2.1.

Animal and Tissue Handling

All animal studies were approved by the Animal Care and Experimentation Committee of the Canton of Bern, Switzerland, and followed the Swiss national guidelines for the performance of animal experiments. We examined eight female New Zealand white rabbits at least 15 weeks old and weighing 3.5 to 4 kg (Charles River Laboratories GmbH, Sulzfeld, Germany). They were housed in the core animal facilities of the University of Bern with a 12/12 h light/dark cycle at 22°C and with food and water ad libitum.

For anesthesia, animals received a premedication of $35\mathrm{mg}/\mathrm{kg}$ ketamine and $10\mathrm{mg}/\mathrm{kg}$ xylazine, followed by isoflurane 2 to 5% and fentanyl $50\mu \mathrm{g}/\mathrm{kg}/\mathrm{h}$ during the whole course of the measurements. Euthanasia was carried out for four animals by bleeding from the femoral artery followed by injection of concentrated $2\mathrm{mmol}/\mathrm{ml}$ KCl solution to stop the heart from beating, and for the remaining four animals by direct injection of KCl. After the in vivo and postmortem measurements, the rabbit heads were sawed off and kept either frozen at ${-20}^{°}\mathrm{C}$ or in neutral-buffered 10% formaldehyde solution (Hospital Pharmacy, Inselspital, Bern, Switzerland).

X-ray images of the catheter locations in the skull were documented with a portable x-ray system (Philips, BV Pulsera R1.2, Eindhoven, The Netherlands).

2.2.

Experimental Setup for Light Delivery and In Situ Measurements of the Fluence Rate

Light was delivered through a dedicated cylindrical diffuser of 20 mm length and 1 mm diameter (RD20, Medlight SA, Ecublens, Switzerland), whose power output was calibrated with an integrating sphere (LMS-200, 20 in. diameter, Labsphere Inc., New Hampshire) before and after experiments. The diffuser was connected to laser diodes emitting at 635 nm (Ceralas PDT, $635/4\mathrm{W}/400\mu \mathrm{m}$, CeramOptec GmbH, Bonn, Germany), 671 nm (RLTMRL-671-1W), or 808 nm (RLTMDL-808-5W, Roithner Lasertechnik GmbH, Vienna, Austria). The power output of each laser was calibrated with a frontal light diffuser (FD1, Medlight SA) and powermeter (detector 818P-010-12, driver 1918-R, SpectraPhysics Newport, California) prior to measurements.

Four catheters (iCAT-2.0-200, OD 2.0 mm, Medlight SA) per animal were placed transcranially and fluoroscopically via burr-holes into defined locations in the brain [see Fig. 1(b)]. They were left in place during and after euthanasia to avoid changes in catheter positions. Catheter locations were defined by a solid guiding plate with a $3\times 3{\mathrm{cm}}^2$ matrix of evenly spaced holes (6 mm hole–hole distance). Catheter positions were chosen to fit to the shape of the rabbit brain ensuring different catheter-to-catheter distances (four to five different distances in the range of $\sim 6$ to 15 mm). The same burr-holes and matrix positions were used for the measurements after long-term storage of the skulls. The guiding plate was fixed to the operation table above the head of the rabbit such that catheter alignment was ensured by two points, the burr-holes in the skull and the holes in the plate. Isotropic probes with a diameter of 0.85 mm (IP85, Medlight SA) were used for the measurement of the local fluence rate. Their response was measured with a calibrated FD1 at all wavelengths before and after the experiment.

Fig. 1

Experimental setup. (a) and (b) schematic showing the arrangement of catheters inserted in the brain containing either light diffuser or isotropic probes. (c) presents an x-ray image taken from the sagittal plane of the rabbit brain. Catheters labeled in red containing either light diffuser or isotropic probe were inserted in the brain such that maximal six relative distances were covered.

A light diffuser or isotropic probe was inserted in the catheter’s lumen to assess the light transmission between the different catheter locations. The light diffuser spanned the full transverse axis of the rabbit brain, leading to symmetric irradiation of the surrounding tissue in the transverse plane. The fluence rate was measured simultaneously at each probe location with a calibrated multichannel photometer (OP710-IN, OptoTest Corporation, Camarillo, California). Measurements were carried out for a minimum of five different positions in the catheters, i.e., in the transverse plane of the brain, typically spaced at intervals of 3 mm, to avoid biased signals due to local inhomogeneities in the tissue, such as blood vessels. During this measurement, the light diffuser remained in place. The influence of the catheter on the fluence rate measurement, i.e., light attenuation and wave guide effects, was determined by illuminating the isotropic probes with and without the catheter in the integrating sphere or directly by a frontal light diffuser. The changes in the measured fluence rate due to the presence of a catheter were $<5\%$ and, therefore, negligible.

Measurements were repeated by rotating light diffuser and isotropic probes through all different catheters [Figs. 1(a) and 1(b)] in order to improve statistics, minimize effects of local tissue inhomogeneities, and reduce the influence of boundary effects due to the finite brain size on the measured data. During reallocation of diffuser and probes, the laser was switched off to prevent unnecessary heating of the brain tissue around the light diffuser. In only one single case an accelerated heartbeat of the animal was noticed during measurements at 635 nm. It is not clear whether this effect was stimulated by the light itself, by heat from the absorbed light, or a combination of both mechanisms.

The fluence rate was measured in the living animal, after euthanasia, and six weeks after long-term storing of the animal’s head fixed by either formaldehyde or freezing. Thawing of the frozen tissue samples was assured by placing them into a fridge at 4°C $\sim 12\mathrm{h}$ prior to measurements. The measurements were carried out in all rabbits at 635, 671, and 808 nm for all tissue conditions, except for one rabbit where there was no measurement at 671 nm for the in vivo and postmortem conditions. A second animal died before in vivo measurements could be performed.

The influence of blood on the postmortem light propagation was assessed by comparing results from a control population of four rabbits euthanized with an injection of KCl and a study population of four rabbits where the blood was drained out during euthanasia. It is noteworthy that only 40 to 50% of the total amount of blood could be exsanguinated. For estimating storage effects on the tissue optical properties, two rabbit heads of each group, i.e., euthanized by KCl or exsanguination, were slowly frozen to ${-20}^{°}\mathrm{C}$. The remaining two rabbit heads of each group were fixed in formalin. In order to assure optimal comparability of experimental results with the data reported in the literature, both long-term storage techniques were chosen to be as similar as possible to the methods applied previously to human tissues and cadavers.

2.3.

Data Processing

3.1.

Fluence Rate Measurements and Interpretation by Monte Carlo Simulations

The exponential decay of the fluence rate as a function of the distance between the source and detector, as described by Eq. (2), was reflected in the experimental data at all wavelengths. Furthermore, the light attenuation, and consequently the effective attenuation coefficient, was highest at 635 nm and became smaller at increasing wavelengths. These observations are represented in Fig. 2(a) by typical profiles of the measured fluence rate and their fit yielding ${\mu }_{\mathrm{eff}}$. However, at large distances $r$ between light source and detector, i.e., $r>10\mathrm{mm}$, measurements revealed a two to five times higher value for the fluence rate than expected from theory. The effect was most prominent at 635 nm and became less distinguishable at longer wavelengths, which may result from a higher ${\mu }_s^{\prime }$ at shorter wavelengths.

Fig. 2

Measured and simulated fluence rate normalized to the fluence rate at the diffuser surface. (a) shows the in vivo normalized measured data fitted by the analytical expression. The fit was constrained by setting the fluence rate at the diffuser surface to the value computed by Eq. (2) for injected laser light power measured prior to the experiment. (b) shows the normalized fluence rate simulated by MMC. The dashed blue line is the fluence rate obtained from Eq. (2) whereas the solid colored lines are the fluence rates in different geometries: a semi-infinite cylinder with the finite light diffuser along the cylinder axis or the generic brain with the light diffuser in one of the semiprincipal axis, lateral or posterior to it.

This behavior was quantified by simulating the fluence rate at the boundary of the rabbit brain by the Monte Carlo method. The simulated fluence rate at the midplane of the ellipsoid representing the rabbit brain is shown in Fig. 2(b) together with the fluence rate obtained from the analytical expression. There was a good agreement between results from the Monte Carlo simulation for a semi-infinite cylinder and the analytical solution from diffusion approximation. Results for the generic rabbit brain, where the light diffuser was positioned either centered, lateral, or posterior, were in agreement with the analytical solution for $1\le r\le 10\mathrm{mm}$. On the contrary, at $r>10\mathrm{mm}$, local deviations of the fluence rate from the analytical expression became prominent. These were also noticeable in the experimental data: they are a consequence of the brain boundaries imposed by the semiprincipal axis of the ellipsoid. The usually larger fluence rate at the brain boundary originates from backscattering of photons. First, the CSF with its small ${\mu }_{\mathrm{eff}}$ is acting as a light cavity leading to a higher photon flux at the brain/CSF transition. Second, the refractive-index mismatch at the skull/air transition is partially backscattering the photons. The fluence rate beyond the skull/air transition drops quickly as there are no photon scattering or absorption events.

Furthermore, we noted that the analytical expression overestimated the fluence rate at the diffuser surface by up to 15% compared to the simulations. However, this effect was negligible considering the large scatter in the experimental data and the fact that the fluence rate at the diffuser surface, given as boundary condition to the fitting procedure, was recomputed during each iteration.

The boundary effects raised the necessity to filter the experimental data for artifacts at large distances, $r>10\mathrm{cm}$, prior to fitting. A general trend was that these effects became more prominent at smaller wavelengths, i.e., 635 and 671 nm. This is due to the increased scattering at smaller wavelengths, since ${\mu }_s^{\prime }\propto {\lambda }^{-\alpha }$ with $\alpha >0$ as described by the Mie theory of scattering.²⁷ Despite the boundary effects, the good agreement between the analytical approach and simulation, however, suggested Eq. (2) to be an appropriate choice for modeling the data obtained in our experimental conditions.

3.2.

Influence of Tissue Storing on the Optical Coefficients

The measured effective light attenuation coefficient ${\mu }_{\mathrm{eff}}$ for rabbit brain is presented in Fig. 3(a) for all experimental conditions and in Fig. 3(b) for all tissue conditions, i.e., in vivo, postmortem, and after long-term storage at ${-20}^{°}\mathrm{C}$ or formalin-fixated. We compared the median of ${\mu }_{\mathrm{eff}}$, and not the mean, because it is less sensitive to skewed distributions of the attenuation values. Standard deviations were computed from the median absolute deviation. The effective light attenuation coefficients for all tissue conditions together with its uncertainties are listed in Table 2.

Fig. 3

The effective attenuation coefficient ${\mu }_{\mathrm{eff}}$ as function of the wavelength is shown in (a) for all experimental conditions and in (b) for all tissue conditions, i.e., a reduced set of data from (a). Magenta markers represent ${\mu }_{\mathrm{eff}}$ obtained from each animal; dashed lines connecting the evolution of ${\mu }_{\mathrm{eff}}$ for each animal during the euthanasia and tissue storing procedure. The relative change in ${\mu }_{\mathrm{eff}}$, $({\mu }_{\mathrm{eff}}-{\mu }_{\mathrm{eff}}^{*})/{\mu }_{\mathrm{eff}}^{*}$, where ${\mu }_{\mathrm{eff}}^{*}$ is the in vivo value, is shown in (c) and was computed for all conditions from the averaged ${\mu }_{\mathrm{eff}}$.

Table 2

Effective attenuation, μeff, absorption, μa, and reduced scattering, μs′, coefficients measured at 635, 671, and 808 nm for different conditions (in vivo, postmortem, frozen, and formalin). Uncertainties are given in parentheses.

The groups postmortem, frozen, and formalin-fixated, shown in Fig. 3(b), contain data from animals euthanized in both ways, i.e., either by exsanguination or injection of KCl, since little changes in ${\mu }_{\mathrm{eff}}$ were observed as function of the sacrifice method. The data suggest that the effect of bleeding on ${\mu }_{\mathrm{eff}}$ was negligible in our series. Cerebral blood circulation may have been sufficiently sustained prior to euthanasia, since 50 to 60% of the total blood volume remained in the animal during the bleeding procedure. Furthermore, light absorption by oxy- or deoxyhemoglobin was much larger at wavelengths $<600\mathrm{nm}$, such that a lower blood volume than normal may influence only little ${\mu }_{\mathrm{eff}}$ at wavelengths $>600\mathrm{nm}$.

Under all predetermined tissue conditions applied, ${\mu }_{\mathrm{eff}}$ decreased as a function of the wavelength. This wavelength dependency was attributed to a decreasing value of ${\mu }_s^{\prime }$ at increasing wavelengths according to the Mie scattering theory as well as to a decrease of ${\mu }_a$, especially in deoxyhemoglobin. These findings are in agreement with results reported for human brain tissue.⁷

The relative changes in the effective attenuation coefficient, $\delta {\mu }_{\mathrm{eff}}=({\mu }_{\mathrm{eff}}-{\mu }_{\mathrm{eff}}^{*})/{\mu }_{\mathrm{eff}}^{*}$, where ${\mu }_{\mathrm{eff}}^{*}$ stands for the in vivo condition, are shown in Fig. 3(c). We observed that the decrease in ${\mu }_{\mathrm{eff}}$ between in vivo and postmortem conditions was largest at 635 nm, which was up to 10%, whereas at higher wavelengths, it was only 5%.

After storage of the rabbit heads at ${-20}^{°}\mathrm{C}$ for six weeks, ${\mu }_{\mathrm{eff}}$ decreased, on average, by 15 to 25% at all wavelengths [Fig. 3(c)]. Which coefficient was the crucial factor, however, remained controversial. Although the absolute values of fitted absorption and reduced scattering coefficient partly had a high cross-correlation and, thus, did not represent a unique solution of Eq. (2) to the experimental data, relative changes in these parameters between different tissue conditions may indicate which coefficient is most affected. These changes, when passing from postmortem to frozen conditions, yield a decrease in ${\mu }_a$ by $\sim 30\%$ at all wavelengths and a decrease of ${\mu }_s\text{'}$ by $\sim 10\%$ with the smallest effect at 808 nm (see also Table 2).

The effective attenuation coefficient after formalin fixation is shown in Fig. 3(b) and its relative changes in Fig. 3(c). Our measurements showed an increase in ${\mu }_{\mathrm{eff}}$ by 5 to 15% after having stored the rabbit heads in formaldehyde for six weeks. The relative changes in the optical coefficients indicate that ${\mu }_a$ increased by $\sim 15\%$ and ${\mu }_s^{\prime }$ by $\sim 5\%$ at all wavelengths.

4.1.

Tissue Freezing

Tissue freezing is an elegant method to store and transport tissue samples, but was shown to significantly alter tissue optical properties.^3,8,13 So far, there are only a few studies investigating these effects, and a summary of their results together with ours can be found in Table 3. In general, it is reported that tissue freezing, either at ${-20}^{°}\mathrm{C}$ or 77 K, reduces the effective attenuation coefficient. However, it remains unclear from these results which coefficient, absorption or reduced scattering, is more affected by the freezing procedure.

Table 3

A summary of literature values about the relative changes in effective attenuation, μeff, absorption, μa, and reduced scattering, μs′, after tissue treatment, i.e., freezing or formalin-fixation. Relative changes are given as averaged values of the respective optical parameter within the wavelength range or at the distinct wavelengths, λ.

On a microscopic level, we expected freezing to cause changes in the tissue structure. Depending on the freezing and thawing procedure as well as on the final freezing temperature, intra- and extracellular ice formation can occur. Intracellular ice crystals may induce mechanical stress on cell walls provoking partial cell damage, which may lead to a certain homogenization of the tissue and, hence, reduction of scattering. After thawing, cell wall ruptures can provoke blood drain and oxidation of deoxyhemoglobin, reducing light absorption in the range of 600 to 800 nm.²⁸ In our experiments, this effect may have been further amplified by the fact that the brain was left in the cranial cavity the entire study. The volumic expansion of the brain tissue during slow freezing was constrained by the skull, thus increasing mechanical stress on the cells. Extracellular ice formation may have changed solute concentrations, which can lead to cellular dehydration provoking protein denaturation,²⁹ which may also have affected tissue optical properties.⁴

It remains unclear what the partially controversial results reported in the literature (Table 3) can be attributed to. However, overall scattering and absorption are likely to decrease when slowly freezing bulky tissue to ${-20}^{°}\mathrm{C}$, which is also reflected in our observations and those made with different tissues.

4.2.

Tissue Fixation in Formalin

Formalin fixation is a preparation method widely used for handling tissue specimens, especially for long-term storage. However, very little is known about its effect on tissue optical properties. In previous studies, an increase in optical scattering was observed after fixation, which is related to the cross-linking of proteins during tissue fixation creating a more scattering media, while absorption mainly remains unaltered.^9,10,30 To our knowledge, there is no study where optical properties were directly measured before and after tissue fixation, but only under conditions of tissue coagulation^4,7 or direct dehydration.¹¹ These results are presented in Table 3.

Formaldehyde acts as a cross-linking agent at the molecular level by linking together soluble and structural proteins,^31,32 resulting in (1) tissue shrinkage by dehydration and (2) alterations in tissue structural properties. Tissue shrinkage decreases the diameter of cells and aggregates responsible for scattering. Following Mie’s scattering theory, ${\mu }_s$ is proportional to the square of the scattering centers’ diameters, which should lead to a decrease in the scattering coefficient and anisotropy factor in the case of tissue shrinkage. For small diameter changes, however, ${\mu }_s^{\prime }$ remains approximately constant, since ${\mu }_s$ and $g$ decrease at the same time.

It remains unclear how changes in tissue structural properties induced by formalin fixation concretely affect light scattering. Furthermore, the dehydration of cells during the fixation process is also likely to change the refractive index. While it is $\sim 1.38$ for fresh tissue,^33,34 the refractive index of dehydrated cells increases to 1.50 to 1.55.³⁵ Even a small difference in the refractive index may yield a larger reduced scattering coefficient, since ${\mu }_s^{\prime }\propto {(n-1)}^2$ or larger.²⁷ Accordingly, values of reduced scattering coefficients are likely to increase by 70% when $n$ increases from 1.38 to 1.50.

Tissue dehydration and shrinkage resulting from the fixation process also lead to an increased concentration of chromophores. Thus, the observed increase in the absorption coefficient may be a result of denser packing of cells due to shrinkage of the tissue samples while the number of chromophores remains constant.⁴ Hsiung et al.³⁰ investigated changes of the optical properties of hamster cheek pouch at 800 nm when preserving it in a 10% neutral-buffered formalin solution. Besides tissue shrinkage, they found both increasing and decreasing scattering signals depending on the tissue type and an increase in the overall contrast between tissue architectural features during the fixation process over 18 h. Aung et al.¹⁰ investigated the refractive index and scattering properties in tissues of prostate cancer. The comparison of reduced scattering coefficients obtained from fixated and frozen samples leads to opposite results: in nuclear regions, ${\mu }_s^{\prime }$ was found to be higher in fixated than in frozen tissue, whereas the opposite was concluded for the samples from non-nuclear regions. These different results may be due to large uncertainties in their determination of $g$. Gnanadesigan et al.³⁶ investigated the effect of temperature and fixation on the optical properties of atherosclerotic tissue with the help of optical coherence tomography. Their results suggest that tissue fixation and temperature do not introduce changes in the attenuation coefficient of coronary arteries, yet they observed increased image intensity after fixation indicating a larger reduced scattering coefficient. As a consequence of an approximately constant ${\mu }_{\mathrm{eff}}$, their results would mean that ${\mu }_a$ decreased during the fixation process. Gabrecht et al.³⁷ showed blue-violet excited autofluorescence of normal and cancerous human bronchial tissue to be increased after formaldehyde fixation, which is an indication for a lowered absorption. However, the only difference in the spectra was localized in the absorption range of hemoglobin around 530 to 560 nm. It was shown elsewhere³⁸ that hemoglobin’s absorption decreases significantly and blood vessels become invisible in OCT³⁰ following the formaldehyde fixation process.

In summary, the knowledge of the effects of formaldehyde fixation on tissue optical properties is very scarce. There are indications that the overall scattering increases due to protein linking, tissue dehydration, and shrinkage. Tissue shrinkage itself may also increase the density of chromophores leading to higher absorption if chromophores remain intact during and after formaldehyde treatment. Light absorption of hemoglobin derived from porphyrin rings is lowered by formaldehyde, but mainly at wavelengths $<600\mathrm{nm}$. On the contrary, coagulation of human brain tissue increases the absorption coefficient to a larger extent than the reduced scattering, which was also observed in our study.

4.3.

Effects of Structural Changes in the Brain on the Optical Coefficient After Long-Term Storage

The repositioning of the catheters in the rabbit brain for the measurement after long-term storage may introduce an additional uncertainty in the absolute values of the optical coefficients obtained from data fitting and, hence, their relative changes after tissue storage. Although care was taken to reintroduce the catheters in the same positions as were originally used in the measurements prior to long-term storage, there were small differences (a few millimeters) in the catheter trajectories between prior and poststorage measurements. The recomputation of the catheter coordinates from sets of x-ray images obtained poststorage was supposed to yield, within the accuracy of the method itself, correct relative distances between the light source and detector. Nevertheless, an altered trajectory also implies a possible change of the surrounding tissue and, therefore, a change in local optical coefficients and fluence rate.

It remains unclear to what extent this effect may bias the results, since no histological processing of the tissue was performed. However, multiple measurements along the catheter trajectories should reduce the impact of the local tissue inhomogeneities and optical properties on the results. Furthermore, the effects of the structural changes in the surrounding tissue may also be one possible explanation of the changes in ${\mu }_{\mathrm{eff}}$ from a single animal between prior and poststorage measurements [see magenta dots in Figs. 3(a) and 3(b)].