2.1.

Integrating Sphere

The integrating sphere was constructed on site at the Juravinski Cancer Centre (Hamilton, Ontario). The sphere wall was coated with two coats of 6080 diffuse white reflectance coating (Labsphere, North Sutton, New Hampshire) and had a measured reflectivity of $0.970\pm 0.002$ . The sphere had a radius of $53\mathrm{mm}$ with a $26\mathrm{mm}$ radius irradiation port, resulting in a fractional port area of 0.0643. The irradiation port was positioned directly opposite the source fiber port (Fig. 1 ), and the port diameter was selected to encompass the majority of lesion sizes seen clinically. The sphere diameter was chosen so that the divergent beam produced by the microlens overlapped the edges of the port opening by $5\mathrm{mm}$ . The overlap ensured that the entire exit port area was irradiated. The divergent beam size was determined by the fiber’s characteristics, confirmed to be the same as provided by the manufacturer (model FD1, Medlight, Switzerland).

Fig. 1

A 3-D rendering of the sphere from (a) above and (b) below.

2.2.

Measurements in Tissue-Simulating Phantoms

Profile and depth fluence measurements were performed in a tissue-simulating liquid phantom consisting of a 1% Intralipid^® solution (Baxter, Toronto, Ontario). This mixture has a negligible absorption coefficient $(2.61\times {10}^{-4}{\mathrm{mm}}^{-1})$ and a reduced scattering coefficient of $1.44{\mathrm{mm}}^{-1}$ at a wavelength of $630\mathrm{nm}$ ,⁵ similar to the mean value of the reduced scattering coefficient measured from the surface of human skin.^{6, 7, 8}

A therapeutic diode laser (630 PDT Laser, Diomed, Andover, Massachusetts) was coupled to the source fiber. This was secured to the top of the sphere so that the tip of the fiber was flush with the sphere’s inner surface. A detection fiber (IP isotropic probe, Medlight, Switzerland) with an isotropic scattering tip was connected to a Newport hand-held optical power meter (Model 840, Irvine, California) and positioned directly below the sphere.

Relative light fluence profiles were obtained by taking power measurements across the diameter of the irradiation port at a depth of $3.0\mathrm{mm}$ in $2.0\mathrm{mm}$ increments. This depth was chosen so that measurements would not be affected by potential surface effects. To measure the depth fluence curve, the fiber was positioned at the center of the irradiation port, and measurements were taken starting at the surface and increasing in depth by $1.0\mathrm{mm}$ to a maximum of $15\mathrm{mm}$ , or until the power decreased below that of the background. These measurements were repeated with three concentrations of india ink (Regal-LA Reeves Incorporated, Downsview, Ontario) (0.1, 0.2, and 0.3%) added to the Intralipid. The absorption coefficients of the three phantoms (0.053, 0.106, and $0.159{\mathrm{mm}}^{-1}$ , respectively) simulate the typical range for human skin found in the literature.^{6, 7, 8}

2.3.

Monte Carlo Simulations

To further characterize the sphere, an existing Monte Carlo (MC) program⁹ was adapted to launch photons from the top of the sphere, with a direction vector inside the cone defined by the properties of the microlens such that the majority of the photons were incident on the tissue surface. Once inside the tissue, each photon’s weight was scored and reduced following each interaction until it re-entered the sphere or its history was terminated. When inside the sphere, the photons were diffusely scattered by the sphere wall until they were incident on the tissue and either reflected back into the sphere or refracted into the tissue.

2.4.

Reflectance Side Port Measurements

The integrating sphere was equipped with a side port with an SMA fiber connector. An optical fiber was connected to a power meter and was used to monitor the power. Power readings were recorded from this port, first with the irradiation port covered by a calibration plate made of the same material and coated with the same paint as the sphere, and then with the sphere positioned over the Intralipid phantom (Sec. 2.2). The phantom measurement was divided by the calibration measurement to yield a unitless reflectance $R_m$ . These reflectance measurements were mimicked in the MC simulations by estimating the irradiance on the inner wall of the sphere, both when the irradiation port was over tissue, and when the tissue was replaced by a flat surface with reflectance properties identical to the sphere wall. These “tissue” and “calibration” readings yielded a unitless reflectance that could be compared to that measured on the phantoms.

2.5.

In Vivo Surface Measurements

To determine the ratio of fluence rates with and without the sphere in vivo, and to investigate whether superficial measurements with the sphere were predictive of the relative fluence at depth, surface measurements were taken on the forearms of volunteers. An isotropic detector was attached to each volunteer’s forearm in the broadest and palest region using hypoallergenic tape. This location was chosen for its relative uniformity in color, texture, and for its lack of hair. The treatment fiber was connected to a white light source and the isotropic detector fiber was connected to a spectrometer (SD 2000, Ocean Optics, Dunedin, Florida). The sphere was positioned so that the isotropic detector was in the center of the irradiation port and the surface fluence was recorded. The treatment fiber was subsequently fixed the same distance from the skin without the sphere in place, and the surface fluence measurement was repeated. The quotient of these two values yielded the relative fluence. This protocol was approved by the Hamilton Health Sciences/Faculty of Health Sciences Research and Ethics Board.

3.1.

Contour Plots

To visualize the effects of the integrating sphere, isofluence-rate contours were constructed from the MC simulation data. These plots were not generated for the measurements in phantoms because the data were too sparse. The contour plots from the MC data for optical properties equivalent to a 1% Intralipid phantom are shown in Fig. 2 . The fluence rates were normalized to unit power emitted from the source fiber [resulting in units of $(\mathrm{W}∕{\mathrm{cm}}^2)∕\mathrm{W}$ ].

Fig. 2

Contour plots of normalized isofluence calculated by Monte Carlo simulations for a 1% Intralipid phantom: (a) without the integrating sphere in place over the tissue and (b) with the integrating sphere in place over the tissue. Units for the contour labels are $\mathrm{W}∕{\mathrm{cm}}^2∕\mathrm{W}$ .

The contour plots show that the sphere had significant effects on the fluence rate distribution. The fluence rate increased and the depth of the $0.2(\mathrm{W}∕{\mathrm{cm}}^2)∕\mathrm{W}$ isoline increased from approximately $0.5\text{to}1.5\mathrm{cm}$ . Additionally, the radius of this isoline at the surface was smaller and confined to the radius of the port opening.

3.2.

Fluence Profile and Depth Measurements

A more detailed understanding of the effects of the sphere was permitted by analysis of the fluence rate profile and depth data. Typical curves are shown in Figs. 3 and 4 . The increase in fluence rate is seen in the depth fluence rate as a vertical shift of the “with sphere” curve. In the profile curves, the introduction of the sphere resulted in an increase in the fluence rate.

Fig. 3

Semilogarithmic depth fluence curves, with (upper curve) and without (lower curve) the sphere in place over a 1% Intralipid phantom with 0.01% india ink from: (a) the phantom measurements and (b) the MC simulation.

Fig. 4

Fluence profiles at a depth of $3\mathrm{mm}$ , with (upper curve) and without (lower curve) the sphere in place over a 1% Intralipid phantom from: (a) the phantom measurements and (b) the MC simulation.

To quantify the effect of the integrating sphere on the fluence profiles, the following terms, borrowed from radiation therapy, were used. The field size was defined as the distance between the 50% of maximum values on the profile curve. The 80% flatness represents the absolute percent deviation from the central axis value across 80% of the field size. The 80 to 20 penumbra was the distance required for the fluence to drop from 80% of its central axis value to 20%. The relative fluence ${\Phi }_{\mathrm{rel}}$ is the ratio of the central axis fluence rates with and without the sphere in place at a specific depth. These parameters are listed in Table 1 for each of the Intralipid/india ink phantoms.

Table 1

Fluence profile parameters for the phantom measurements and MC simulation at a depth of 3m .

The average field size at a depth of $3\mathrm{mm}$ was $53\mathrm{mm}$ (phantom) and $61\mathrm{mm}$ (MC) without the sphere, and $48\mathrm{mm}$ (phantom) and $53\mathrm{mm}$ (MC) with the sphere. The ink concentration had no effect on the field size. The sphere restricts light to the irradiation port at the surface $\left(53\mathrm{mm}\right)$ , and this reduced field size was maintained even at a depth of $3\mathrm{mm}$ .

The sphere created a more uniform beam profile, as indicated by the smaller flatness. The flatness also improved as the absorption coefficient increased.

The penumbra decreased when the sphere was in place, contributing to a sharper, more defined edge to the treatment field. This value also decreased with ink concentration.

There was a significant increase in the light fluence rates when the sphere was employed. The relative fluence was as high as 1.8 (phantom) and 2.0 (MC), and decreased steadily as the absorption coefficient increased, to minimum values of 1.5 and 1.3. This was because a larger percentage of the incident light was absorbed, and therefore less light was reflected back into the sphere, reducing the ratio.

The relative fluence was also calculated from the depth fluence measurements. These data were fitted to an exponential function with an exponential constant equal to the effective attenuation coefficient (data not shown) and a multiplicative constant. Since the optical properties were the same in both scenarios, only the multiplicative constant varied. The ratio of these fitted constants was the relative fluence.

The relative fluence from the depth fluence curves and the profile curves are shown in Fig. 5 . Each of the four sets of data shows the same relationship between the relative fluence and the absorption coefficient of the tissue.

Fig. 5

Relative fluence as a function of absorption coefficient for the depth fluence and profile curves. For clarity, error bars are only shown on the phantom profile data.

The large relative uncertainties in the phantom measurements were the result of $0.5\mathrm{mm}$ uncertainty in determining the depth. Surface tension in the liquid phantom made it difficult to determine when the probe was actually at depth zero. This uncertainty resulted in larger uncertainties in the fluence rate, especially at greater ink concentrations where the fluence gradient was steeper. This uncertainty was not present in the MC simulations, since the depth was strictly defined, and the corresponding error bars are appreciably smaller.

3.3.

Reflectance Measurements

The measured side port reflectance from the phantom and the MC simulations is shown in Fig. 6 . Both decreased as the absorption coefficient increased, similar to the trend of the relative fluence as a function of the absorption coefficient. They also agree very closely, though the phantom value is consistently slightly larger than the MC value.

Fig. 6

Reflectance as a function of the absorption coefficient. The x’s represent the phantom data and the filled circles represent the MC data.

3.4.

In Vivo Measurements

Relative fluence measurements were performed on the forearms of 21 volunteers with a variety of skin types ranging from very fair (type 1 on the Fitzpatrick scale)¹⁰ to very dark (type 6). The relative fluence (with sphere/without sphere) ranged from 1.67 to 3.00 at $630\mathrm{nm}$ with a mean of 2.26 and a median of 2.27. These values are considerably higher than those measured at depth in the phantom (1.30 to 2.00).

The spectral relative fluence for six of the volunteers is shown in Fig. 7 . These sample curves were chosen to show the range in relative fluence for the six skin types on the Fitzpatrick scale. It is clear that larger relative fluence corresponds to lighter skin color (lower absorption coefficients). The curves for subjects with lighter skin also have local minima at approximately 540 and $580\mathrm{nm}$ , which correspond to absorption peaks of oxyhemoglobin.¹¹ Over the measured spectral range, there are no local features due to melanin,¹² but the entire relative fluence curve is shifted vertically as the melanin concentration is reduced.

Fig. 7

Spectral relative fluence rate on the skin surface for volunteers from each of the different skin types on the Fitzpatrick scale. The curves were smoothed for clarity using Bezier functions.

3.5.

Treatment Time

In Sec. 3.3, it was shown that an integrating sphere can increase the light fluence rate for a PDT treatment, but that the improvement depended on the absorption coefficient. Irradiating for the same treatment time with the sphere in place will result in patients receiving different surface light doses, depending on their individual tissue optical properties. If the patient-specific increase in fluence rate were known, the treatment time could be adjusted accordingly, providing individualized dosimetry and, perhaps, more consistent treatment results.

The increase in fluence rate in the tissue is the result of reflected light redirected back onto the skin surface. The amount of reflected light should be related to the reflectance measured through the side port, and could, in principle, be used to predict the interstitial fluence rate change. To test this hypothesis, MC simulations were performed with a range of absorption and reduced scattering coefficients, and the relative fluence and reflectance were calculated as described previously. These results are shown in Fig. 8 . When the scattering coefficient was held constant and the absorption coefficient was increased, the relative fluence decreased, as previously seen. Conversely, when the absorption coefficient remained constant and the scattering coefficient was increased, the relative fluence increased. When the relative fluence was plotted against the side port reflectance, a strong linear relationship was evident (see Fig. 9 ), described by,

Fig. 8

Relative fluence as a function of absorption coefficient for different reduced scattering coefficients.

Fig. 9

Relative fluence as a function of reflectance. The data were fitted with the linear relationship shown in Eq. 2.

4.1.

Characterization of Sphere Effects

The contour plots, profile, and depth fluence curves confirm that the sphere is effective at increasing the light fluence rates in tissue. In the contour plots, this was evident in a shift of the isofluence lines roughly $1\mathrm{cm}$ deeper into the tissue. In the profile curves, this was seen by an increase in the central axis fluence value at a depth of $3\mathrm{mm}$ , ranging from 30 to 100%, depending on the absorption coefficient of the tissue. Finally, in the depth fluence curves, this was indicated by the constant fractional increase in fluence measured at each depth.

The sphere was also successful at improving the beam characteristics. Profiles with the sphere in place showed an improvement in flatness across the field size as well as a reduction in the penumbra, allowing for a better defined, more uniform treatment field. The field size at a $3\mathrm{mm}$ depth was sufficiently described by the size of the irradiation port. This is important, because it indicates that the treatment area is sufficiently illuminated at depth.

4.2.

In Vivo Results

The hemoglobin spectral features and the variation with skin types of the relative fluence curves from Fig. 7 indicate that the efficacy of the sphere is dependent on the skin’s optical properties which, in turn, are dependent on the concentrations of melanin and oxyhemoglobin.

The relative fluence measured on the surface of the skin on volunteers’ forearms was up to 50% higher than the values determined from the phantom and MC data at depth. These results were confirmed with MC simulations in which an isotropic “detector” was located just above the tissue surface. This difference was not investigated in further detail, as the subsurface fluence rate is the clinically relevant parameter.

When the sphere was positioned over the treatment area, it was observed that the treatment was no longer sensitive to patient movement, as the direct contact of the sphere with the tissue prevented any misalignment.

4.3.

Treatment Time

As discussed in Sec. 3.4, it was hypothesized that the relative fluence could be predicted from the reflectance measurement. This was investigated by running additional MC simulations with different combinations of absorption and reduced scattering coefficients. It was shown that the relative fluence increased monotonically with the reduced scattering coefficient, while the reverse behavior was seen with the absorption coefficient. These observations are consistent with the fact that, for a given index of refraction, the diffuse reflectance from a semi-infinite volume of tissue $R_d$ depends solely on the transport albedo,

To test this, $R_s$ was calculated from the Monte Carlo data by tracking the average number of reflections inside the sphere. For the sphere geometry used in this set of simulations, each photon that re-enters the sphere is reflected off the sphere wall 16 times before reaching the irradiation port. Combined with a measured sphere wall reflectance $\left(R_w\right)$ of $0.970\pm 0.002$ , this yields a value for $R_s$ of $0.61\pm 0.02$ . With these results, the slope of the fitted value from Eq. 2 of $1.29\pm 0.03$ is similar to the calculated slope of the line from Eq. 8 of $1.47\pm 0.14$ . The fitted $y$ -intercept of $0.96\pm 0.01$ is also close to the theoretical $y$ -intercept of 1.

These results indicate that the patient-specific relative fluence for any given sphere can be determined from the reflectance, using Eqs. 2, 8. The parameters in these equations are dependent on the sphere geometry but can be determined empirically. The treatment time can be adjusted accordingly.

4.4.

Penetration Depth

The previous results raised the question whether the reflectance measurements could also be used to determine the penetration depth in the skin. This would be beneficial for dosimetry, as it would allow the treatment time to be adjusted to ensure that the entire thickness of the tumor is irradiated to a minimum fluence, Eq. 6 indicates that the measured reflectance $R_m$ can be used to determine the tissue reflectance $R^{*}$ . To investigate the relationship between $R^{*}$ and $R_m$ , the diffuse reflectance coefficient $R_d$ was calculated using the tissue optical properties from the MC simulations and Eq. 9.¹³

Fig. 10

Transport albedo as a function of reflectance. The open squares represent the original sphere geometry ( $r_{\text{sphere}}=53.0\mathrm{mm}$ and $r_{\text{port}}=26.0\mathrm{mm}$ ), and the closed circles represent another sphere geometry ( $r_{\text{sphere}}=33.8\mathrm{mm}$ and $r_{\text{port}}=15.0\mathrm{mm}$ ).

The penetration depth is calculated as the reciprocal of the effective attenuation coefficient ${\mu }_{\mathrm{eff}}$ , where ${\mu }_{\mathrm{eff}}={\left[3{\mu }_a({\mu }_s^{\prime }+{\mu }_a)\right]}^{1∕2}$ in the case of the diffusion limit. As such, the absorption and scattering coefficients cannot be determined independently from the albedo. However, if the scattering coefficient were known a priori, the absorption coefficient could be calculated and the effective attenuation coefficient and penetration depth could be determined.

If the reduced scattering coefficient is not known in advance, typical values taken from the literature might provide a reasonable estimate of the penetration depth. This could be used in conjunction with the laser power and treatment time to determine the fluence at a specific depth. This would be an ideal light dose metric, as it would remove the effects of different tissue optical properties that currently limit treatment efficacy, and it would be defined at a more clinically relevant location.

To test this, the transport albedo and the penetration depth were calculated for a set of optical properties typical for skin. The reduced scattering coefficient was increased by 25%, and the previously calculated transport albedo was used to calculate an absorption coefficient. The incorrect scatter and absorption coefficients were then used to calculate a penetration depth. The difference between this and the actual penetration depth was 36%, resulting in an uncertainty of less than $1\mathrm{mm}$ . Given that the penetration depth can vary by up to $3\mathrm{mm}$ ,¹⁴ knowing this value to within one millimeter would still be useful in PDT dosimetry.