Optimization of light sources for prostate photodynamic therapy

Abstract

To deliver uniform photodynamic dose to the prostate gland, it is necessary to develop algorithms that optimize the location and strength (emitted power × illumination time) of each light source. Since tissue optical properties may change with time, rapid (almost real-time) optimization is desirable. We use the Cimmino algorithm because it is fast, linear, and always converges reliably. A phase I motexafin lutetium (MLu)-mediated photodynamic therapy (PDT) protocol is on-going at the University of Pennsylvania. The standard plan for the protocol uses equal source strength and equal spaced loading (1-cm). PDT for the prostate is performed with cylindrical diffusing fibers (CDF) of various lengths inserted to longitudinal coverage within the matrix of parallel catheters perpendicular to a base plate. We developed several search procedures to aid the user in choosing the positions, lengths, and intensities of the CDFs. The Cimmino algorithm is used in these procedures to optimize the strengths of the light catheters at each step of the iterative selection process. Maximum and minimum bounds on allowed doses to points in four volumes (prostate, urethra, rectum, and background) constrain the solutions for the strengths of the linear light sources. Uniform optical properties are assumed. To study how different opacities of the prostate would affect optimization, optical kernels of different light penetration were used. Another goal is to see whether the urethra and rectum can be spared, with minimal effect on PTV treatment delivery, by manipulating light illumination times of the sources. Importance weights are chosen beforehand for organ volumes, and normalized. Compared with the standard plan, our algorithm is shown to produce a plan that better spares the urethra and rectum and is very fast. Thus the combined selection of positions, lengths, and strengths of interstitial light sources improves outcome.

Keywords: Cimmino Optimization; diffusion theory; light dosimetry; photodynamic therapy; prostate; tissue optical properties.

Figure 1

(a) Experimental setup for measuring the in-vivo optical properties of canine prostate. The prostate template was drilled with a 5-mm equal spaced grid. Cylindrical diffusing fibers (CDF) were inserted into the catheters to illuminate the entire prostate gland. An isotropic detector (not shown) is placed in one of the catheters, which is moved to locations at a distance of 3, 6, 9, 12, 15 mm from the light source. The detector reading at each location is peaked to ensure that it is at the middle of the linear fiber.

Figure 2

Comparison of 100% isodose lines for uniform-strength (solid line) vs. Cimmino optimized loading (dashed line) — for fixed template and CDF source lengths— for two optical properties: left (a) µ_a = 0.3 cm⁻¹, µ_s’ = 14 cm⁻¹ and right (b) µ_a = 0.1, µ_s’ = 2 cm⁻¹. Contours for prostate, urethra, and rectum are also shown in the figure.

Figure 3

Comparison of 100% isodose lines of Cimmino optimized results (optimized source lengths, loading, and template) for 12 linear sources (solid lines) and Cimmino optimized results (optimized loading only, user selected source lengths and template) (dashed lines) for two optical properties: (a) µ_a = 0.3 cm⁻¹, µ_s’ = 14 cm⁻¹ and (b) µ_a = 0.1, µ_s’ = 2 cm⁻¹. The source location for the dashed lines is the same as Fig. 2.

Figure 4

Comparison of 100% isodose lines of Cimmino optimized results for 12 linear sources with 0.5 cm step size with the maximum dose constraint of 200% (solid lines) and 300% (dashed lines) for rectum for two optical properties: (a) µ_a = 0.3 cm⁻¹, µ_s’ = 14 cm⁻¹ and (b) µ_a = 0.1, µ_s’ = 2 cm⁻¹. In this example, the source locations, lengths, retractions, and strengths are chosen by the Cimmino algorithm (see Table 2).

Figure 5

Comparison of 100% isodose lines of Cimmino optimized results (solid lines) for 51 linear sources with 0.5 cm spacing and the best Cimmino plan using 12 sources (dashed lines, loading pattern in Fig. 4) for two optical properties: (a) µ_a = 0.3 cm⁻¹, µ_s’ = 14 cm⁻¹ and (b) µ_a = 0.1, µ_s’ = 2 cm⁻¹.

Figure 6

A comparison of prostate coverage for µ_a = 0.1, µ_s’ = 2 cm⁻¹ (solid line) and µ_a = 0.3 cm⁻¹, µ_s’ = 14 cm⁻¹ (dashed line) using the source strengths listed in Table 2 for Cimmino 3, Opt 2.