Light dosimetry calculations for esophageal photodynamic therapy using porfimer sodium Linda R. Jones, Norris W. Preyer, Jr., Monica A. Davis, Carson Grimes, Kristie Edling, Nicholas Holdgate Department of Physics and Astronomy, College of Charleston, Charleston SC 29424 Herbert C. Wolfsen, Michael B. Wallace Division of Gastroenterology and Hepatology, Mayo Clinic, 4500 San Pablo Road, Jacksonville FL 32224 Abstract Background : Photodynamic therapy using porfimer sodium (Ps-PDT) is approved for use in patients with Barrett's high-grade dysplasia and esophageal carcinoma. Ps-PDT light dosimetry, however, is critically important to treatment outcomes since insufficient ablation results in residual dysplasia and carcinoma while excessive treat- ment results in stricture formation. Aim : The aim of this study was to model esophageal PDT with optical absorption and scattering coefficients derived from an ex-vivo porcine multilayer esophagus model. Methods : Optical coefficients were derived for the mucosal and muscle layers of normal pig esophagus. The mucosal layer (mucosa, muscularis mucosa and submucosa) was separated from the muscle layer. Diffuse reflectance and transmittance were measured with an integrating sphere spectrophotometer. Absorption and reduced scattering coefficients were determined with the inverse adding doubling method. Multilayer Monte Carlo simulation and single-layer mathematical dosimetry equations were employed to model esoph- ageal PDT with the derived coefficients. Porfimer sodium addition was modeled with an increase in both absorption and scattering. Depth of injury, assumed to require a threshold light dose, was estimated for various light doses commonly used in clinical practice. Depth of injury was then compared to clinical outcomes reported in the literature for various light doses. Table 1. Comparison of esophageal optical constants. Wavelength (nm) Tissue Type µ eff mm-1 µ a mm-1 µ s’ mm-1 Source 514 Esophagus in vivo 0.80 +/ - 0.15 1.90 +/ - 1.3 Bays 19 514 Pig esophagus 0.995 0.152 2.017 This work 630 Pig mucosa layer in vitro 0.522 0.068 1.27 This work 630 Pig Muscle layer in vitro 0.521 0.109 0.722 This work 630 Pig esophagus 0.482 0.061 1.210 This work 633 Esophagus in vitro 0.386 0.04 1.2 Cheong 21 630 Esophagus in vivo 0.24 +/ - 0.10 0.70 +/ - 0.23 Bays 19 630 From graph Esophagus in vivo ~1.3 Georgakoudi 20 630 From graph Barretts esoph, non -dysplastic ~ 3 Georgakoudi 20 630 From graph Barretts esoph, low grade dyspl. ~ 1.5 Georgakoudi 20 Table 2. Multilayer optical model of the normal esophagus at 630 nm. Thickness (mm) µ a mm -1 µ s’ mm -1 µ s mm -1 g Air core 20 mm diameter 0 0 Mucosal layer 1.55 0.068 1.27 25.4 0.95 24 Muscle layer 2.0 0.109 0.722 12.2 0.941 25 Adipose tissue 10. 0.10 26 15.4 26 66.9 26 0.77 26 Table 4. Homogenous optical model of the photosensitized esophagus at 630 nm. Thickness (mm) µ a mm -1 µ s’ mm -1 µ s mm -1 µ eff mm-1 ∂ (mm) g esophagus 3.55 0.061 1.96 39.2 0.608 1.64 0.95 (estimated) Grossweiner Required input: Jacques Required input: Penetration depth Penetration depth Diffuse reflectance Backscattering factor Drug concentration Power, time Power, time Assumption: Threshold amount of energy = 39 J/cm 2 Assumption: Threshold amou nt of singlet oxygen = 10 19 photons/g Single layer esophageal model Mathematical dosimetry equations Multiple layer esophageal model Monte Carlo simulation Esophageal Optical Constants Equations were proposed independently by Grossweiner and Jacques to predict the depth of necrosis for a given cylindrical light dose. Jacques gives the threshold dose of absorbed light for Photofrin®-mediated PDT as 10 19 photons per gram of tissue, assuming a Photofrin® concentration of 5 mg/kg. Grossweiner uses an equivalent threshold dose of 39 J/cm 2 . Jacques developed the following equation to determine the depth of necrosis, or effective depth of treatment, in a homogeneous tissue: where depth of necrosis (znecrosis) is a function of absorbed energy (CEt), quantum yield of singlet oxygen (Φ) and the required threshold amount of singlet oxygen (Pthreshold). Absorbed energy depends on the concentration of the drug (C), optical penetration depth (∂) and a backscattering factor (k), which must be determined for each treatment site. Expressions of this nature approximate the target tissue as a single homogenous layer. Grossweiner proposed a similar dosimetry expression incorporating the effects of drug photobleaching d Necrosis = ∂ ln (DG) where ∂ is the optical penetration depth of the tumor tissue, D is the ratio of the incident light dose to the energy fluence at the necrosis threshold, and G is a function of the tissue optical constants. Grossweiner calculated light dosimetry graphs for Photofrin® at standard conditions. A fitting routine is required to obtain the necrosis depth because the right hand side of the equation is also a function of the necrosis depth. An alternative form of the equation calculates the incident light dose necessary to provide a given depth of necrosis in order to be able to solve the equation directly on a spreadsheet: TABLE 5. Review of clinical results Source Light dose (J/cm) Strictures Recurrence, Residual HGD Predicted depth of necrosis, Grossweiner 34 * Depth of necrosis Jacques 33 ** Panjehpour et al 2005 36 85 5.3 – 5.6 % 31.6 % 0.20 mm 0.20 mm 2mg/kg 95 5.3 – 5.6 % 29.4 % 0.40 mm 0.42 mm 5-7 cm fiber 105 5.3 – 5.6 % 33.3 % 0.55 mm 0.55 mm 115 15.3 % 17 % 0.70 mm 0.73 mm Beejay et al 2001 37 2mg/kg 130 -300 mean 168 Retreated with 50 -300 55% 0 0.85 to 2.15 mm (First treatment) 0.90 to 2.3 mm Laukka et al 1995 38 3-4 mg/kg 200 -250 J/cm 20 % 17% 1.50 to 1.85 mm 1.63 to 2.00 Corti et al 2000 39 HPD 5 mg/kg 200 -300 J/cm 7% 48% 1.50 to 2.15 mm 1.63 to 2.29 Overholt et al. 1999 40 2 mg/kg 100 -300 J/cm 34% 8% LGD 12% HGD 23% cancer 0.45 to 2.15 mm 0.49 to 2.29 mm Wang et al 41 low-dose BE trial 1.5 -2.0 mg/kg HPD 175 -275 J/cm 0 BE reduced in all, eliminated in 13% 1.31 to 2.00 mm 1.41 to 2.16 Wolfsen 2002 42 2 mg/kg 175 J/cm 25% 0 HGD 50% residual BE 1.31 mm The photosensitizer was Photofrin (or Porfimer sodiu m) unless otherwise indicated.      Φ = threshold necrosis P CEtk b z ε δ ln ) ( ) ' / 1 ( ' * ' 2 / / G D e L t P L t P D Laq tM P D where DG e n n d o o o d ∂ ∂ = = = = π e reflectanc diffuse t coefficien reflection internal ) 1 /( ) 1 ( ] 1 [ 3 ) / 2 1 ( ' 3 2 4 1 = = − + = + = + = d i i i d R r r r b bR M M M δ α Table 3. Multilayer optical model of the photosensitized esophagus at 630 nm. Thickness (mm) µ a mm -1 µ s mm -1 g Air core 20 mm diameter 0 0 Mucosal layer 1.55 0.0749 37.9 0.95 Muscle layer 2.0 0.1113 27.2 .941* Adipose tissue 10. 0.100 81.9 0.77 The dosimetry equations predict that approximately 105 J/cm is sufficient to achieve the desired therapeutic effect for a target thickness of 0.6 mm. The equations also predict that approximately 200 J/cm will deliver the threshold energy to the muscle layer (muscularis propria), which could potentially injure or destroy the muscle tissues, depending on clinical variables such as the uniformity of light energy distribution, concentration of porfimer sodium, depletion of oxygen and photobleaching. However, the dosimetry equations assume an optically homogenous esophagus along with a homogenous photosensitizer content. Therefore the Monte Carlo model is expected to be more accurate. Monte Carlo simulations predict that 155 J/cm will deliver the threshold energy to a depth of 0.6 mm. While a slightly lower light dose of 150 J/cm yields a predicted necrosis depth of only 0.1 mm, an increase of the light dose to 160 J/cm yields a much deeper mucosal necrosis to a depth of 0.95 mm. Such a large difference in tissue effect with small changes in light dose may explain the variation in clinical responses noted in patients treated with PDT. The Monte Carlo simulation does not predict a threshold energy density in the muscle layer (muscularis propria) for any of the light doses up to 300 J/cm. Given the rate of stricture reported in most series of patients treated with porfimer sodium PDT, however, the threshold for damage to the mucosal muscle layer is probably much lower than the threshold for necrosis. Proposed optical model of the normal esophagus Results of the dosimetry equations Monte Carlo simulation of esophageal PDT with 5-cm cylindrical fiber. 5 mg/kg porfimer sodium in mucosa, 1.6 mg/kg in muscle