A Monte Carlo simulation for Moving Light Source in Intracavity PDT

Abstract

We developed a simulation method for modeling the light fluence delivery in intracavity Photodynamic Therapy (icav-PDT) for pleural lung cancer using a moving light source. Due to the large surface area of the pleural lung cavity, the light source needs to be moved to deliver a uniform dose around the entire cavity. While multiple fixed detectors are used for dosimetry at a few locations, an accurate simulation of light fluence and fluence rate is still needed for the rest of the cavity. We extended an existing Monte Carlo (MC) based light propagation solver to support moving light sources by densely sampling the continuous light source trajectory and assigning the proper number of photon packages launched along the way. The performance of Simphotek GPU CUDA-based implementation of the method – PEDSy-MC – has been demonstrated on a life-size lung-shaped phantom, custom printed for testing icav-PDT navigation system at the Perlman School of Medicine (PSM) – calculations completed under a minute (for some cases) and within minutes have been achieved. We demonstrate results within a 5% error of the analytic solution for multiple detectors in the phantom. PEDSy-MC is accompanied by a dose-cavity visualization tool that allows real-time inspection of dose values of the treated cavity in 2D and 3D, which will be expanded to ongoing clinical trials at PSM. PSM has developed a technology to measure 8-detectors in a pleural cavity phantom using Photofrin-mediated PDT that has been used during validation.

1. INTRODUCTION

Malignant pleural mesothelioma (MPM) is one of the most common tumors affecting the serosal cavities and remains an incurable disease that has no effective single modality treatment, including surgery.¹ MPM is an aggressive tumor of the mesothelial surfaces of the pleura. The incidence is 15 cases per million people in the United States, and the prognosis is very poor with a median survival of 6–18 months from diagnosis and a 2-year survival rate of 10–33%² There is expected to be a worldwide increase in MPM cases due to uncontrolled exposures to asbestos materials with predicted deaths in the next 40 years of 72,000 in the US, 250,000 in Europe, and 103,000 in Japan.²

PDT has been investigated for over 100 years and is only now achieving rapid growth.^3–6 As is well-known PDT involves light, photosensitizers and molecular oxygen. In general PDT has fewer side effects and toxicity than more common modalities such as radiation and chemotherapy. One emphasis has been on the development of photosensitizers. Three generations of photosensitizer have been investigated:^3,4 1^st generation includes the porphyrins, 2^nd generation includes the common drug-5-Aminilevulinic Acid, and the 3^rd generation includes anti-body conjugates, encapsulated particles, and nanoparticles. In this article solid internal tumors are of particular concern, to name a few, non-small lung (including MPM), pancreas, brain, head and neck, and prostate.⁵

The extensive research in the treatment mechanisms, dosimetry and light sources⁶ have been carried over the years, revealing the complexity of PDT. What has been less emphasized is a description of the mathematics and computer simulations involved in advancing PDT. By comparison, it is a critical part of the study of radiation oncology. While there is a vast literature on x-ray radiation^7–10 and several commercial software programs to aid physicians in this treatment, there is little similar information for PDT researchers and physicians. In fact, to date there is no commercial software for PDT that encompasses all of the three main areas; light propagation, photo-physics, and oxygen. For reference, we give a few examples of the commercial software for radiation treatment that is available.

• Siemens Healthineer’s “Eclipse” radiation treatment planning software optimizes a radiotherapy treatment plan based on a physician’s dose instructions, and information about the size, shape and location of the tumor to be treated with radiation. The treatment plan becomes the basis for electronic instructions that tell the radiotherapy machine how to deliver the treatment: what angles to use, how much dose to deliver from each angle, and how the treatment beam should be shaped to match the shape of the tumor.

• Elekta’s “XiO” is a comprehensive 3-D intensity modulated radiation therapy (IMRT) treatment planning platform that combines advanced planning tools with robust dose calculation algorithms. It supports a range of treatment modalities, including 2-D, 3-D, MLC-based IMRT, solid compensator-based IMRT and brachytherapy.

• MIM’s “SureCalc MonteCarlo^™” software provides next-generation plan and adaptive therapy assessment with ART Assist^™.

• Accuray’s “Precision” radiotherapy treatment planning software and “ProSoma” a 3D virtual simulator for external beam radiation therapy provides tools to support clinicians’ decision making through the use of enhanced visualization.

• Miranda Medical’s “Embrace MR^™” accelerates testing radiotherapy cancer care with multimodality features.

The main method used in the radiation treatment planning software above is the Monte Carlo (MC) method is considered the most accurate, easiest to implement and to customize, numerical tool for simulating light propagation in the translucent medium, which is primarily characterized by its non-trivial absorption and scattering properties, anisotropy, and interface reflections and refractions.¹¹ This, and its scalability and portability characteristics, are the reasons why it became an ideal tool for simulating light transport in biological tissues on personal computers with single and multicore CPU architectures,^12–19 with a variety of implementations supporting spatially-varying optical properties,¹³ anatomically accurate geometries,^17–19 steady-state¹² and time-resolved^13,16,19 solutions as well as pulse broadening analysis.¹⁶

In MC, identical photon packets are launched from the source and each is followed independently and in parallel. This allows the use of massively-parallel GPU processors to quickly track thousands of photon packets simultaneously. The current GPU adaptations of MC provide different levels of complexity in defining anatomic structures starting with simple semi-infinite²⁰ and layered²¹ geometries and continuing with more versatile but less accurate voxel-based^21–25 geometries and more accurate but less straightforward in implementation boundary-based geometries, where different types of tissues are defined by surfaces²⁶ or tetrahedral meshes.^27,28 A variety of different types of light sources are supported in these MC implementations: a collimated beam,^{11,12,18,21–23,27} an isotropic point light source^{13,15,18,22,26,27,29–31}, a Pencil shaped^{15,17,18,21–23,26–31}, a line (like a fiber)^{16,20,27,31,32}, and a plane^31,32. However, all these sources are static – their positions do not change in time – which prohibits their use to model icav-PDT for pleural lung cancer where a moving light source is used as a therapeutic light.

Dosimetry and treatment planning are crucial in administering a safe and potentially effective PDT.^23,33–39 For example, the “integrating sphere effect” needs to be taken into account when the light dose is estimated within the lung cavity.⁴⁰ There are open-source implementations of MC^18,29,41,42 that can be used for calculating the dose distributions within the tumor tissue that helps optimize the dose. FullMonteWeb³¹ stands out as a comprehensive Cloud-based treatment planning platform to model light dose distribution for interstitial PDT and to optimize treatment parameters, including fiber positions and power allocation³⁶ with a choice of CUDA²⁷ or FPGA⁴³ acceleration. Besides conventional light dose, other dose metrics are gaining a scientific ground – irradiance threshold,^44,45 PDT-dose^46,47, and singlet oxygen dose^39,46 – to potentially become the principal predictors of responses to PDT treatments of solid tumors. Designing and implementing an MC light transport with a moving light source will be the first step in providing a treatment planning platform for icav-PDT to treat plural lung cancer or potentially any other tumor located in proximity to a tissue surface that forms a cavity.

Dosie^™-MC is a CUDA voxel-based implementation of MC light transport that calculates light distribution in a heterogeneous translucent medium such as human tissue, mixed with “air pockets” that form cavities. The tumor and surrounding volume are subdivided into a regular grid of cubic voxels, where each voxel is assigned a set of optical properties: absorption coefficient, scattering coefficient, scattering anisotropy factor, and refractive index. Dosie-MC solves a variant of the radiative transfer equation⁴⁸ by launching and tracking millions of photon packets within the tumor volume, where packets independently travel from one voxel to another, depositing their energy in the voxels that they pass due to absorption and changing their directions due to scattering events. Dosie-MC estimates the light fluence and fluence rates in all the non-air voxels from the voxels’ accumulated energy and also at the desired locations in the air pockets by registering the packets that pass the surrounding unit area. The resulting fluence and fluence rate distributions are visualized as 3D maps, level sets, point clouds, and 2D slices within Dosie interactive GUI. The unique feature of Dosie is that Dosie-MC is integrated with Photokinetics calculations that allow calculating non-conventional dose metrics such as PDT-dose and singlet oxygen dose.^24,25 All the main types of static-light sources are supported by Dosie-MC. In this work, we present a method to enable moving-light sources within the current Dosie-MC framework and describe how its implementation was validated against the analytic approximation and real-size Phantom measurements performed at Perlman School of Medicine (PSM).

The main indication considered in this paper is MPM. Researchers at PSM have investigated PDT dose dosimetry in the pleural lung cavity of 11 patients in a Photofrin-mediated study⁴⁹ and obtained good data in 64% or 7/11 patients using a recently developed an IR navigation system for clinical use.^50,51 In a phase II/III randomized clinical trial,⁵² patients with MPM received lung-sparing surgery in conjunction with PDT dose dosimetry on one arm, while patients on other randomized arm received only the surgery. For those patients receiving PDT, Photofrin (Pinnacle Biologics, Chicago, IL, USA) was administered at a dose of 5 mg per kg of body weight 24 hours before surgery. PDT treatment was performed with 632 nm light reaching a total fluence of 60 J/cm². The light was delivered via a bare optical fiber embedded in a modified endotracheal tube filled with 0.1% Intralipid. The pleural cavity was also filled with Intralipid to aid with light scattering. The mean Photofrin concentration for all 19 patients was $4.53\mu \text{M}$ and mean PDT dose for 19 patients was $448.5\mu \text{MJ}/\text{cm}2$. The maximum variation among patient was 9.2 times and the maximum variation within each patient was 3.4 times. The navigation system^50,51 showed that uniform total light fluence of 10J/cm could be achieved. Further studies are planned for the 8-channel system to test the repeatability of the measurements. We have discussed one clinical trial on MPM so far and it is of interest to mention other clinical trials for this indication in Table 1.

Table 1.

Clinical Trials of pleural mesothelioma⁵³

Title	NCT	Phase	Drug	# of patients
A Randomized Phase 2 Trial of Radical Pleurectomy and Post- Operative Chemotherapy with or Without Intraoperative Porfimer Sodium -Mediated Photodynamic Therapy for Patients with Epitheliod Malignant Pleural Mesothelioma	NCT02153229 a	Phase II, randomized	Porfimer sodium and surgery	102
Pembrolizumab in Combination with Chemotherapy and Image-Guided Surgery for Malignant Pleural Mesothelioma	NCT03760575 a	Phase I	Pembrolizumab and image guided surgery	20
0T-101 in Combination with Pembrolizumab in Subjects with Malignant Pleural Mesothelioma Failing to Respond to Checkpoint Inhibition	NCT05425576 a	Phase II, Nonrandomized	0T-101 in combination of pembrolizumab	63
Surgery and Photodynamic Therapy in Treating Patients with Malignant Mesothelioma	NCT00054002 b	Phase II	Porfimer sodium and surgery	12
Light Dosimetry for Photodynamic Therapy with Porfimer Sodium in Treating Participants with Malignant Mesothelioma or Non-Small Cell Lung Cancer with Pleural Disease Undergoing Surgery	NCT03678350 c	Phase I	Porfimer sodium and intraoperative surgery	12

Locations:

^aAbramson Cancer Center, University of Pennsylvania,

^bRoswell Park Comprehensive Cancer Center (CCC),

^cRoswell Park CCC and Lumedia

2. METHOD MONTE CARLO FOR MOVING POINT LIGHT SOURCE

In the original implementation of GPU voxel-based Monte Carlo (MC) light transport simulation^24,25 (CUDA MC-Module of Dosie^™ from Simphotek, Inc.) the supported light sources are static – their locations and the emission profiles are fixed. A large number (millions) of photon packets, $N$, is randomly launched at the light source location, according to the emission profile, and is propagated through the translucent and air-like media independently from each other. Each such packet receives a unit weight that is equivalent to the portion of the total energy of the light emitted from the light source of power $P$ (in W) within time frame $T$ (in s):

$$e_p=PT/N$$ (1)

(in J). Once launched, the packet is moved along a straight line, voxel by voxel, while its original weight is gradually reduced by a factor $e^{-{\mu }_a\left(r\right)l}$, where $l$ is the distance that the packet covers within the outgoing voxel (say, centered at a location $r$) and ${\mu }_a\left(r\right)$ is the absorption coefficient associated with such a voxel (in 1/m). The fraction $\Delta w\left(r\right)$ by which the weight is reduced is accumulated in each such outgoing voxel $w\left(r\right):=w\left(r\right)+\Delta w\left(r\right)$ till either the packet weight becomes too small or the packet leaves the target volume boundary.

Each packet may undergo multiple scattering events, may reflect/refract at the interfaces (when the index of refraction associated with the outgoing voxel differs from that of the incoming voxel), and may freely travel the air-like medium without any weight loss. The length of the free propagation without scattering is chosen randomly according to the scattering coefficient ${\mu }_s\left(r\right)$, by using the corresponding exponential distribution.⁴⁸ When the scattering coefficient changes across outgoing and incoming voxels, ${\mu }_s\left(r_{out}\right)\ne {\mu }_s\left(r_{in}\right)$, the free propagation length is adjusted appropriately. At each scattering event, the packet changes is trajectory according to the Henyey-Greenstein phase function,⁵⁴ which is parameterized by the scattering anisotropy factor $g$ associated with the voxel where the scattering event happens.

Once MC simulation is completed, the fluence value at each absorbing voxel (i.e., $\left.{\mu }_a\left(r\right)\ne 0\right)$ is recovered from the accumulated weight $w\left(r\right)$ as follows: $\Phi \left(r\right)=e_{p}w\left(r\right)/\left(V{\mu }_a\left(r\right)\right)$ (in J/m²), where $V$ is the volume of the voxel. For non-absorbing voxels (e.g., the ones that represent air, ${\mu }_a\left(r\right)=0$) as well as the absorbing voxels Dosie supports setting up spherical detectors (defined by their locations and radii) that accumulate the weights of all the packets that pass the detectors’ interiors. The fluence at the detectors can be estimated as $\Phi \left(r_d\right)=e_p{w}^D\left(r_d\right)/S_D\left(r_d\right)$ (in J/m²), where $S_D\left(r_d\right)$ is the area of the detector’s cross-section and $w^D\left(r_d\right)$ is the resulting accumulated weight for the detector at the location $r_d$.

Moving light source is enabled by densely sampling the continuous light source trajectory $r\left(t\right),t\in [0,T]$. An ordered set of $M>1$ isotropic point light sources at the locations $\left\{r_m=r\left(t_m\right),m=1\dots M\right\}$, recorded at times $\left\{t_{m,} \right.\left.m=1\dots M\right\}$, are used in this extension of MC simulation to model the light transport from a moving light source that emits light of the same power $P$ within the time frame $T=t_M$ while moving along the trajectory $r\left(t\right)$, as shown in Figure 1. As in the case of the static-light MC, photon packets of the same energy $e_p$, as in Eq. (1), are launched from each location. As such, the number of photon packets, $N_m$, to be launched at a location $r_m$, is proportional to the time $T_m$ (in s) that the light source spends within $r_m$’s neighborhood: $N_m=⌊N{T}_m/T⌋$ (for certain locations this number should be increased by 1 to guarantee that $N={\sum }_1^M N_m$; e.g., when $\left.{\sum }_{n=1}^m ⌊N{T}_n/T⌋+1\le {\sum }_{n=1}^m N{T}_n/T\right)$.

Figure 1.

Moving light source trajectory is sampled by $M$ locations $\left\{r_m\right\}$, registered at times $\left\{t_m\right\}$. An isotropic point light source is assumed at each such location.

In the moving-light MC, the weight losses $\Delta w\left(r\right)$ of photon packets that are launched at a location $r_m$ and that pass the voxel at a location $r$ will be accumulated in $w_m\left(r\right)$. Once the moving-light MC simulation is completed, the fluence at a time $t_m$ within an absorbing voxel around a location $r$ can be estimated as $\Phi \left(t_m,r\right)=e_p{\sum }_{n=1}^m w_n\left(r\right)/\left(V{\mu }_a\left(r\right)\right)$. A similar formula can be used to estimate the fluence at the detectors: $\Phi \left(t_m,r_d\right)=e_p{\sum }_{n=1}^m w_n^D\left(r_d\right)/S_D\left(r_d\right)$, where $w_m^D\left(r_d\right)$ is accumulated in the same way as for the static light source, accounting for the photon packets launched at the time $t_m$.

The new moving-light dosimetry system, ‘PDT Dose Explicit Dosimetry System’ or PEDSy, comprises both hardware and software. The hardware that includes the laser, the moving isotropic light source attached to a wand, the light source tracking navigation system, detectors mounted on the inside cavity surface, and photodiodes with associated recording devices to monitor the detector outputs is being developed at PSM. The software that includes the new moving-light MC CUDA implementation of Dosie^™ (PEDSy-MC module), integrated with Photokinetics calculations to estimate PDT dose for the entire cavity, is being developed at Simphotek. In the original static-light MC CUDA implementation,^24,25 the photon packets are equally distributed among all the available CUDA threads. In PEDSy-MC, the photon packets that are launched at the same location are grouped and each CUDA thread may receive one or more groups to run MC simulation as described above. To improve GPU usage, we keep the number of groups scheduled to one CUDA thread to a minimum while equally distributing the photon packets among the CUDA threads.

PEDSy-MC calculates the total fluence values for all the voxels at the end of the light source trajectory, i.e., $\Phi (T,r):={\Phi }_{0\to \text{T}}(T,r)$. This will eliminate the need to keep the deposited weights $w\left(r\right)$ for all intermediate times $t_m$. The voxel weights are stored in CUDA global memory and shared between all the active threads. If the fluence is needed at several time samples $\left\{{\tau }_1<\cdots <{\tau }_K\right\}\subset \left\{t_m,m=1\dots M\right\}$ then one can run PEDSy-MC $K$ times to estimate fluence for consecutive time intervals, ${\Phi }_{{\tau }_{\text{k}-1}\to {\tau }_{\text{k}}}\left({\tau }_{\text{k}},r\right)$, so that the total fluence at a desired time sample ${\tau }_K$ is the sum of the fluence values at the preceding time intervals: $\Phi \left({\tau }_{\text{k}},r\right)={\Phi }_{0\to {\tau }_1}\left({\tau }_1,r\right)+\cdots +{\Phi }_{{\tau }_{\text{k}-1}\to {\tau }_{\text{k}}}\left({\tau }_{\text{k}},r\right)$. The detectors accumulated weights $w_m^D\left(r_d\right)$, for each time $t_m$, are stored in CUDA shared memory. It allows monitoring the evolution of the total fluence $\Phi \left(t_m,r_d\right)$ at each detector position $r_d$ within a single MC run in PEDSy-MC.

3. VALIDATION

Dosie-MC was used to examine the accuracy of light dosimetry for pleural PDT in MPM.⁵⁵ For treating MPM PDT is coupled with surgical resection of the tumorous tissue. Within the thoracic cavity, the light delivery is continuously administered by a moving point source applied by a radiation oncologist or surgeon. An ellipsoid-shaped thin-wall phantom⁵⁵ surrounded in a turbid medium was used to model the intracavity lung geometry. For validation purposes, an isotropic static-light source was introduced and surrounded by a turbid medium. The primary component of the light (i.e., the direct non-scattered light) was determined by measurements performed in the air, in the absence of surrounding turbid medium. The scattered component was found by submerging the air-filled phantom cavity in a scattering (Intralipid) and absorbent (ink) medium. The isotropic light source (model SD 1250, Medlight SA, Switzerland) was located at the center and three isotropic detectors were placed at angles of 0°, 45°, and 90° with respect to the vertical axis of the phantom (with corresponding locations $\left\{q_1,q_2,q_3\right\}$). Three isotropic detectors (model IP 1250, Medlight SA, Switzerland) were located outside the transparent phantom’s wall through 3 transparent catheters. The comparison of the measurements of light fluence rate and Dosie-MC simulated values on the surface of the cavity is shown in Table 2 for two different sets of the optical properties.

Table 2.

Results of Dosie-MC normalized total fluence rate calculations, $\phi \left(q_j\right)/P$ (in cm⁻²), at 3 detector locations for two sets of optical parameters, compared with the total fluence rate measurements.

Location, j	Measured	Dosie-MC	% Diff	Measured	Dosie-MC	% Diff
	${\mu }_a=0.34{\text{cm}}^{-\text{1}},{{\mu }^{\prime }}_s=6.7{\text{cm}}^{-\text{1}}$			${\mu }_a=0.83{\text{cm}}^{-\text{1}},{{\mu }^{\prime }}_s=6.7{\text{cm}}^{-\text{1}}$
1	0.0248	0.0256	3.2	0.0162	0.0175	8
2	0.0349	0.0345	−1.1	0.0244	0.0247	1.2
3	0.0313	0.0291	−7.0	0.0199	0.0202	1.5

The results for the total light fluence at three detector locations are expressed as $\phi \left(q_j\right)/P$ (units are 1/cm²), where $\phi \left(q_j\right)$ is the fluence rate at the detector $q_j$ and $P$ is the source power. In these examples, the experimental results and MC results differ by 1% to 8%, which is acceptable accuracy for PDT.

Dosie’s performance analysis revealed its ability to reach light dose target accuracy within 4–11 seconds of simulation on GPU for the air-filled cavity. Different seeds have been used for Monte Carlo simulation to estimate an average noise in the solution in each voxel along the cavity. For the first set of optical properties shown in Table 2 (one can use the optical mean free path $mfp=1/{\mu }_{tr}=0.14\text{cm}$ and ${\mu }_{\text{eff}}=\sqrt{3{\mu }_a{\mu }_{tr}}=2.67/\text{cm}$, where ${\mu }_{tr}={\mu }_a+{\mu }_s^{\prime }$, as the measure of medium transparency), Dosie-MC required launching 2.5M photon packets and ran 4 seconds for the cavity grid of 3.9M voxels (83% of voxels are in tissue) on NVIDIA Quadro M1000M GPU to have the average noise under 12.5%, while 11 seconds simulation (with 5M photon packets) lowered the noise down to less than 9%.

3.1. Comparison to analytic solution for the case of moving light source

We demonstrated the accuracy of PEDSy-MC in calculating fluence maps for the case of moving light source against measurements done in a full-sized chest-shaped cavity. The surface of the transparent chest-shaped phantom, shown in Figure 2(a), has been digitized at PSM by applying a contour reconstruction algorithm⁵¹ to recorded point cloud data. A moving fiber-based point light source, fixed on a tip of a “wand,” is tracked by an infrared (IR) navigation system that provides the trajectory of the wand. Dosie uses the reconstructed surface contours, shown in Figure 2(b) (magenta), to create an STL geometry, which in turn is used to voxelize the target volume for PEDSy-MC simulation. There is an opening in the lower front portion of the phantom where the light source wand was inserted and moved around. The trajectory of the light source mounted on the wand (blue) captured during the experimental procedure is shown in Figure 2(b).

Figure 2.

(a) Full-sized, transparent chest-shaped phantom; (b) Chest-shaped phantom inside contour (magenta) and the trajectory of the light source (blue) recorded by IR navigation system.

The captured trajectory of the light wand of over 1,250 seconds of treatment time, $\left\{r\right(t),t\in [\mathrm{0,1250}\left]\right\}$, was used to estimate the fluence values at 3 detectors mounted on the inside cavity surface. If the cavity is filled with air with no light scattering within the cavity or from the cavity surface, the following simple analytic formula can be used as a good approximation for the fluence values accumulated at the detector positions at a time $t_m$:

$${\Phi }_j\left(\left\{r\right(t\left)\right\},t_m\right)={\int }_0^{t_m} dtP/\left(4\pi d_j^2\left(t\right)\right),$$ (2)

where $d_j\left(t\right)$ is the distance from the light source to the $j^{\text{th}}$ detector at time $t$, for all $j=\mathrm{1,2},3$. Rather than for the full treatment time of over 1250 sec, the calculations were done over short time intervals of 15–80 sec at the times when the light source was near one of the three detectors, named “Red1”, “Red2”, and “Blue”. Based on Eqn. (2), the following fluence values ${\Phi }_j\left(\left\{r\right(t\left)\right\},t_m+\Delta t_m\right)-{\Phi }_j\left(\left\{r\right(t\left)\right\},t_m\right)$ were calculated and compared with the corresponding PEDSy-MC light fluence calculations for a few times $\left\{t_m\right\}$ and time intervals $\left\{\Delta t_m\right\}$. PEDSy-MC calculations were within 6% error with the analytic approximation, as shown in Table 3.

Table 3.

PEDSy-MC fluence (J/cm2) calculations for different times and time intervals in the wand trajectory compared to the analytic fluence, based on Eqn. (2), at 3 detectors, named Red1, Red2, and Blue.

Start Time (s)	Time Interval (s)	PEDSy-MC Fluence	Analytic Fluence	Detector	Analytic Mismatch
884	15	78.94	74.80	Red1	−6%
981	80	503.92	499.56	Red1	−1%
1105	15	44.33	42.17	Red1	−5%
1129	15	32.96	32.16	Red1	−2%
1223	25	274.62	265.94	Red1	−3%
280	15	161.68	153.44	Red2	−5%
310	20	182.40	178.11	Red2	−2%
107	35	455.59	458.87	Blue	1%
190	30	256.91	251.63	Blue	−2%
244	45	1053.55	1035.04	Blue	−2%

3.2. Phantoms and measurements

Direct light measurements together with light source position tracking have been performed in a 3D-printed phantom, shown in Figure 2(a), with an air-filled cavity. The light source is mounted on a customized treatment wand⁵⁰, shown in Figure 3, and moved within the cavity for 15 min.

Figure 3.

Picture of the wand and the light source.

The light source is placed at the center of a balloon applicator that is filled with 0.1% Intralipid as the light diffuser.⁵⁰ The sphere-like-balloon has a 2 cm radius. In most cases, the boundary of the balloon had to touch the isotropic detectors gently during measurements. The wand was tracked using a commercial IR navigation system (Polaris, NDI, waterloo, Canada)⁵¹ at a 60 Hz rate. The IR camera is made up of a pair of stereo cameras, measuring the light reflection from a modulated laser source, wavelength 850 nm, built into the camera. The light is reflected by the markers (silver spheres) mounted on the treatment wand. Three isotropic detectors with a 0.5 mm scattering tip were fixed on the inner surface of the phantom. The isotropic detectors were connected to channels of photodiodes (as a part of the dosimetry system⁵⁶ developed in the PEDSy-hardware) to measure the light fluence rate (mW/cm²) and record the data at each second for three channels, i.e., three isotropic detectors. The wand with a 0.5W light source was moved inside the phantom, showing a strong measured signal at each detector when passing by. The detector locations were measured manually using the wand before treatment. The phantom shapes are recovered by position data inside the pleural cavity.⁵⁰ The position data for reconstruction was obtained before treatment. The wand tip was moved along the inner surface of the cavity for >10 min and the position data were recorded. The obtained contour was in Cartesian coordinates, which were converted to spherical coordinates by an established algorithm. Grids were defined for the whole contour and the boundary for each grid was found. These boundaries were interpolated to reconstruct the cavity surface.

We compared the instantaneous fluence rate measurements in the air-filled chest-shaped phantom with an analytic trend approximation of $1/d^2$, where $d$ is the distance from the light source to the nearby detector. There was an excellent agreement between measurements and the trend calculations for one of the detectors, labeled ‘Sensor Red 1’ as shown in Figure 4(a) for the treatment time period from 875–1250 seconds. There is less agreement for other time periods for ‘Sensor Red 1’ (see Figure 4(b) for the treatment time period 760–940 seconds) and for the other 2 detectors, which may be due to some geometric factors related to a specific detector or to the size or orientation of the light source wand, neither of which has a perfectly isotropic response or emission.

Figure 4.

(a) ‘Sensor Red 1’ data (bottom) versus $1/d^2$ calculations (top) for the treatment time period from 875–1250 seconds; (b) Sensor Red 1’ data (bottom) versus $1/d^2$ calculations (top) for the treatment time period from 760–940 seconds.

3.3. Comparison to measurements

The PEDSy-MC calculations showed good agreement with the air-filled chest-shaped phantom fluence measurements at the “Red1” detector, revealed less agreement at the “Red2” detector, and a substantial disagreement with the “Blue” detector as shown in Table 4. Still, the disagreements are consistent for each type of detector, which may be due to some geometric factor related to a specific detector or a configuration of a light wand and that detector. Representing the wand-mounted light source as a point light source in an MC simulation may not give a good match with the measurements all the time.

Table 4.

PEDSy-MC fluence (J/cm2) calculations for different times and time intervals in the wand trajectory compared to the measured fluence and analytic fluence values, based on Eqn. (2), at 3 detectors: Red1, Red2, and Blue.

Start Time (s)	Time Interval (s)	PEDSy-MC Fluence	Measured Fluence	Analytic Fluence	Detector	Measured Mismatch	Analytic Mismatch
884	15	78.94	89.59	74.80	Red1	12%	−6%
981	80	503.92	662.17	499.56	Red1	24%	−1%
1105	15	44.33	42.51	42.17	Red1	−4%	−5%
280	15	161.68	208.08	153.44	Red2	22%	−5%
310	20	182.40	239.18	178.11	Red2	24%	−2%
107	35	455.59	269.40	458.87	Blue	−69%	1%
190	30	256.91	150.02	251.63	Blue	−71%	−2%

4. PERFORMANCE AND VISUALIZATION

4.1. Performance

We tested the performance of static-light Dosie-MC on the ellipsoid-shaped phantom⁵⁵ surrounded by highly-scattering medium (tissue translucency: $mfp=0.089\text{cm}$ and ${\mu }_{\text{eff}}=3.79/\text{cm}$) for two target computer architectures: Lenovo ThinkPad with NVIDIA Quadro M1000M (512 Cores, Maxwell architecture) GPU and a Dell Workstation with NVIDIA Quadro RTX 4000 (2304 Cores, Turing architecture) GPU (Dosie-MC is built on CUDA ver. 8.0 with maximum Compute Capability 5.2). In the second architecture, RTX 4000 was set up as a GPU processor dedicated only for CUDA computations, while M1000M was the only graphics card in the first architecture. As expected, RTX 4000 has shown a significant computation speedup (~8x) that roughly follows linear dependency on the number of GPU cores. Calculation times also grow linearly with the number of launched photon packets.

The Dell workstation was used for the PEDSy-MC chest-shaped phantom simulations for a moving light source in the bottom portion of the phantom (see Figure 2) during the first 1,200 seconds of the wand irradiation (the trajectory is sampled with 22,372 wand positions). PEDSy-MC simulations are relatively fast for the case of non-scattering medium, so we made the tests a little bit more realistic by adding the absorption/scattering around the phantom surface to see how fast PEDSy-MC is for different numbers of simulated photon packets: 80, 160, and 320M (millions). The cavity is defined within the grid of 16.7M voxels (1 mm cubes; 73% of voxels represent tissue; tissue translucency: $mfp=0.22\text{cm},{\mu }_{\text{eff}}=1.16/\text{cm}$; the rest is an air cavity). The simulation times are shown in Table 6. The calculations converge around 160M launched photon packets as the noise level reduces to 1%, so there is no need to continue increasing this number.

Table 6.

PEDSy-MC time performance on dedicated NVidia Quadro RTX 4000 GPU for the moving light source (total irradiation time is 1,200 sec, sampled at 22,732 wand positions) within the chest-shaped phantom with realistic scattering medium ($\left.mfp=0.22\text{cm},{\mu }_{\text{eff}}=1.16/\text{cm}\right)$. The last columns show how the solutions differ from each other when the number of simulation photons is doubled and what is the calculation’s maximum uncertainty level at the voxels.

#Simulation photons (000,000)	#Simulation photons per wand position	#Simulation photons per irradiation sec (000)	Simulation time (sec)	Max diff. with previous	Noise level
80	3,576	66.7	3.5	2.9%	1.8%
160	7,152	133.3	7	1.5%	1.1%
320	14,304	266.7	14	1.1%	0.9%

4.2. Visualization

PEDSy-MC is integrated with Dosie^™ GUI that allows not only plotting 3D maps of calculated spatial distributions of light fluence but also supports cavity-dose visualization method to inspect the fluence values over the treated cavity in real-time in an interactive and comprehensive way. The chest-shaped phantom contour (see Figure 2) is used as an example of a cavity over which the fluence is visualized with all necessary 3D clues that help to identify the corresponding regions on the original 3D geometry. The cavity contour is mapped to a cylindrical coordinate system, which allows “unwrapping” the cavity over 2D canvas, while using the distance-to-axis information to subsequently “extrude” the contour from the 2D canvas. When done in this way, the original terrain remains which helps identify the 3D regions corresponding to the regions of interest on the canvas and provides an additional clue to localize “hidden” regions.

Figure 5(a) shows a Dosie snapshot of a split view of the chest-shaped phantom (front and back) with light fluence values “painted” over the phantom contour surface. The unwrapped version of the contour with the corresponding fluence spatial distribution painted over the full cavity, thereby forming a Cavity Canvas, is shown in Figure 5(b). 3D Cavity markers are placed and visualized at the locations of Blue and Red1 detectors.

Figure 5.

Dosie^™ snapshot of calculated special distribution of light fluence for the light wand trajectory described in Table 6. (a) On the left is the light fluence map painted over the Split view of the chest-shaped phantom that represents the front and the back of the phantom cavity surface. (b) On the right is the resulting Cavity canvas view. Red regions signify the fluence reaching the threshold values around the detectors “Blue” and “Red1”.

5. DISCUSSION AND CONCLUSIONS

For the next steps, we plan to enable monitoring the evolution of the fluence $\Phi (t,r)$ in the voxels. It would be impractical to keep the accumulated weights $w_m\left(r\right)$ for all the voxels (the total number of voxels, $n_x\times n_y\times n_z$, can be too large to keep all $n_x\times n_y\times n_z\times M$ weights) in the CUDA global memory when the light source trajectory is approximated by thousands of light source positions $\left\{r_m\right\}$. Instead, PEDSy-MC will be monitoring only the voxels that belong to the cavity, which is where the simulated fluence values are needed in the treatment planning for icav-PDT. The number of such voxels should be on the order of $n_x\times n_y$ which makes it possible to fit all the cavity weights (for approximately $n_x\times n_y\times M$ voxels) in the CUDA global memory. We also plan to extend Simphotek’s PK-Module^24,25 of Dosie^™ to enable photokinetics calculations in the presence of a moving light source - it is required for a currently developed treatment planning PEDSy device^49,57,58 based on PDT-dose⁴⁷ and singlet oxygen dose.⁴⁶ Photokinetics calculations require fluence rate maps as the input. Thus, we will enable monitoring the evolution of the fluence rate $\phi (t,r)$ (in W/m²) in the cavity voxels, so that PDT-dose and singlet oxygen dose can be simulated at any time $t_m$ during icav-PDT.

Representing the wand-mounted light source as a point light source in an MC simulation may not give a good match with the measurements all the time as the actual source is placed within a balloon with a highly transparent scattering medium. In the future, we will extend the current set of the supported light sources in Dosie to model the “balloon” light source more accurately by running parametric test MC calculations to determine special and angular light emission distributions over the balloon surface, having translucency and the size of the balloon as the parameters.

Table 5.

Comparison of Dosie-MC simulation times for NVidia Quadro GPUs for two computer configurations on an ellipsoid-shaped phantom with highly scattering medium $\left(mfp=0.089\text{cm}\right.$ and $\left.{\mu }_{\text{eff }}=3.79/\text{cm}\right)$ varying #launched photon packets.

Computer	GPU	GPU #cores	Memory Bandwidth (GB/s)	Dosie-MC run time (sec)
				300 K photons	1 M photons	3 M photons	10 M photons
Lenovo ThinkPad	M1000M (shared)	512	80	9	32	81	246
Dell workstation	RTX 4000 (dedicated)	2304	416	1	4	11	34