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1.
Photochem Photobiol ; 96(2): 310-319, 2020 03.
Article in English | MEDLINE | ID: mdl-31556122

ABSTRACT

Uniform light fluence distribution for patients undergoing photodynamic therapy (PDT) is critical to ensure predictable PDT outcomes. However, current practice when delivering intrapleural PDT uses a point source to deliver light that is monitored by seven isotropic detectors placed within the pleural cavity to assess its uniformity. We have developed a real-time infrared (IR) tracking camera to follow the movement of the light point source and the surface contour of the treatment area. The calculated light fluence rates were matched with isotropic detectors using a two-correction factor method and an empirical model that includes both direct and scattered light components. Our clinical trial demonstrated that we can successfully implement the IR navigation system in 75% (15/20) of the patients. Data were successfully analyzed in 80% (12/15) patients because detector locations were not available for three patients. We conclude that it is feasible to use an IR camera-based system to track the motion of the light source during PDT and demonstrate its use to quantify the uniformity of light distribution, which deviated by a standard deviation of 18% from the prescribed light dose. The navigation system will fail when insufficient percentage of light source positions is obtained (<30%) during PDT.


Subject(s)
Chlorophyll/analogs & derivatives , Infrared Rays , Photochemotherapy/methods , Pleural Neoplasms/drug therapy , Chlorophyll/chemistry , Humans
2.
Photochem Photobiol ; 96(2): 340-348, 2020 03.
Article in English | MEDLINE | ID: mdl-31729774

ABSTRACT

Explicit dosimetry of treatment light fluence and implicit dosimetry of photosensitizer photobleaching are commonly used methods to guide dose delivery during clinical PDT. Tissue oxygen, however, is not routinely monitored intraoperatively even though it is one of the three major components of treatment. Quantitative information about in vivo tissue oxygenation during PDT is desirable, because it enables reactive oxygen species explicit dosimetry (ROSED) for prediction of treatment outcome based on PDT-induced changes in tumor oxygen level. Here, we demonstrate ROSED in a clinical setting, Photofrin-mediated pleural photodynamic therapy, by utilizing tumor blood flow information measured by diffuse correlation spectroscopy (DCS). A DCS contact probe was sutured to the pleural cavity wall after surgical resection of pleural mesothelioma tumor to monitor tissue blood flow (blood flow index) during intraoperative PDT treatment. Isotropic detectors were used to measure treatment light fluence and photosensitizer concentration. Blood-flow-derived tumor oxygen concentration, estimated by applying a preclinically determined conversion factor of 1.5 × 109 µMs cm-2 to the blood flow index, was used in the ROSED model to calculate the total reacted reactive oxygen species [ROS]rx. Seven patients and 12 different pleural sites were assessed and large inter- and intrapatient heterogeneities in [ROS]rx were observed although an identical light dose of 60 J cm-2 was prescribed to all patients.


Subject(s)
Dihematoporphyrin Ether/therapeutic use , Photochemotherapy/methods , Photosensitizing Agents/therapeutic use , Pleural Neoplasms/drug therapy , Reactive Oxygen Species/metabolism , Animals , Humans , Mice , Pleural Neoplasms/metabolism , Xenograft Model Antitumor Assays
3.
Proc SPIE Int Soc Opt Eng ; 100472017 Jan 28.
Article in English | MEDLINE | ID: mdl-28690354

ABSTRACT

Uniform delivery of light fluence is an important goal for photodynamic therapy. We present summary results for an infrared (IR) navigation system to deliver light dose uniformly during intracavitory PDT by tracking the movement of the light source and providing real-time feedback on the light fluence rate on the entire cavity surface area. In the current intrapleural PDT protocol, 8 detectors placed in selected locations in the pleural cavity monitor the light doses. To improve the delivery of light dose uniformity, an IR camera system is used to track the motion of the light source as well as the surface contour of the pleural cavity. A MATLAB-based GUI program is developed to display the light dose in real-time during PDT to guide the PDT treatment delivery to improve the uniformity of the light dose. A dualcorrection algorithm is used to improve the agreement between calculations and in-situ measurements. A comprehensive analysis of the distribution of light fluence during PDT is presented in both phantom conditions and in clinical cases.

4.
Photochem Photobiol ; 93(4): 1115-1122, 2017 07.
Article in English | MEDLINE | ID: mdl-28083883

ABSTRACT

This preclinical study examines light fluence, photodynamic therapy (PDT) dose and "apparent reacted singlet oxygen," [1 O2 ]rx , to predict local control rate (LCR) for Photofrin-mediated PDT of radiation-induced fibrosarcoma (RIF) tumors. Mice bearing RIF tumors were treated with in-air fluences (50-250 J cm-2 ) and in-air fluence rates (50-150 mW cm-2 ) at Photofrin dosages of 5 and 15 mg kg-1 and a drug-light interval of 24 h using a 630-nm, 1-cm-diameter collimated laser. A macroscopic model was used to calculate [1 O2 ]rx and PDT dose based on in vivo explicit dosimetry of the drug concentration, light fluence and tissue optical properties. PDT dose and [1 O2 ]rx were defined as a temporal integral of drug concentration and fluence rate, and singlet oxygen concentration consumed divided by the singlet oxygen lifetime, respectively. LCR was stratified for different dose metrics for 74 mice (66 + 8 control). Complete tumor control at 14 days was observed for [1 O2 ]rx ≥ 1.1 mm or PDT dose ≥1200 µm J cm-2 but cannot be predicted with fluence alone. LCR increases with increasing [1 O2 ]rx and PDT dose but is not well correlated with fluence. Comparing dosimetric quantities, [1 O2 ]rx outperformed both PDT dose and fluence in predicting tumor response and correlating with LCR.


Subject(s)
Dihematoporphyrin Ether/therapeutic use , Fibrosarcoma/drug therapy , Neoplasms, Radiation-Induced/drug therapy , Photochemotherapy , Photosensitizing Agents/therapeutic use , Animals , Dihematoporphyrin Ether/administration & dosage , Dose-Response Relationship, Drug , Female , Fibrosarcoma/etiology , Fibrosarcoma/metabolism , Mice, Inbred C3H , Neoplasms, Radiation-Induced/metabolism , Photosensitizing Agents/administration & dosage , Singlet Oxygen/metabolism
5.
Photochem Photobiol ; 91(5): 1210-8, 2015.
Article in English | MEDLINE | ID: mdl-26037487

ABSTRACT

Photodynamic therapy (PDT) can treat superficial, early-stage disease with minimal damage to underlying tissues and without cumulative dose-limiting toxicity. Treatment efficacy is affected by disease physiologic properties, but these properties are not routinely measured. We assessed diffuse reflectance spectroscopy (DRS) for the noninvasive, contact measurement of tissue hemoglobin oxygen saturation (St O2 ) and total hemoglobin concentration ([tHb]) in the premalignant or superficial microinvasive oral lesions of patients treated with 5-aminolevulinic acid (ALA)-PDT. Patients were enrolled on a Phase 1 study of ALA-PDT that evaluated fluences of 50, 100, 150 or 200 J cm(-2) delivered at 100 mW cm(-2) . To test the feasibility of incorporating DRS measurements within the illumination period, studies were performed in patients who received fractionated (two-part) illumination that included a dark interval of 90-180 s. Using DRS, tissue oxygenation at different depths within the lesion could also be assessed. DRS could be performed concurrently with contact measurements of photosensitizer levels by fluorescence spectroscopy, but a separate noncontact fluorescence spectroscopy system provided continuous assessment of photobleaching during illumination to greater tissue depths. Results establish that the integration of DRS into PDT of early-stage oral disease is feasible, and motivates further studies to evaluate its predictive and dosimetric value.


Subject(s)
Aminolevulinic Acid/administration & dosage , Blood Physiological Phenomena , Hemoglobins/chemistry , Mouth Diseases/therapy , Photochemotherapy , Administration, Oral , Dose-Response Relationship, Drug , Humans , Mouth Mucosa/drug effects , Mouth Mucosa/radiation effects , Predictive Value of Tests
6.
Proc SPIE Int Soc Opt Eng ; 93082015 Mar 02.
Article in English | MEDLINE | ID: mdl-25999654

ABSTRACT

The goal of this study was to develop and improve an infrared (IR) navigation system to deliver light dose uniformly during intracavitory PDT by tracking the movement of the light source and providing real-time feedback on the light fluence rate on the entire cavity surface area. In the current intrapleural PDT protocol, several detectors placed in selected locations in the pleural cavity monitor the light doses. To improve the delivery of light dose uniformity, an IR camera system is used to track the motion of the light source as well as the surface contour of the pleural cavity. Monte-Carlo simulation is used to improve the calculation algorithm for the effect of light that undergoes multiple scattering along the surface in addition to an improvement of the direct light calculation using an improved model that accounts for the anisotropy of the light from the light source.

7.
Proc SPIE Int Soc Opt Eng ; 89262014 Feb 01.
Article in English | MEDLINE | ID: mdl-25999648

ABSTRACT

Determination of optical properties (absorption (µa) and scattering (µs') coefficients) in human tissue is important when it comes to accurate calculation of fluence rate in and around tissue area. ALA application to the tissue induces production of protoporphyrin IX when activated by red light. Changes in the tissue optical properties can send information such as treatment outcome and tissue drug concentration. Patients in this study were treated with PDT for head and neck mucosal dysplasia. They were enrolled in a phase I study of escalating light doses and oral ALA with 60mg/kg. Red light at 630nm was administered to the tumor from a laser. The light dose was escalated from 50-200J/cm2 with a measured fluence rate at tissue surface of 100mW/cm2. We developed a light detection device for the purpose of determining optical properties in vivo using the semi-infinite method. The light detection device consists of two parallel, placed 5mm apart. In one of the catheters a 2 mm long linear diffusing light source is placed while in the second catheter, a calibrated isotropic detector is placed. The detector is scanned along the length of the light source containing catheter. Scans are done with the device placed on the treatment area (tumor) and on the normal tissue. Optical properties were measured in-vivo before and after PDT delivery for both normal tissue and tumor.

8.
Proc SPIE Int Soc Opt Eng ; 75512010 Mar 04.
Article in English | MEDLINE | ID: mdl-26005243

ABSTRACT

This study examines the light fluence (rate) delivered to patients undergoing pleural PDT as a function of treatment time, treatment volume and surface area. The accuracy of treatment delivery is analyzed as a function of the calibration accuracies of each isotropic detector and the calibration integrating sphere. The patients studied here are enrolled in a Phase I clinical trial of HPPH-mediated PDT for the treatment of non-small cell lung cancer with pleural effusion. Patients are administered 4mg per kg body weight HPPH 24-48 hours before the surgery. Patients undergoing photodynamic therapy (PDT) are treated with light therapy with a fluence of 15-60 J/cm2 at 661nm. Fluence rate (mW/cm2) and cumulative fluence (J/cm2) is monitored at 7 different sites during the entire light treatment delivery. Isotropic detectors are used for in-vivo light dosimetry. The anisotropy of each isotropic detector was found to be within 15%. The mean fluence rate delivery and treatment time are recorded. A correlation between the treatment time and the treatment volume is established. The result can be used as a clinical guideline for future pleural PDT treatment.

9.
Proc SPIE Int Soc Opt Eng ; 71642009 Jan 24.
Article in English | MEDLINE | ID: mdl-25914792

ABSTRACT

In-vivo light dosimetry for patients undergoing photodynamic therapy (PDT) is one of the critical dosimetry quantities for predicting PDT outcome. This study examines the relationship between the PDT treatment time and thoracic treatment volume and surface area for patients undergoing pleural PDT. In addition, the mean light fluence (rate) and its accuracy were quantified. The patients studied here were enrolled in Phase II clinical trial of Photofrin-mediated PDT for the treatment of non-small cell lung cancer with pleural effusion. The ages of the patients studied varied from 34 to 69 years old. All patients were administered 2mg per kg body weight Photoprin 24 hours before the surgery. Patients undergoing photodynamic therapy (PDT) are treated with laser light with a light fluence of 60 J/cm2 at 630nm. Fluence rate (mW/cm2) and cumulative fluence (J/cm2) was monitored at 7 different sites during the entire light treatment delivery. Isotropic detectors were used for in-vivo light dosimetry. The anisotropy of each isotropic detector was found to be within 30%. The mean fluence rate deliver varied from 37.84 to 94.05 mW/cm2 and treatment time varied from 1762 to 5232s. We found a linear correlation between the total treatment time and the treatment area: t (sec) = 4.80 A (cm2). A similar correlation exists between the treatment time and the treatment volume: t (sec) = 2.33 V (cm3). The results can be explained using an integrating sphere theory and the measured tissue optical properties assuming that the saline liquid has a mean absorption coefficient of 0.05 cm-1. Our long term accuracy studies confirmed light fluence rate measurement accuracy of ±10%. The results can be used as a clinical guideline for future pleural PDT treatment.

10.
Proc SPIE Int Soc Opt Eng ; 7164: 71640B, 2009 Feb 18.
Article in English | MEDLINE | ID: mdl-25914793

ABSTRACT

The object of this study is to develop optimization procedures that account for both the optical heterogeneity as well as photosensitizer (PS) drug distribution of the patient prostate and thereby enable delivery of uniform photodynamic dose to that gland. We use the heterogeneous optical properties measured for a patient prostate to calculate a light fluence kernel (table). PS distribution is then multiplied with the light fluence kernel to form the PDT dose kernel. The Cimmino feasibility algorithm, which is fast, linear, and always converges reliably, is applied as a search tool to choose the weights of the light sources to optimize PDT dose. Maximum and minimum PDT dose limits chosen for sample points in the prostate constrain the solution for the source strengths of the cylindrical diffuser fibers (CDF). We tested the Cimmino optimization procedures using the light fluence kernel generated for heterogeneous optical properties, and compared the optimized treatment plans with those obtained using homogeneous optical properties. To study how different photosensitizer distributions in the prostate affect optimization, comparisons of light fluence rate and PDT dose distributions were made with three distributions of photosensitizer: uniform, linear spatial distribution, and the measured PS distribution. The study shows that optimization of individual light source positions and intensities are feasible for the heterogeneous prostate during PDT.

11.
Proc SPIE Int Soc Opt Eng ; 7380: 738049, 2009 Jul 13.
Article in English | MEDLINE | ID: mdl-25983368

ABSTRACT

A compact robotic platform is designed for simultaneous multichannel motion control for light delivery and dosimetry during interstitial photodynamic therapy (PDT). Movements of light sources and isotropic detectors are controlled by individual motors along different catheters for interstitial PDT. The robotic multichannel platform adds feedback control of positioning for up to 16 channels compared to the existing dual-motor system, which did not have positioning encoders. A 16-channel servo motion controller and micro DC motors, each with high resolution optical encoder, are adopted to control the motions of up to 16 channels independently. Each channel has a resolution of 0.1mm and a speed of 5cm/s. The robotic platform can perform light delivery and dosimetry independently, allowing arbitrary positioning of light sources and detectors in each catheter. Up to 16 compact translational channels can be combined according to different operational scheme with real-time optimal motion planning. The characteristic of high speed and coordinating motion will make it possible to use short linear sources (e.g., 1- cm) to deliver uniform PDT treatment to a bulk tumor within reasonable time by source stepping optimization of multiple sources simultaneously. Advanced robotic control algorithm handles the various unexpected circumstance in clinical procedure, e.g., positiontorque/current control will be applied to prevent excessive force in the case of resistance in the fiber or motorized mechanism. The robotic platform is fully compatible with operation room (OR) environment and improves the light delivery and dosimetry in PDT. It can be adopted for diffusing optical tomography (DOT), spectroscopic DOT and fluorescent spectroscopy.

12.
Proc SPIE Int Soc Opt Eng ; 61392006 Jan 21.
Article in English | MEDLINE | ID: mdl-26113756

ABSTRACT

The Monte Carlo (MC) method of calculating light distributions in turbid media such as tissue has become the gold standard, especially in complex geometries and heterogeneous tissue. The utility of the MC method, however, is limited by is computational intensity. In an effort to reduce the time needed for MC calculations, we have adapted a macro-Monte Carlo (MMC) method (Neuenschwander, et al. 1995, Phys. Med. Biol. 40, 543-574) to the solution of tissue optics problems. Traditional MC routines trace individual photons step-by-step through the tissue. Instead, the MMC approach relies on a data set consisting of spheres in which the light absorbed in each voxel is pre-calculated using a traditional MC routine. At each MMC step, the pre-calculated absorbed light dose in the appropriate sphere, aligned to the current position and direction of the sphere, is recorded in the dose matrix. The position and direction of the photon exiting the sphere are chosen from the exit distribution of the pre-calculated sphere, and the process is repeated. By choosing the size of the pre-calculated sphere appropriately, arbitrarily complex boundary geometries can be simulated. We compare the accuracy and calculation time of the MMC method with a traditional MC algorithm for a variety of tissue optical properties and geometries. We find that the MMC algorithm can increase the speed of calculation by as much as two orders of magnitude, depending on the optical properties being simulated, without a significant loss in accuracy.

13.
Proc SPIE Int Soc Opt Eng ; 61392006 Jan 21.
Article in English | MEDLINE | ID: mdl-26113757

ABSTRACT

Optimal delivery of light in photodynamic therapy (PDT) requires not only optimal placement and power of light sources, but knowledge of the dynamics of light propagation in the tissue being treated and in the surrounding normal tissue, and of their respective accumulations of sensitizer. In an effort to quantify both tissue optical properties and sensitizer distribution, we have measured fluorescence emission and diffuse reflectance spectra at the surface of a variety of tissue types in the thoracic cavities of human patients. The patients studied here were enrolled in Phase II clinical trials of Photofrin-mediated PDT for the treatment of non-small cell lung cancer and cancers with pleural effusion. Patients were given Photofrin at dose of 2 mg per kg body weight 24 hours prior to treatment. Each patient received surgical resection of the affected lung and pleura. Patients received intracavity PDT at 630nm to a dose of 30 J/cm2, as determined by isotropic detectors sutured to the cavity walls. We measured the diffuse reflectance spectra before and after PDT in various positions within the cavity, including tumor, diaphragm, pericardium, skin, and chest wall muscle in 5 patients. The measurements we acquired using a specially designed fiber optic-based probe consisting of one fluorescence excitation fiber, one white light delivery fiber, and 9 detection fibers spaced at distances from 0.36 to 7.8 mm from the source, all of which are imaged via a spectrograph onto a CCD, allowing measurement of radially-resolved diffuse reflectance and fluorescence spectra. The light sources for these two measurements (a 403-nm diode laser and a halogen lamp, respectively) were blocked by computer-controlled shutters, allowing sequential fluorescence, reflectance, and background acquisition. The diffuse reflectance was analyzed to determine the absorption and scattering spectra of the tissue and from these, the concentration and oxygenation of hemoglobin and the local drug uptake. The total hemoglobin concentration in normal tissues varied from 50 to 300 µM, and the oxygen saturation was generally above 60%. One tumor measured exhibited higher hemoglobin concentration and lower saturation.

14.
Proc SPIE Int Soc Opt Eng ; 61392006 Jan 21.
Article in English | MEDLINE | ID: mdl-26113758

ABSTRACT

We report results of in-vivo light dosimetry of light fluence (rate) in human prostate during photodynamic therapy (PDT). Measurements were made in-vivo at the treatment wavelength (732nm) in 15 patients in three to four quadrants using isotropic detectors placed inside catheters inserted into the prostate. The catheter positions are determined using a transrectal ultrasound (TRUS) unit attached to a rigid template with 0.5-cm resolution. Cylindrical diffusing fibers with various lengths are introduced into the catheters to cover the entire prostate gland. For the last four patients, distributions of light fluence rate along catheters were also measured using a computer controlled step motor system to move multiple detectors to different distances (with 0.1 mm resolution). To predict the light fluence rate distribution, a kernel-based model was used to calculate light fluence rate using either (a) the mean optical properties (assuming homogeneous optical properties) for all patients or (b) using distributions of optical properties measured for latter patients. Standard deviations observed between the calculations and measurements were 56% and 34% for (a) and (b), respectively. The study shows that due to heterogeneity of optical properties significant variations of light fluence rate were observed both intra and inter prostates. However, if one assume a mean optical properties (µa = 0.3 cm-1, µs' = 14 cm-1), one can predict the light fluence rate to within a maximum error 200% for 80% of the cases and a mean error of 105%. To improve the prediction of light fluence rate further would require determination of distribution of optical properties.

15.
Proc SPIE Int Soc Opt Eng ; 56892005 Jan 22.
Article in English | MEDLINE | ID: mdl-26113754

ABSTRACT

Isotropic detectors with spherical scattering tips are commonly used for in-vivo dosimetry of light fluence rate during photodynamic therapy (PDT). These detectors are typically calibrated in-air. It has been well established that the response of an isotropic detector is a function of the refractive index (n) of the surrounding medium when it is surrounded by an infinite medium of uniform n. However, there are few, if any, studies of the isotropic detector response when the detector is placed in a secondary medium, such as air, before it is placed inside the infinite uniform medium. This condition often arises when one places the isotropic detector inside an air-filled catheter which is then inserted into a turbid medium, such as tissue. We have performed theoretical and experimental studies to determine the correction factors in water (n = 1.33), which has a refractive index similar to that of tissue (n = 1.4). We found that the resulting correction factor is almost the same (within 20%) as the correction factor for the outermost medium (the water) rather than the immediate medium surrounding the isotropic detector (air). The detector correction factor is also a function of the index of refraction of the probe material. For a 1-mm diameter probe from CardioFocus, the detector correction factor varied from 1 (in air) to 1.09 (at air-water interface) to 1.49 (completely submerged in water). At the air-water interface the spherical bulb of the isotropic detector is placed half in air and half in water. For a 0.5-mm diameter probe from the same company, it varied from 1 (in air) to 1.32 (at air-water interface) to 1.87 (in water). For a 0.3-mm diameter probe from the same company, it varied from 1 (in air) to 1.32 (at air-water interface) to 1.71 (in water). We have also found that the detector response changes by less than 10% when the detector position is varied from touching the catheter wall closest to the light source, to not touching, to touching the catheter wall farthest from the light source. The calibration factors between individual isotropic detectors of the same type varied within 5% for all detector types. Thus mean correction factor can be used for each individual isotropic detector of the same type.

16.
Proc SPIE Int Soc Opt Eng ; 5689: 299-310, 2005 Apr 22.
Article in English | MEDLINE | ID: mdl-26136613

ABSTRACT

Among the challenges to the clinical implementation of photodynamic therapy (PDT) is the delivery of a uniform photodynamic dose to induce uniform damage to the target tissue. As the photodynamic dose depends on both the local sensitizer concentration and the local fluence rate of treatment light, knowledge of both of these factors is essential to the delivery of uniform dose. In this paper, we investigate the distribution and kinetics of the photosensitizer motexafin lutetium (MLu, Lutrin®) as revealed by its fluorescence emission. Our current prostate treatment protocol involves interstitial illumination of the organ via cylindrical diffusing fibers (CDF's) inserted into the prostate though clear catheters. For planning and treatment purposes, the prostate is divided into 4 quadrants. We use one catheter in each quadrant to place an optical fiber-based fluorescence probe into the prostate. This fiber is terminated in a beveled tip, allowing it to deliver and collect light perpendicular to the fiber axis. Excitation light is provided by a 465 nm light emitting diode (LED) source coupled to a dichroic beamsplitter, which passes the collected fluorescence emission to a CCD spectrograph. Spectra are obtained before and after PDT treatment in each quadrant of the prostate and are analyzed via a linear fitting algorithm to separate the MLu fluorescence from the background fluorescence originating in the plastic catheter. A computer-controlled step motor allows the excitation/detection fiber to be moved along the catheter, building up a linear profile of the fluorescence emission spectrum of the tissue as a function of position. We have analyzed spectral fluorescence profiles obtained in 4 patients before and after MLu-mediated PDT. We find significant variation both within individual prostates and among patients. Within a single quadrant, we have observed the fluorescence signal to change by as much as a factor of 3 over a distance of 2 cm. Comparisons of pre- and post-PDT spectra allow a quantification treatment-induced photobleaching. Like the drug distribution, the extent of photobleaching varies widely among patients. In two cases, we observed bleaching of approximately 50% of the drug, while others exhibited negligible photobleaching.

17.
Proc SPIE Int Soc Opt Eng ; 5315: 113-124, 2004.
Article in English | MEDLINE | ID: mdl-26139956

ABSTRACT

Oblique incident light fields are sometimes unavoidable for photodynamic therapy of skin cancers, e.g., for large fields on uneven surface. We have performed Monte-Carlo simulation for circular fields (R = 0.25, 0.35, 0.5, 1, 2, 3, and 8 cm) for reduced scattering coefficient µs' = 10 cm-1 and attenuation coefficient µa = 0.1 - 1.0 cm-1. We used anisotropy g = 0.9 and the index of refraction n = 1.4 for all Monte-Carlo simulations. Compared to a broad beam of normal incidence, the peak fluence rate along the central-axis for a slanted beam is increased for otherwise the same geometrical conditions and optical properties. The effective attenuation coefficient is slightly decreased for a slanted beam compared to a normal incident beam. The beam profile for a slanted beam at a fixed depth is no longer symmetrical but is higher towards the lateral side of beam incidence. Since the broad beam with finite radius R can be considered as a convolution of a pencil beam, solution for a slanted pencil beam can be used to determine the light fluence distribution for circular beams with oblique beam incidence. An analytical solution can be obtained for the pencil beam obliquely incident on a semi-infinite medium. The solution can be approximated using the diffusion or P3 theory with one point source or two point sources located at appropriate depths with appropriate weights along the beam pathlength inside the phantom, with corresponding image sources to fulfill the extended boundary condition. The analytical solution agrees well with Monte-Carlo Simulation at depths z > 2cosθ t /µ' t , θt is the incident angle after refraction at the interface. Measurements using an isotropic detector were made in a liquid phantom composed of intralipid and ink to verify the Monte-Carlo simulation results.

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