2.1.

Optical Phantoms and the Inverse Solution

Similar to a previous study,⁴⁸ the inverse solution for extracting optical properties from the measured DR combines an experimental LUT and fitting algorithms. The LUT was generated by measuring the DR from tissue-simulating phantoms with known optical properties. To simulate tissue scattering, polystyrene microspheres with a diameter of $1\mu \mathrm{m}$ (07310-15, Polysciences Inc., Pennsylvania) were used. To simulate tissue absorption, black India ink (Higgins Ink, Chartpak Inc., Massachusetts) was used. A $6\times 4$ matrix of 24 phantoms consisting of six different concentrations of black India ink (0.025%, 0.05%, 0.1%, 0.2%, 0.35%, and 0.5% of the concentrated ink solution) and four different concentrations of microspheres (0.2%, 0.45%, 0.7%, and 1% w/v) was created [Fig. 1(a)]. Within the selected concentrations of India ink and microspheres, a ${\mu }_{\mathrm{a}}$ range of 0.05 to $47{\mathrm{cm}}^{-1}$ and a ${\mu }_{\mathrm{s}}^{\prime }$ range of 5 to $42{\mathrm{cm}}^{-1}$ were covered for a wavelength range 430 to 700 nm [Figs. 1(b) and 1(c)]. These optical properties were selected based on various reports studying human brain tissues and mucosal tissues.^{20,29,30,47,49} To evaluate the LUT, selected phantoms containing ferrous stabilized hemoglobin (H0267, Sigma-Aldrich, Missouri) and microspheres with different concentrations were created. The DR from these phantoms was measured and the recovered optical properties were compared to target values.

Fig. 1

Matrix of optical phantoms for LUT development: (a) top surface images of 24 phantoms captured with a standard digital camera, (b) absorption coeffients ${\mu }_{\mathrm{a}}$, and (c) reduced scattering coefficients ${\mu }_{\mathrm{s}}^{\prime }$. In (a), six concentrations of black India ink are 0.025%, 0.05%, 0.1%, 0.2%, 0.35%, and 0.5%, and four different concentrations of microspheres are 0.2%, 0.45%, 0.7%, and 1% w/v. These correspond to six spectra of ${\mu }_{\mathrm{a}}$ in (b) and four spectra of ${\mu }_{\mathrm{s}}^{\prime }$ in (c).

In all phantoms, target optical properties were controlled and calculated by applying Beer–Lambert’s law to the actual absorbance of pure solute absorbers (India ink or hemoglobin) measured with a spectrophotometer (Ultraspec 3000, Pharmacia Biotech Inc., New Jersey) for ${\mu }_a$, and by applying Mie theory to microsphere concentration for ${\mu }_{\mathrm{s}}^{\prime }$.⁵⁰ Hemoglobin H0267 has an absorption spectrum similar to that of human blood with secondary absorption peaks at 540 and 580 nm and stable oxygen saturation.^49,51,52 Polystyrene microspheres with a diameter of $1\mu \mathrm{m}$ were preferred as scatterers because their scattering anisotropy is in a similar range to that of many biological tissues ($g=0.89$ to 0.93 in UV–vis) and because their well-controlled size and index of refraction permits accurate calculation of scattering properties using Mie theory.^45,50,53 Black India ink is widely used to simulate secondary absorbers in tissue due to its exponential decrease of absorption with wavelength, low cost, spectral stability, and low-fluorescence.^54–57

To fit the optical properties, the least squares fitting routine fminsearch() in MATLAB^® was used, so the absorption coefficients and the reduced scattering coefficients were constrained in the form of Eqs. (1) and (2). This optimization method is based on the Nelder–Mead simplex algorithm and has been used widely for spectral analysis in spectral imaging.^58–60 The total absorption coefficient, ${\mu }_{\mathrm{a}}$, accounts for absorption of a primary absorber (human blood) and of secondary absorbers (i.e., NADH, FAD, and collagen).^20,28,49 In general, the total absorption coefficients of all secondary absorbers can be described as an exponential decay with wavelength^20,28 while the absorption coefficient of blood is determined predominantly by those of Hb and ${\mathrm{HbO}}_2$.^44,61 A similar fitting method for total absorption coefficients can be found elsewhere.^48,61

In Eq. (1), $A$ and $B$ are fitting coefficients that determine the contribution of secondary absorber so that $A$ (${\mathrm{cm}}^{-1}$) is the amplitude constant while $B$ (${\mathrm{nm}}^{-1}$) is the rate constant; $\lambda$ is the wavelength; $f_1$ ($\mathrm{mol}/\mathrm{l}$) is the total concentration of hemoglobin, $f_2$ (dimensionless) is the oxygen saturation, and ${ϵ}_{\mathrm{HbO}2}$ (${\mathrm{cm}}^{-1}.{\mathrm{M}}^{-1}$) and ${ϵ}_{\mathrm{Hb}}$ (${\mathrm{cm}}^{-1}.{\mathrm{M}}^{-1}$) are molar extinction coefficients of oxygenated and deoxygenated hemoglobin, respectively. In tissue measurements, $A$, $B$, $f_1$, and $f_2$ were calculated by applying the least squares fitting to the LUT-recovered ${\mu }_{\mathrm{a}}$ and the known spectra of ${ϵ}_{\mathrm{HbO}2}$ and ${ϵ}_{\mathrm{Hb}}$.⁶² In hemoglobin phantoms without collagen and NADH, $A$ was set to zero and the extracted $f_2$ should be nearly 100% due to the nature of ferrous-stabilized hemoglobin.⁵² In human tissues, ${\mu }_{\mathrm{s}}^{\prime }$ is monotonically decreasing with wavelength, and the fitting equation for ${\mu }_{\mathrm{s}}^{\prime }$ can be expressed in the form of Eq. (2) where $a$ with unit of ${\mathrm{cm}}^{-1}$ is the factor characterizing magnitude of scattering, $b$ (dimensionless) is the factor that characterizes wavelength dependence of scattering, and $\lambda$ is the wavelength in nanometers (nm).^30,44,61

2.2.

Brain Tissue Samples

Fresh brain specimens were obtained from brain tissue removed during tumor resection surgery. The study protocol is approved by the McMaster/Hamilton Health Sciences Integrated Research Ethics Board, and patients consented to participate. Prior to the DRS measurement, each specimen was washed with saline, and the spectroscopic measurements were performed within 30 min of the surgery. A total of 22 sites were measured from specimens of seven patients. At each site, reflectance and fluorescence measurements were repeated four times to allow averaging and standard deviation calculation. Following the measurements, each site was marked with tissue marking dyes (Davidson Marking system, Bradley Products Inc., Minneapolis, Minnesota) in different colors. After the optical measurements, the specimens were preserved in formaldehyde and then cut into $5\text{-}\mu \mathrm{m}$-thick slices with hematoxylin and eosin stain. Tumor grade was assigned by a single pathologist (JP), using World Health Organization guidelines.⁶³ The biopsy results identified four GBM patients (12 sites) and three LGG patients (10 sites). The surface area of tissue samples is at least five times larger than the surface area of the optical probe, which has a diameter of 3 mm. Thickness of tissue samples is at least 0.5 cm and is much larger than the optical penetration depth range of 100 to $300\mu \mathrm{m}$ for a human brain tumor at visible wavelengths.⁶⁴

2.3.

Instruments

DR signals between 430 and 700 nm were generated using a broadband light source (Dolan-Jenner MI-150, Edmund Optics, New Jersey), while fluorescence signals were generated using a solid-state laser (PNV-001525-140, Teem Photonics, Meylan, France) at 355 nm with 300-ps pulses. Note that optical properties in the 350- to 430-nm range were extrapolated using the calculated parameters ($A$, $B$, $f_1$, $f_2$, $a$, and $b$ from the fitting results). Measurements of both DR and steady state fluorescence (SSF) signals were performed with the same customized optical probe consisting of one source fiber and three detection fibers at source-detector collection distances (SDD) of 0.23, 0.59, and 1.67 mm. A schematic and detailed description of the system can be found elsewhere.^65–67 All fibers used in DRS and SSF measurements have a core diameter of $200\mu \mathrm{m}$ and numerical aperture of 0.22. After DRS and SSF measurements were performed, the fluorescence decay was recorded using a $400\text{-}\mu \mathrm{m}$ core optical fiber in the bundle.⁶⁸ When observing highly absorbing phantoms, only background noise was collected with the furthest fibers, thus reducing the prediction accuracy of the inverse solution. Therefore, in the current study, only the two detection fibers closest to the source fiber were used to develop the LUT and to extract optical properties from the measured reflectance. To calculate the DR $R$ from the sample, the measured reflectance intensity of the sample was normalized to the reflectance intensity of a reflection standard with 99.9% reflectivity (Labsphere, Inc., New Hampshire) after subtracting background.⁶⁵

3.1.

Validation of the Inverse Solution

Figure 2(a) shows examples of DR spectra collected from six phantoms with the same microsphere concentration (0.7% w/v) and different India ink concentrations (from 0.05% to 1%). Figure 2(b) shows the sparse matrix of DR collected from all 24 phantoms at SDD of 0.23 and 0.59 mm. The LUT was evaluated with randomly selected phantoms consisting of hemoglobin and microspheres. Figures 3(a) and 3(b) compare the extracted and the target optical properties spectra for a selected phantom with microsphere concentration of 0.7% w/v and hemoglobin concentration of $8\mathrm{mg}/\mathrm{ml}$. The target optical properties are those calculated with Beer–Lambert’s law and Mie theory while the extracted values are those calculated from the inverse solution. As shown in Figs. 3(a) and 3(b), the method was able to retrieve ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ with average errors of 6% and 3%, respectively, from 350 to 700 nm. The intensive evaluation of the inverse solution was performed on a total of 10 hemoglobin phantoms with a total of 3500 pairs of target optical properties in 430 to 700 nm (Fig. 4). On average, errors of 9% and 6% were observed for ${\mu }_a$ and ${\mu }_{\mathrm{s}}^{\prime }$, respectively. Furthermore, the fitting approach was able to retrieve $f_1$ and $f_2$ in all hemoglobin phantoms with average errors of 5.8% and 7%, respectively. For example, the recovered $f_1$ and $f_2$ values for the phantom shown in Fig. 3 were $7.9\pm 0.8\mathrm{mg}/\mathrm{ml}$ and $96\%\pm 3\%$, respectively, versus target values of $8\mathrm{mg}/\mathrm{ml}$ and 100%, respectively.

Fig. 2

(a) Examples of diffuse reflectance $R$ for six different ink concentrations while microsphere concentration remains constant and $\mathrm{SDD}=0.23\mathrm{mm}$, and (b) $R$ as a sparse matrix mapped to optical property space $R$ [${\mu }_{\mathrm{a}}$ ($\lambda$),${\mu }_{\mathrm{s}}^{\prime }$ ($\lambda$)] for $\mathrm{SDD}=0.23$ and 0.59 mm. In (a), concentration of microsphere is 0.7% whereas concentrations of black India ink are 0.025%, 0.05%, 0.1%, 0.2%, 0.35%, and 0.5%, corresponding to six spectra (i) to (vi). In (b), the sparse matrix represents reflectance data per SDD collected from 24 phantoms (six ink concentrations × four microsphere concentrations).

Fig. 3

An example of data analysis for a phantom with Hb concentration of $8\mathrm{mg}/\mathrm{ml}$, microsphere concentration of 0.7%: (a) diffuse reflectance collected with fiber at SDD of 0.23 and 0.59 mm, (b, c) theoretical (target) versus extracted optical properties. Equations (1) and (2) were used to extrapolate data in 350 to 430 nm. In addition, $f_1$ and $f_2$ values of $7.9\pm 0.8\mathrm{mg}/\mathrm{ml}$ and $96\%\pm 3\%$ were obtained by using Eq. (1).

Fig. 4

Evaluation of LUT over 10 different hemoglobin phantoms. In general, average percentage errors of 9% and 6% were obtained for ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$, respectively.

3.2.

Brain Tissue Measurements

Figure 5 compares the DR [Fig. 5(a)] and optical properties [Figs. 5(b) and 5(c)] measured for the GBM group and the LGG group. In Fig. 5, data were averaged over all 12 GBM sites and 10 LGG sites. On average over the entire spectrum (Fig. 5), DR was 3.2 times higher, ${\mu }_{\mathrm{a}}$ was 48% higher, and ${\mu }_{\mathrm{s}}^{\prime }$ was 140% higher for the GBM group. Data at 650 nm are also shown for comparison (Table 1). Note that 650 nm was selected because this is the region where blood absorption is small, and it is less likely that bleeding during surgery will affect tumor discrimination with optical measurement.^35–39 The absorption coefficients were determined by the primary absorber (hemoglobin) and secondary absorbers. Below 600 nm, absorption of hemoglobin dominated and determined the shape and intensity of the absorption spectrum. Hemoglobin absorption could be from blood within the tissue that has diagnostic value and/or blood on or close to the tissue surface that is the result of bleeding and has no diagnostic value. Although all tissue samples were washed through with saline solution before measurement, a large portion of unwanted blood residues still remained and significantly affected the measured absorption coefficients below 600 nm. As shown in Table 1, at 650 nm DR was 2.8 times higher, ${\mu }_{\mathrm{a}}$ was about 3 times higher, and ${\mu }_{\mathrm{s}}^{\prime }$ was 2.4 times higher for the GBM group. Figure 6 shows the DR [Fig. 6(a)] and optical properties [Figs. 6(b) and 6(c)] at 650 nm for all GBM and LGG sites. If we define sensitivity as the percentage of GBM sites that were correctly identified as GBM, and specificity as the percentage of LGG sites that were correctly identified as not GBM, the discrimination had a sensitivity of 100% (12/12) and specificity of 80% (8/10) if a cut-off at 20% was applied for DR at 650 nm to optimize the discrimination [Fig. 6(a)]. Sensitivity and specificity of 92% and 80% were achieved if a cut-off of $0.6{\mathrm{cm}}^{-1}$ was applied to ${\mu }_{\mathrm{a}}$ at 650 nm [Fig. 6(b)]. These numbers were 100% and 90% if a cut-off of $10{\mathrm{cm}}^{-1}$ was applied to ${\mu }_{\mathrm{s}}^{\prime }$ at 650 nm [Fig. 6(c)]. Although oxygen saturation was calculated at $83.4\pm 17.3\%$ for GBM and $55.4\pm 9.9\%$ for LGG using Eq. (1), the results might be affected by a long period of air exposure of the brain tissue specimen and were not used to optimize the discrimination for the ex vivo measurements.

Fig. 5

LGG group versus GBM group average spectral analysis: (a) diffuse reflectance, (b) absorption coefficient ${\mu }_{\mathrm{a}}$, and (c) reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$. Data were averaged over all sites (12 GBM sites and 10 LGG sites) and error bars are the standard deviation.

Table 1

Average over all GBM and LGG sites: diffuse reflectance at 650 nm (R650), optical properties at 650 nm (μa,650 and μs,650′), ratio of fluorescence to reflectance at 460 nm (F/R)460, and fluorescence life-time at 460 nm (τ460).

Fig. 6

LGG group versus GBM group: (a) diffuse reflectance at 650 nm ($R_{650}$), (b) ${\mu }_{\mathrm{a}}$ at 650 nm, and (c) ${\mu }_{\mathrm{s}}^{\prime }$ at 650nm. Data at 650 nm were selected for due to small blood absorption in this region, and thus it is less likely for blood absorption to affect tumor discrimination.^35–39

Figure 7 shows the average fluorescence intensity with an emission peak at 460 nm [Fig. 7(a)], the average fluorescence lifetime [Fig. 7(b)], and the ratio of fluorescence and diffuse reflectance at 460 nm ${(F/R)}_{460}$ versus diffuse reflectance at 650 nm ($R_{650}$) for GBM sites and LGG sites. Although the measured fluorescence signal could identify the characteristic emission peak of brain tissues at 460 nm [Fig. 7(a)], the measured fluorescence signal alone is not able to discriminate tumor types due to high tissue absorption in this wavelength range. To enable tumor discrimination, a graph of the ratio of fluorescence to diffuse reflectance at the emission peak ${(F/R)}_{460}$ versus $R_{650}$ was used instead.^38,39 If a cut-off of 20 for $F_{460}/R_{460}$ was applied, sensitivity and specificity of 100% and of 90% were achieved. Although the measured fluorescence signal ($F_{460}$) is distorted by absorption and $F_{460}$ alone cannot be used to differentiate various brain tumor types, $F_{460}$ can be corrected by using the measured reflection signal and the measured optical properties at the emission wavelength.^37,65 In general, intrinsic fluorescence ($f_{460}$) and fluorophore concentration are related to the ratio of ($F/R$).^37,65 As shown in Fig. 7(b) and Table 1, fluorescence lifetime alone was not able to discriminate GBM due to the high variation of life-time values, most likely caused by the low signal-to-noise ratio of the autofluorescence and high degree of heterogeneity in GBM.²³ Figure 8 summarizes sensitivity and specificity when different parameters were used to discriminate GBM from LGG. In general, $R_{650}$, ${\mu }_{\mathrm{s},650}^{\prime }$ and ratio ${(F/R)}_{460}$ versus $R_{650}$ could achieve discrimination with a sensitivity of 100%. Combining diffuse reflectance and steady-state fluorescence shows an increase in specificity from 80% to 90%.

Fig. 7

LGG group versus GBM group: (a) SSF spectrum and (b) fluorescence life-time $\tau$ spectrum, (c) ratio of fluorescence to reflectance at 460 nm ${(F/R)}_{460}$ versus reflectance at 650 nm ($R_{650}$). Fluorescence intensity has been normalized to integrating time and laser power corresponding to each measurement. In (a) and (b), data were averaged over all sites (12 GBM sites and 10 LGG sites) and error bars are the standard deviations.

Fig. 8

Summary of sensitivity and specificity when using different parameters for GBM discrimination: diffuse reflectance at 650 nm ($R_{650}$), optical properties at 650 nm (${\mu }_{\mathrm{a},650}$ and ${\mu }_{\mathrm{s},650}^{\prime }$), and ratio ${(F/R)}_{460}$ versus $R_{650}$.