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.
A light dosimetry system is developed for prostate PDT, which integrates four main components: a light fluence rate
calculation engine, an optimization tool for treatment planning, a light delivery system, and an in vivo light fluence rate
measurement system. Three-dimensional light fluence rate distribution in a prostate is calculated using a kernel
algorithm, which takes into account of heterogeneous optical properties. A Cimmino optimization algorithm is used to
optimize the parameters of the cylindrical diffusing fibers (CDFs) to generate uniform PDT dose (or light fluence rate
under uniform drug distribution) to cover the heterogeneous prostate. The light delivery system is composed of a 12-
channel beamsplitter and the intensities of each channel (i.e., source) are controlled individually by programmable
motorized attenuators. Our tests show that the light fluence rate calculation is fast and the accuracy is close to that of a
finite-element method model, and the approach that uses the treatment CDFs to determine optical properties, improves
the accuracy of light fluence rate prediction. The light delivery system allows real time control of the light source
intensities for both PDT dosimetry and PDT light delivery. Integrating the fast light fluence rate calculation, optimization,
instant source intensity adjustment, and in vivo light fluence rate measurement, the dosimetry system is suitable for
prostate PDT.
Photodynamic therapy (PDT) dose, D, is defined as the absorbed dose by the photosensitizer during photodynamic therapy. It is proportional to the product of photosensitizer concentration and the light fluence. This quantity can be directly characterized during PDT and is considered to be predictive of photodynamic efficacy under ample oxygen supply. For type-II photodynamic interaction, the cell killing is caused by the reaction of cellular receptors with singlet oxygen. The production of singlet oxygen can be expressed as &eegr;D, where &eegr; is the singlet oxygen quantum yield d is a constant under ample oxygen supply. For most PDT, it is desirable to also take into account the effect of tissue oxygenation. We have modeled the coupled kinetics equation of the concentrations of the singlet oxygen, the photosensitizers in ground and triplet states, the oxygen, and tissue receptor along with the diffusion equation governing the light transport in turbid medium. We have shown that it is possible to express eta as a function of local oxygen concentration during PDT and this expression is a good approximation to predict the production of singlet oxygen during PDT. Theoretical estimation of the correlation between the tissue oxygen concentration and hemoglobin concentration, oxygen saturation, and blood flow is presented.
To accurately calculate light fluence rate distribution for light dosimetry in prostate photodynamic therapy (PDT),
heterogeneity of optical properties has to be taken into account. Previous study has shown that a finite-element method
(FEM) can be an efficient tool to deal with the optical heterogeneity. However, the calculation speed of the FEM is not
suitable for real time treatment planning. In this paper, two kernel models are developed. Because the kernels are based
on analytic solutions of the diffusion equation, calculations are much faster. We derived our extensions of kernel from
homogeneous medium to heterogeneous medium assuming spherically symmetrical heterogeneity of optical properties.
The kernel models are first developed for a point source and then extended for a linear source, which is considered a
summation of point sources uniformly spaced along a line. The kernel models are compared with the FEM calculation.
In application of the two kernel models to a heterogeneous prostate PDT case, both kernel models give improved light
fluence rate results compared with those derived assuming homogeneous medium. In addition, kernel model 2 predicts
reasonable light fluence rates and is deemed suitable for treatment planning.
We have developed an efficient Levenberg-Marquardt iterative algorithm utilizing a three-dimensional field
measurements coupled to a two-dimensional optical property reconstruction scheme. This technique takes advantage of
accurate estimation of light distribution in 3D forward calculation and reduced problem size and less computation time
in 2D inversion. Important advances in terms of improving algorithm efficiency and accuracy include use of an iterative
general minimum residual method (GMRES) for computing the field solutions, application of the dual mesh scheme and
adjoint method for Jacobian construction, and implementation of normalization scheme to reduce the absorption-scattering
cross talk. The synthetic measurement data were calculated for a cubic phantom containing a single
absorption anomaly and a single scattering anomaly. The model had a background of &mgr;a=0.03mm-1 and &mgr;s=1.4mm-1.
The absorption and scattering anomalies have the &mgr;a = 0.06 mm-1 and &mgr;s' = 2.0 mm-1. Five sources and 72 detectors are
used per slice. A typical human prostate is composed of 6 slices. The reconstruction images successfully recover the
both anomalies with good localization. Experiment data from tissue simulated phantom are also presented. The clinical
DOT imaging was performed before photodynamic therapy based on the protocol. The preliminary results showed the
reconstructed prostate &mgr;a varied between 0.025 and 0.07 mm-1 and &mgr;s' ranged from 1.1 to 2 mm-1. These results show
that this new 2D-3D hybrid algorithm consistently outperform the 2D-2D or 3D-3D counterparts.
In photodynamic therapy (PDT), it is desirable to determine the light fluence distribution accurately for treatment planning. Earlier studies have shown heterogeneous distribution of optical properties in patients' prostates. Finite-element method (FEM) is suitable for dealing with heterogeneous media and irregular geometries. Cylindrical diffusing fibers (CDFs) were modeled as linear sources of finite lengths, using the same parameters as those used in the treatments. Meshes were generated in the three-dimensional (3D) prostate geometry, reconstructed using transrectal ultrasound images of the prostate. Heterogeneous optical properties measured in the prostate were applied in the calculation and the refractive-index mismatch boundary condition was studied. Compared with the measurements, the FEM calculations using heterogeneous optical properties show better agreements than those using homogeneous optical properties.
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 (mua = 0.3 cm-1, mus' = 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.
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.
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