of merit feature: ${\mu }_a$ around 0.1 to $0.09{\mathrm{cm}}^{-1}$ which are typical for a healthy head, high ${\mu }_s^{\prime }$, high SNR, and good fit to the model. However, the ${\mathrm{StO}}_2$ appears to be $\sim 10\%$ higher than that for a healthy brain. Conversely, the DCS curve is characterized by low intensity and high $\beta$, which was probably affected by the typical afterpulsing observed in this class of photon counting detectors, i.e., in a simplistic manner, afterpulsing is the detection of a second, false photon by the detector after the initial photon in a probabilistic fashion (see details in C). This led to the observation that the fitting procedure ended up with a BFI value much lower than usual, but because the data are dominated by noise, this is not a reliable value.

Under these circumstances, a blind measurement analysis could lead to the wrong conclusion: the hemorrhage is there, but the way in which it influenced the signal is unclear. In conditions of reasonably maintained blood flow, low partial pressure of tissue oxygenation (${\mathrm{PtiO}}_2$) readings are reported in the literature,⁴⁹ which are a symptom of low oxygen extraction by the tissues. Therefore, higher than normal (i.e., greater than 70%) tissue oxygen saturation is expected in the blood, which is confirmed by this measurement.

The $g_1(\tau )$ DCS curve is certainly affected by the hemorrhage indicating a heterogeneous result—possibly a probed volume with large volumes of low and high scatterer dynamics leading to a complex shape.

Overall, if the presence of the hemorrhage is taken into account, it may be possible to select a different region to either try to obtain brain values or to get information reflecting the hemorrhagic region itself.

3.2.7.

Case 6

The case example presented in Fig. 11 is similar to the previous case: the probe was positioned over the skull in a region that included tissue with a subdural hemorrhage. In fact, this patient (male, 63 years) had experienced a fall from 2 m of height that led to a contusion (GCS = 14) and following lesion on the left cerebral hemisphere necessitating a craniotomy procedure to extract the hematoma on the temporal left side of the head. The probed region was assigned ST + CB + SAH + NB as tissue composition.

Fig. 11

CT scan with the ROI marked in red, DTOF curves, and autocorrelation curve for case example 6: acquisition partially intersecting a hemorrhage. This case should, in principle, be relatable to case example 5. However, the intersected area is more diverse, and the effect on the optical signals appears quite different: a faster decay for the DTOFs and an autocorrelation curve that does not reach 0. All figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

The DTOF curves show a faster linear decay than a healthy tissue, with sufficient dynamic range and comparable dispersion with respect to their IRF for both of the wavelengths. On the DCS side, the initial part of the intensity autocorrelation curve is similar to a healthy-like case, but its final portion did not properly reach 0 after the exponential decay, rather it presents a secondary exponential decay. This is most likely indicative of a shallow region with low blood flow.

Quantitatively, on the TRS side, the SNR is high, and the relative and difference of FWHM agree with the expectations for a diffused DTOF for both wavelengths. Moreover, the data agree very well with the model. Interestingly, the information found is relatable to the previous example. In this ROI, the ${\mu }_a$ values are still low, between 0.07 and $0.1{\mathrm{cm}}^{-1}$, ${\mathrm{StO}}_2$ is quite high (80%), whereas ${\mu }_s^{\prime }$ coefficients are $\sim 6{\mathrm{cm}}^{-1}$, lower than healthy tissue-related ones.

The DCS curve deviated from the homogeneous model significantly, although the intensity rate was decent and $\beta$ in line with normal values. Therefore, the BFI cannot be considered reliable. It is also worth noting that the final part of the curve affects the calculated numbers due to the physics, even if the cutoff threshold for the fitting procedure of the DCS curve occurs at an autocorrelation value of 0.3. Moreover, the second exponential decay in the tail of the autocorrelation function may suggest that the method is detecting atypical tissue, as if a sudden change in the morphology creates a second layer that abruptly modifies the decay.

This case is difficult the evaluate. Clinical interpretation of the CT scan reveals significant heterogeneity and abnormalities under the probe, and the optical data show deviations from the physical models for the DCS curves. A conservative approach would err toward invalidating the optical measurements, whereas it surely highlights potential issues with CW measurements, which may not reveal these problems so clearly.

3.2.8.

Case 7

Another possible situation is represented by the presence of accumulation of CSF between the skull bone and the brain, as shown in Fig. 12. The patient for this case was the same one as in case 4. The tissue composition for this ROI is ST + CB + CSF + NB.

Fig. 12

CT scan with marked the ROI in red, DTOF curves, and autocorrelation curves for case example 7: acquisition on a CSF accumulation below the skull. For the DTOF curve, the similarity to the healthy case H0 makes them almost impossible to tell apart. On the contrary, for the DCS curve, the slower decorrelation toward zero and the shape seems to be affected by the CSF composition. The figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

Observing the DTOF curves, it is immediately evident that they have an appearance that resembles that of normal tissue: the dispersion, the dynamic range, and the shape are very similar. On the DCS side, the shape is highly distorted, possibly revealing multiple decay constants.

Also, at a quantitative level, the values are in line with an acquisition obtained from a healthy head for the TRS, although resulting in a low ${\mathrm{StO}}_2$. For the DCS, the models cannot be used to fit the data.

This case is particularly problematic when interpreting the data and the worst is that, from a careful evaluation of the quality of the TRS data, it is practically impossible to notice that something is hidden behind the findings. As previously mentioned, CSF is a fluid with low scattering and absorption properties. It appears that the presence of CSF is tricky and difficult to recognize, especially considering that it is only an intermediate layer in this measurement. Moreover, considering that, given the thickness of the intermediate layers, the gray matter may have not been reached, it is reasonable to obtain a low tissue saturation. In this context, the CT scan is a primary source of information. A pre-measurement view of the CT scan should not be omitted in this case.

3.2.9.

Case 8

Fig. 13 shows an example in which, after an injury, air got trapped between the skull and the frontal lobe of the brain. This is a quite common situation, especially after a concussion and after a surgery,⁵⁰ known as pneumocephalus. Moreover, there is a natural cavity, the sinuses, which are at times more pronounced in some people and that can be present up to a couple of centimeters above the eyebrow line. In this case example, the patient (male, 29 years) had TBI (initial GCS = 3) caused by a fall that led to a therapeutical decompressive craniectomy on the left cerebral hemisphere. The indicated ROI also appears to include the brain and skull, with a tissue description as SST + CB + A + NB.

Fig. 13

CT scan with the ROI marked in red. DTOF curves and autocorrelation curve for case example 8, where the probe was above a region filled with air trapped below the skull. As for the initial portion of the autocorrelation curve, the resemblance with the healthy tissue one is high, whereas this is not true for the final decay, which is actually more related to scattering events. The figures of merit are tabulated. Red circle: ROI ($Ø30\mathrm{mm}$). Magenta curve: current subject’s $g_1(\tau )$ curve.

The qualitative analysis of the TRS curves reveals a very strong analogy with a healthy head situation, even if the linear decay is a little less rapid. For the DCS curve, on the other hand, the situation is similar to that of cases 6 and 8, where a second decay appears in the final part of the curve.

In quantitative terms, ${\mu }_a$ coefficients appear normal, whereas ${\mathrm{StO}}_2$ and ${\mu }_s^{\prime }$ higher than for a healthy head. As regards the $g_1(\tau )$ curve, the intensity rate is quite reduced (14 kHz), but $\beta$ and BFI values seem reasonable, with a proper fit, and comparable to a healthy scenario.

Consequently, it looks like diffuse optics cannot clearly distinguish between a normal head and one where air is comprised. Most likely, the presence of a region with trapped air, a non-diffusive medium, led to a complex result that could have confused traditional quality control methods.

4.

Discussion

Several reasons are listed for the lack of widespread implication of NIRS-based monitoring in TBI. Among them, there are contamination from extracranial or extracerebral tissues, difficult implementation due to scalp and facial injuries, confounding effects caused by subdural, epidural and extracranial hematomas, and dead tissue.^{18,18–20,84,85} However, improvements in the computational modeling of DO and its integration with subject-specific imaging do represent a clear possibility to expand its use in brain pathology assessments.

In this work, we have characterized structural and optical signal abnormalities in severe brain injury, malignant MCA, and SAH patients. Overall, the results described problematic tissue types and how they affected the DO signals in a major attempt to understand if certain impaired brain regions are measurable and to promote data quality examination. In fact, the complex multi-layered structure of the adult human cranium already sets a limit to the accuracy of NIRS.^86,87

We have recruited a pool of 36 patients that included 9 malignant MCA, 26 TBI, and 1 SAH. In 19% of the cases, surgery was performed on the subject, allowing for thirteen measurement acquisitions in the absence of skull. The surgical procedures included decompressive craniectomy, craniotomy, and resection.

Initially, we have described eight case examples with pathologies and one case of a healthy subject qualitatively and quantitatively. The selected cases had the objective of showing typical situations that one can meet when this type of patient is recruited and to provide a fairly representative sample, albeit limited to the variety of measurements that have been obtained. In some cases, the simple view of the curves made it possible to immediately understand the difference compared with the healthy case, whereas in others, it did not. Moreover, even at the level of numerical values, it was at times impossible to discern whether it was a curve generated by healthy or damaged tissue. Later on, some guidelines for measurement practice were outlined and related to the literature to provide insights and practical examples.

To the authors’ knowledge, there is no similar attempt in other studies on head-injured subjects and by hybrid DO technique. Some existing work regarding healthy subjects has been undertaken in, for instance, Refs. 88 and 77. In the latter, a strict quality control practice was also set,⁷⁷ partially as we aimed to discuss in this paper. Some studies have reported oddities when CW-NIRS devices were used with hematomas, craniotomies, and craniectomies^20,23,89,90 but did not inspect the cases. Other studies rather focused on the detection of hematomas, either by bi-hemispheric cerebral comparison or absorption values,^{67,87,91–93} by standard CW monitors. Instead, the effect of CSF has been mainly studied by means of simulation^23,25,86,94 because it is difficult to isolate it in real experiments, whereas the skull effect was studied on a reduced number of subjects ($N=10$) and by NIRS simulations.⁹⁵ Some more comprehensive studies focused on measurements of ischemic infarction patients, in which, however, averaged values for several cerebral positions were reported and limited information regarding the raw data/curves was provided.^77,96

Despite the heterogeneous complexity of the morphology across the brain, the associated values partially indicate different brain conditions as well as depend on separate confounding factors. Anatomical lesions, disease progression, and therapeutic interventions (i.e., decompressive craniectomy) can all modify the regions beneath the probes. Nevertheless, TRS-DCS techniques offer some useful applications: i.e., the significant light absorption caused by hemorrhages can help diagnose injury types. In addition, the comparison of the optical properties of various areas of the head for patients where other stimulation is not possible by checking their symmetry, as previously reported, could be introduced. However, it is always preferable to refer to images of the underlying structures, if available, before performing any measurements.

Therefore, we believe that this work shows how the combination of hybrid DO with other techniques could enhance multimodal neuromonitoring, offering biomarkers that represent different aspects of pathogenetic mechanisms for a holistic (and more accurate) understanding of the brain status.

We provide a large, annotated dataset that could be used for further analysis and interpretation in the future.

It must be noted that the characterization reported in this paper, especially at the quantitative level, is affected by the properties and intrinsic features of the device used, which determine its performance and establish its limitations. Therefore, the experimental conditions and conclusions presented in this article should be reconsidered and adapted for each device/probe and cannot be fully generalized.

As previously stated, analyzing data with a model based on a homogeneous semi-infinite medium is not ideal in cases of heterogeneous probed volumes, such as for the data presented in this article. As noted in the literature reported in Secs 3.3, 3.2.3 and Table 4, a multi-layer analysis would be advantageous. However, to date, such models remain unstable due to the physics of the problem (strong dependence on specific assumed anatomical parameters) and have not been implemented as practical bedside, real-time analysis methods. Due to this, although preliminary exploratory analyses suggested potential differences in optical properties and blood flow among tissue types (e.g., skull bone and hematoma), these findings were not pursued further due to limitations in potential inaccuracies in quantitative values, as well as sample size and study design.

In this article, skin was not considered in the tissue assessment, because it was present in every measurement, even though the data are affected by its presence. In Ref. 23, the authors noticed that the light intensity was halved after scalp removal. Moreover, the scalp and skull possess highly diverse optical properties that provoke a completely different effect on the light passing through and the curve’s shape.²³ The skin’s ${\mu }_a$ is quite higher than the skull’s: the authors argued that the skull would almost not attenuate the light passing through. Therefore, taking skin in relation to its thickness into account may be important.

A potential criticism is the choice to use only a few case examples from which to begin to discuss possible guidelines and improvements for using DO in these cerebral tissues. This approach might seem reductive, but the examples serve as a starting point. In a qualitative manner, we have considered various clinical and in vivo studies carried out in other populations such as ischemic infarction patients, patients with carotid stenosis, the elderly without any known brain injuries, and healthy subjects. Nonetheless, this study provides a good starting point for visualizing extreme cases of brain damage, though additional measurements are needed to reach solid conclusions.

Overall, this study provides case example studies of complex, yet common clinical situations, serving as a starting point for designing new devices, probes, and algorithms and for implementing quality control assessment. The output dataset can be utilized for further quantitative analysis, such as estimating optical properties for different tissue categories and carrying out numerical simulations. We strongly recommend that even real time, bedside display of the output should be supplemented with priors from the clinical and radiological evaluations to avoid false results. Finally, we highlight that there might be situations in which typical diffuse optical neuro-monitoring is simply impractical for certain tissue volumes.

5.

Conclusions

In light of the findings and literature review, this article has successfully shown key morphological alterations and their relation to the performance of hybrid optical devices. The interpretations are truly multiple and yet necessary to confirm the practicality of this technique in the myriad of possible conditions.

6.

Appendix A: Identification of the Regions of Interest on CT Scans

It was arbitrarily chosen to consider the ROI as a circular area with a radius of 15 mm and an area of $\sim 700{\mathrm{mm}}^2$. This choice was made upon the fact that the interfiber distance between the TRS source and detector tips for the device was 30 mm, and consequently, the optical sensor was probing with higher probability the density region at $\sim 15\mathrm{mm}$ deep.

Few steps were followed for the manual identification of each ROI. If the CT scan contained the reconstruction of the fiducial staples left on the patient’s skin (examples are provided in Fig. 2), the slice with higher contrast for this object was taken as an axial plane. The ROI was then selected “underlying” the staple contrast position. Unfortunately, there was no post-measurement CT scan with staples for all included subjects. In this eventuality, the retrieval of the ROI took advantage of the angular and radial information collected at the time of the acquisition. A mannequin head was used to relate distances and angles on a real volume and then adapt the position as much as possible to the morphology found in the CT.

For few subjects, the actual position was not recorded: in this case, an estimation based on the data collection experience was carried out. The procedure consisted of reaching the axial slice with the highest contrast for the crystalline biconvex lens of the eyes and then adding to this plane a vertical shift of 15 mm (the average value between the crystalline and the eyebrows for other subjects), adding further 40 mm to reach the middle of the forehead and select this axial plane. Then, in this plane, a line was depicted following the midline of the brain up to the front, and 45-deg angles were also drawn up to the forehead surface approximately in correspondence with the middle of the eyes and symmetrically for the two cerebral hemispheres. The crossing point on the forehead line was used to position the ROI in the area below, tangent to it.

7.

Appendix B: CT Scans Example of Regular Versus Swollen Subcutaneous Tissue

In Fig. 14, we facilitate a visual example of regular subcutaneous tissue in comparison with swollen subcutaneous tissue to make inexperienced users aware of the appearance of the CT scans. We would like to point out that expert personnel trained in interpreting CT scans were responsible for identifying the tissue categorization. Consequently, this task may not be as straightforward for inexperienced viewers to achieve.

Fig. 14

Examples of tissue composition encompassing regular ST and swollen tissue are provided to illustrate a reasonable understanding to inexperienced readers. (a) Green ROI was identified as having a tissue composition as “ST + CB + NB,” where no significant tissue thickness can be identified between skin and skull. (b) Instead, the green ROI circle includes a tissue labeled as “SST + CB + CSF + NB,” where there is a clear thick dark region between the skull (white) and the outer skin. Swollen tissue contains water, which explains the dark color in the CT scan for this region.

8.

Appendix C: Expected Optical Signals Shape and Values Range

We report the nature of typical signals measured from an uninjured, presumably healthy brain for those readers who are not familiar with TRS and DCS data.

Ideally, the decay for the DCS autocorrelation curve is exponential, decreasing with the square root of the delay time.^3,71,97–99 When the normalization of the curve works as expected, the $g_1(\tau )$ curve starts near one and approaches exponentially to zero for increasing $\tau$.^3,71,97–99 For the source–detector separations and typical instrumentation, such as those used in this study, it reaches zero at $\sim {10}^{-4}$ s.^3,71,97–99 Even for a specific instrument, this is influenced by the BFI and other optical parameters.^3,37 In a healthy brain, good-quality data are obtained with the observed count rate well above the noise level (0.5 kHz) and well below the saturation level (200 to 300 kHz, accounting for correlator and detector effects), with an instrument parameter ($\beta$) near 0.5 for unpolarized light.^{3,13,100–102} The fitted BFI value normal range is $1\times {10}^{-9}$ to $8\times {10}^{-8}{\mathrm{cm}}^2/\mathrm{s}$^26,27,37,103 which depends strongly on how the reduced scattering coefficient was calculated.

It is often the case that the DCS signal is affected by detector non-idealities such as dead time, shot noise, thermal noise, dark current, and afterpulsing probability, among others. As a side note, the afterpulsing effect of a detector is a phenomenon where, following a primary detection event, spurious pulses are generated that are not due to actual incident photons but are instead a result of the detector’s internal processes.¹⁰⁴ This effect is particularly significant in some detector types, where residual charge carriers or trapped electrons from the initial detection event can be released at later times, causing additional false signals. For instance, the false afterpulsing pulses can create artificial correlations, leading to inflated values of the $g_1(\tau )$ at short delay times, a high $\beta$ parameter, and cause additional noise.¹⁰⁵ Although some of these could be “corrected” with a sufficiently thorough characterization of the individual detector behavior, it is not advisable to do so when these become the dominant processes due to low photon counts.

In an ideal scenario, the “TRS curves” from both wavelengths show an expected behavior: the peak of the DTOF is shifted to later times with respect to the IRF peak, and the curve is broader meaning that the FWHM of the DTOF is much larger than that of the IRF due to the broad distribution of the propagation times in tissue.^33,62 DTOFs are generally attenuated in amplitude (often visualized and/or processed normalized to the peak) with a long decaying tail. This tail decays linearly for long path lengths where absorption occurs with greater probability and dominates over scattering.^33,62 The delay of the peak comes from the finite time that light employs to go from the source to the detector.³³ The broadening of the DTOF is a consequence of the different paths that photons travel inside of media because of multiple scattering events.^33,62

Retrieving the proper shape of the DTOF, built by the number of detected photons yields information about the optical properties of scattering and absorption that characterize the probed medium area. To obtain a good quality signal, the maximum signal level has to be a few decades above the noise background prior to the DTOFs.^33,62 Moreover, both DTOFs at the two wavelengths should behave similarly, which is expected in a healthy-like tissue where oxy- and deoxyhemoglobins affect them in a similar way. This could change dramatically in case of deeply deoxygenated, i.e., often hypoxic and/or ischemic, tissue. Overall, a dynamic range of three to four decades (or higher) for the DTOF curves is generally acceptable to ensure a proper fit of the optical parameters, especially guaranteeing to extrapolate the absorption information from the linear decay of the tail.⁶² The DTOF peak delay from the IRF peak of at least $\sim 0.7$ to 0.8 ns is also common and is generally acceptable;³³ otherwise, it may entail insufficient diffusion time of the photons within the medium, hence rendering accurate the measurement of IRF even more crucial.

The relative FWHM is expected to be a value greater than one when there is typical broadening due to photon diffusion in the tissue. In fact, the FWHM of the IRF defines the temporal resolution of the device. When the photon’s arrival time broadens due to the scattering events and the emerging DTOF modifies its decay given the amount of absorption events while traversing a tissue, the output DTOF retains this information: the more scattering events (and properties, the more), the broader the histogram of photon arrival times. Therefore, the FWHM of the DTOF is generally broader than the IRF one.⁶² This is typical for a structure such as the healthy human head and its optical properties.⁵⁸

$\mathrm{\Delta }\mathrm{FWHM}$ should be positive in standard diffusion/absorption conditions.^40,106

The SNR level depends on many factors, such as the background noise of the detectors or how well external light is shielded. Its acceptable value has to guarantee a clear distinction between the DTOF curve and the background level,¹⁰⁶ and generally, an SNR = 10 can be chosen as a non-strict value below which data should be considered for exclusion. Generally, a rule of thumb for good values in a healthy brain are ${\mu }_a\sim {\mathrm{cm}}^{-1}$, ${\mu }_s^{\prime }\sim 10{\mathrm{cm}}^{-1}$, and ${\mathrm{StO}}_2$ around 56% to 66%.^7,33,58 Nonetheless, these are indicative values and literature examples carried out on large cohorts of patients are useful as a starting point, i.e., from Refs. 58, 77, and 88.

In both cases, we have provided a qualitative guideline based on experience and the literature that could be adopted, even at the bedside as a figure of merit. For further quantitative analysis, we refer the readers to excellent reviews of the topics such as in Refs. 32, 33, 58, 69, 88, 107, and 108 and their citations.

9.

Appendix D: Additional Healthy Case Examples

In this appendix, we provide further examples of typical TRS and DCS curves from healthy subjects to not only provide further data as an illustration but also to demonstrate that even the presumably healthy brain impresses significant heterogeneity on the measurement.^{32,33,57,58,109} We have produced them in the same fashion as healthy case H0 in Figs. 15Fig. 16Fig. 17–18.

Fig. 15

Typical curves for TRS and DCS measured on a healthy volunteer: healthy case H1. The DTOF curves and their fit are shown. The fitting region of the DTOF curves is indicated in light blue dashed lines. It is important to point out that in the DTOF graphs, the 0 ns on the time axis was arbitrarily set and does not coincide with the peak of the IRF curve to be able to show the entire curve and its initial background. The typical distance between the IRF curves and their diffuse DTOFs can be appreciated, as well as the slower linear decay of the tail of the DTOF for both wavelengths. The latter also presents almost a decade of higher background before the curve, with a consequently decreased dynamic range for the DTOF. The fit follows very closely the curves of raw data points. The autocorrelation curve also presents a typical behavior as described in the text.

Fig. 16

Typical curves for TRS and DCS measured on a healthy volunteer: healthy case H2. The DTOF curves and their fit are shown. The fitting region of the DTOF curves is indicated in light blue dashed lines. It is important to point out that in the DTOF graphs, the 0 ns on the time axis was arbitrarily set and does not coincide with the peak of the IRF curve to be able to show the entire curve and its initial background. The typical distance between the IRF curves and their diffuse DTOFs can be appreciated, as well as the slower linear decay of the tail of the DTOF for both wavelengths. The latter also presents almost a decade of higher background before the curve, with a consequently decreased dynamic range for the DTOF. The fit follows very closely the curves of raw data points. The autocorrelation curve also presents a typical behavior as described in the text.

Fig. 17

Typical curves for TRS and DCS measured on a healthy volunteer: healthy case H3. The DTOF curves and their fit are shown. The fitting region of the DTOF curves is indicated in light blue dashed lines. It is important to point out that in the DTOF graphs, the 0 ns on the time axis was arbitrarily set and does not coincide with the peak of the IRF curve to be able to show the entire curve and its initial background. The typical distance between the IRF curves and their diffuse DTOFs can be appreciated, as well as the slower linear decay of the tail of the DTOF for both wavelengths. The latter also presents almost a decade of higher background before the curve, with a consequently decreased dynamic range for the DTOF. The fit follows very closely the curves of raw data points. The autocorrelation curve also presents a typical behavior as described in the text.

Fig. 18

Typical curves for TRS and DCS measured on a healthy volunteer: healthy case H4. The DTOF curves and their fit are shown. The fitting region of the DTOF curves is indicated in light blue dashed lines. It is important to point out that in the DTOF graphs, the 0 ns on the time axis was arbitrarily set and does not coincide with the peak of the IRF curve to be able to show the entire curve and its initial background. The typical distance between the IRF curves and their diffuse DTOFs can be appreciated, as well as the slower linear decay of the tail of the DTOF for both wavelengths. The latter also presents almost a decade of higher background before the curve, with a consequently decreased dynamic range for the DTOF. The fit follows very closely the curves of raw data points. The autocorrelation curve also presents a typical behavior as described in the text.

10.

Appendix E: Summary of the Case Examples

The case examples are summarized in Table 5 to facilitate the comparison among cases.

Table 5

Summary of the case examples presented in the results, to help the reader in their comparison. TBI, traumatic brain injury; SAH, subarachnoid hemorrhage; MCA, malignant cerebral artery stroke; SNR, signal-to-noise ratio; BFI, blood flow index; μa, absorption coefficient; μs′, reduced scattering coefficient; CSF, cerebrospinal fluid.