Computational Optimization of Irradiance and Fluence for Interstitial Photodynamic Therapy Treatment of Patients with Malignant Central Airway Obstruction

Abstract

There are no effective treatments for patients with extrinsic malignant central airway obstruction (MCAO). In a recent clinical study, we demonstrated that interstitial photodynamic therapy (I-PDT) is a safe and potentially effective treatment for patients with extrinsic MCAO. In previous preclinical studies, we reported that a minimum light irradiance and fluence should be maintained within a significant volume of the target tumor to obtain an effective PDT response. In this paper, we present a computational approach to personalized treatment planning of light delivery in I-PDT that simultaneously optimizes the delivered irradiance and fluence using finite element method (FEM) solvers of either Comsol Multiphysics^® or Dosie™ for light propagation. The FEM simulations were validated with light dosimetry measurements in a solid phantom with tissue-like optical properties. The agreement between the treatment plans generated by two FEMs was tested using typical imaging data from four patients with extrinsic MCAO treated with I-PDT. The concordance correlation coefficient (CCC) and its 95% confidence interval (95% CI) were used to test the agreement between the simulation results and measurements, and between the two FEMs treatment plans. Dosie with CCC = 0.994 (95% CI, 0.953-0.996) and Comsol with CCC = 0.999 (95% CI, 0.985-0.999) showed excellent agreement with light measurements in the phantom. The CCC analysis showed very good agreement between Comsol and Dosie treatment plans for irradiance (95% CI, CCC: 0.996-0.999) and fluence (95% CI, CCC: 0.916-0.987) in using patients' data. In previous preclinical work, we demonstrated that effective I-PDT is associated with a computed light dose of ≥45 J/cm² when the irradiance is ≥8.6 mW/cm² (i.e., the effective rate-based light dose). In this paper, we show how to use Comsol and Dosie packages to optimize rate-based light dose, and we present Dosie's newly developed domination sub-maps method to improve the planning of the delivery of the effective rate-based light dose. We conclude that image-based treatment planning using Comsol or Dosie FEM-solvers is a valid approach to guide the light dosimetry in I-PDT of patients with MCAO.

Keywords: I-PDT; MCAO; computational optimization; fluence; interstitial photodynamic therapy; irradiance; malignant central airway obstruction; rate-based light dose; treatment planning.

Figure 1

Schema of the step-by-step treatment planning procedure for I-PDT.

Figure 2

Dosie Power Optimization based on Domination Sub-maps method.

Figure 3

(a–d) Dosie screenshots of Domination Sup-maps (i.e., irradiance in mW/cm²) over the tumor of a typical patient with locally advanced MCAO tumor for four CDFs: (a) CDF-A; (b) CDF-B; (c) CDF-C; and (d) CDF-D. Non-yellow colors in (a–d) represent regions where a particular CDF dominates the other three CDFs. Power allocation optimization is carried within each such domination sub-map and then the results are combined to see if the effective rate-based light dose is reached in the presence of all CDFs. (e) A fragment of the patient’s 3D mesh with tumor and surrounding critical structures that shows locations where CDFs A–D were inserted.

Figure 3

(a–d) Dosie screenshots of Domination Sup-maps (i.e., irradiance in mW/cm²) over the tumor of a typical patient with locally advanced MCAO tumor for four CDFs: (a) CDF-A; (b) CDF-B; (c) CDF-C; and (d) CDF-D. Non-yellow colors in (a–d) represent regions where a particular CDF dominates the other three CDFs. Power allocation optimization is carried within each such domination sub-map and then the results are combined to see if the effective rate-based light dose is reached in the presence of all CDFs. (e) A fragment of the patient’s 3D mesh with tumor and surrounding critical structures that shows locations where CDFs A–D were inserted.

Figure 4

(a–c) Dosie selective screenshots of Domination Sup-map for CDF A, ${\mathrm{d}\mathrm{o}\mathrm{m}\mathrm{n}}_{\mathrm{A}|\mathrm{B},\mathrm{C},\mathrm{D}}(\mathbf{r})$, over (a) the tumor and critical structures ($\mathbf{r}\in {\mathsf{\Omega }}_T\cup {\mathsf{\Omega }}_{CS}$); (b) critical structures only ($\mathbf{r}\in {\mathsf{\Omega }}_{CS}$); and (c) the tumor only ($\mathbf{r}\in {\mathsf{\Omega }}_T$). In a–c, regions that are colored yellow are dominated by CDF A. Other regions show the corresponding calculated domination sub-maps values in mW/cm². The snapshots are taken from a different viewing angle than in Figure 3. (d) Shows labeled organs’ surfaces and CDF-A location within 3D mesh.

Figure 5

FEM-Based Treatment Plan for I-PDT of MCAO. The above figure shows a representative treatment plan and simulation results for a patient with MCAO that was treated with I-PDT. (a) High-resolution diagnostic CT scan. The treating physician segmented the tumor treatment volume (in red) and then the surrounding critical structures were segmented. The total tumor volume was 26.1 cm³. For this patient, segmentations were performed for the pulmonary artery (in purple), ascending and descending aorta (in pink), bronchus (in green), and vertebra (in yellow), and then for the tissue surrounding the tumor (not shown). These segmentations were used to create 3D CAD models that could be imported into the FEM software, which in this case was Comsol. (b) Three-dimensional mesh of the tumor (in red), pulmonary artery (in purple), aortic arch (in pink), and bronchus (in green). The mesh was created from the 3D CAD models in Comsol and used for our FEM simulations of light distribution. For this patient, the light irradiance and fluence distribution was computed for the tumor, surrounding normal tissue, pulmonary artery, and the aortic arch. (c) Fiber placement from the bronchus and into the tumor geometry. The plan was to insert 4 CDFs with illumination lengths of 1.5 cm. Each fiber would emit 240 mW/cm for 750 s. (d) Resulting irradiance distribution. Based on the treatment plan, 99.97% of the tumor volume would receive ≥8.6 mW/cm². The irradiance ranged 7–1528 mW/cm². (e) Resulting rate-based light dose (the total fluence calculated when the irradiance ≥ 8.6 mW/cm²). Based on the treatment plan, 79.6% of the tumor volume would have received the effective rate-based light dose (i.e., ≥8.6 mW/cm² and 45 J/cm²). This volume of the tumor is indicated in red in (e).

Figure 6

FEM-Based Manual Optimization of Fiber Placement. The above figure shows the irradiance distribution from the placement of the four CDFs used to treat a representative patient with MCAO who was treated with I-PDT. (a–d) show the resulting irradiance distribution for, respectively, fiber positions 1, 2, 3, and 4 when the input light intensity was 240 mW/cm per fiber. The goal of the treatment planning was to deliver ≥8.6 mW/cm² to the tumor volume. In the figures, the volume of the tumor that is ≥8.6 mW/cm² is given in red. Based on the simulations, 46.4%, 57.6%, 69.6%, and 48.3% of the tumor volume will receive ≥8.6 mW/cm² when light is emitted from, respectively, Fiber 1, Fiber 2, Fiber 3, and Fiber 4.

Figure 7

The effective rate-based light dose volume histogram calculated for 4 representative patients using both FEM software packages.