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1.  Optimization of light source parameters in the photodynamic therapy of heterogeneous prostate 
Physics in Medicine and Biology  2008;53(15):4107-4121.
The three-dimensional (3D) heterogeneous distributions of optical properties in a patient prostate can now be measured in vivo. Such data can be used to obtain a more accurate light fluence kernel. (For specified sources and points, the kernel gives the fluence delivered to a point by a source of unit strength). In turn, the kernel can be used to solve the inverse problem that determines the source strengths needed to deliver a prescribed PDT dose distribution (light fluence) within the prostate (assuming uniform drug concentration). We have developed and tested computational procedures to use the new heterogeneous data to optimize delivered light fluence. New problems arise, however, in quickly obtaining an accurate kernel following the insertion of interstitial light sources and data acquisition. (1) The light-fluence kernel must be calculated in 3D and separately for each light source, which increases kernel size. (2) An accurate kernel for light scattering in a heterogeneous medium requires ray tracing and volume partitioning, thus significant calculation time. To address these problems, two different kernels were examined and compared for speed of creation and accuracy of dose. Kernels derived more quickly involve simpler algorithms. Our goal is to achieve optimal dose planning with patient-specific heterogeneous optical data applied through accurate kernels, all within clinical times. The optimization process is restricted to accepting the given (interstitially-inserted) sources, and determining the best source strengths with which to obtain a prescribed dose. The Cimmino feasibility algorithm is used for this purpose. The dose distribution and source weights obtained for each kernel are analyzed. In clinical use, optimization will also be performed prior to source insertion to obtain initial source positions, source lengths, and source weights, but with the assumption of homogeneous optical properties. For this reason, we compare the results from heterogeneous optical data with those obtained from average homogeneous optical properties. The optimized treatment plans are also compared with the reference clinical plan, defined as the plan with sources of equal strength, distributed regularly in space, which delivers a mean value of prescribed fluence at detector locations within the treatment region. The study suggests that comprehensive optimization of source parameters (i.e., strengths, lengths, and locations) is feasible, thus allowing acceptable dose coverage in a heterogeneous prostate PDT within the time constraints of the PDT procedure.
doi:10.1088/0031-9155/53/15/007
PMCID: PMC3276881  PMID: 18612172
PDT; in-vivo; optical properties; heterogeneity; prostate; Cimmino feasibility algorithm; optimization
2.  Determination of in vivo light fluence distribution in heterogeneous prostate during photodynamic therapy 
Physics in Medicine and Biology  2008;53(8):2103-2114.
Light fluence delivered to the tumor volume is an important dosimetry quantity in photodynamic therapy (PDT). The in vivo measurements in 4 patients showed that light fluence rates varied significantly in a prostate during PDT. The maximum and the mean fluence rates in a quadrant varied from 74 to 777 mW/cm2 and from 45 to 385 mW/cm2, respectively, among 13 quadrants of 4 patients’ prostates. To determine three-dimensional (3D) light fluence rate distribution in a heterogeneous prostate, a kernel model was developed. The accuracy of the model was examined with a finite-element-method (FEM) model calculation, a phantom measurement, and the in vivo measurements. The kernel model calculations showed good agreements with the FEM model calculation and the measurements. The maximum and the mean deviations of the kernel model calculation from the in vivo measurements in the 4 patients were 23% and 4%, respectively. The kernel model, which is based on an analytic expression of a point source in a spherical symmetrical heterogeneity, has the advantage of fast calculation and is suitable for real time PDT treatment planning.
doi:10.1088/0031-9155/53/8/007
PMCID: PMC3276882  PMID: 18369279
photodynamic therapy; light fluence rate; prostate; heterogeneity; kernel model; finite element method model; cylindrical diffusing fiber
3.  Explicit dosimetry for photodynamic therapy: macroscopic singlet oxygen modeling 
Journal of biophotonics  2010;3(5-6):304-318.
Singlet oxygen (1O2) is the major cytotoxic agent responsible for cell killing for type-II photodynamic therapy (PDT). An empirical four-parameter macroscopic model is proposed to calculate the “apparent reacted 1O2 concentration”, [1O2]rx, as a clinical PDT dosimetry quantity. This model incorporates light diffusion equation and a set of PDT kinetics equations, which can be applied in any clinical treatment geometry. We demonstrate that by introducing a fitting quantity “apparent singlet oxygen threshold concentration” [1O2]rx,sd, it is feasible to determine the model parameters by fitting the computed [1O2]rx to the Photofrin-mediated PDT-induced necrotic distance using interstitially-measured Photofrin concentration and optical properties within each mouse. After determining the model parameters and the [1O2]rx,sd, we expect to use this model as an explicit dosimetry to assess PDT treatment outcome for a specific photosensitizer in an in vivo environment. The results also provide evidence that the [1O2]rx, because it takes into account the oxygen consumption (or light fluence rate) effect, can be a better predictor of PDT outcome than the PDT dose defined as the energy absorbed by the photosensitizer, which is proportional to the product of photosensitizer concentration and light fluence.
doi:10.1002/jbio.200900101
PMCID: PMC3071971  PMID: 20222102
photodynamic therapy; explicit dosimetry; singlet oxygen; mathematical modeling
4.  Determination of optical properties in heterogeneous turbid media using a cylindrical diffusing fiber 
Physics in medicine and biology  2012;57(19):6025-6046.
For interstitial photodynamic therapy (PDT), cylindrical diffusing fibers (CDF’s) are often used to deliver light. This study examines the feasibility and accuracy of using CDF’s to characterize the absorption (μa) and reduced scattering (μs′) coefficients of heterogeneous turbid media. Measurements were performed in tissue-simulating phantoms with μa between 0.1 and 1cm−1 and μs′ between 3 and 10 cm−1 with CDF’s 2 to 4 cm in length. Optical properties were determined by fitting the measured light fluence rate profiles at a fixed distance from the CDF axis using a heterogeneous kernel model in which the cylindrical diffusing fiber is treated as a series of point sources. The resulting optical properties were compared with independent measurement using a point source method. In a homogenous medium, we are able to determine the absorption coefficient μa using a value of μs′ determined a priori (uniform fit) or μs′ obtained by fitting (variable fit) with standard(maximum) deviations of 6% (18%) and 18% (44%), respectively. However, the CDF method is found to be insensitive to variations in μs′, thus requiring a complementary method such as using a point source for determination of μs′. The error for determining μa decreases in very heterogeneous turbid media because of the local absorption extremes. The data acquisition time for obtaining the one-dimensional optical properties distribution is less than 8 seconds. This method can result in dramatically improved accuracy of light fluence rate calculation for CDFs for prostate PDT in vivo when same model and geometry is used for forward calculations using the extrapolated tissue optical properties.
doi:10.1088/0031-9155/57/19/6025
PMCID: PMC3444568  PMID: 22968172
photodynamic therapy; optical properties
5.  A review of in-vivo optical properties of human tissues and its impact on PDT 
Journal of Biophotonics  2011;4(11-12):773-787.
A thorough understanding of optical properties of biological tissues is critical to effective treatment planning for therapies such as photodynamic therapy (PDT). In the last two decades, new technologies, such as broadband diffuse spectroscopy, have been developed to obtain in vivo data in humans that was not possible before. We found that the in vivo optical properties generally vary in the ranges μa =0.03–1.6 cm−1 and μs’=1.2–40 cm−1, although the actual range is tissue-type dependent. We have also examined the overall trend of the absorption spectra (for μa and μs’) as a function of wavelength within a 95% confidence interval for various tissues in vivo. The impact of optical properties on light fluence rate is also discussed for various light application geometries including superficial, interstitial, and within a cavity.
PMCID: PMC3321368  PMID: 22167862
In-vivo optical properties; light propagation; PDT; Laser-Tissue interaction
6.  Reconstruction of in-vivo optical properties for human prostate using interstitial diffuse optical tomography 
Optics Express  2009;17(14):11665-11672.
A CW interstitial diffuse optical tomography has been developed to characterize the in-vivo optical properties of prostate gland during photodynamic therapy. The spatial distributions of light fluence rate can be described by the diffusion equation. Optical properties of the prostate are reconstructed by solving the inverse problem with an adjoint method. The 3D reconstructed in-vivo optical properties for a human prostate is illustrated and compared with the results generated by a well-established point-by-point method. Moreover, the calculated fluence rate using the reconstructed optical properties matches the measured data.
PMCID: PMC3276880  PMID: 19582081
7.  Fluence Rate-Dependent Intratumor Heterogeneity in Physiologic and Cytotoxic Responses to Photofrin Photodynamic Therapy 
Photodynamic therapy (PDT) can lead to the creation of heterogeneous, response-limiting hypoxia during illumination, which may be controlled in part through illumination fluence rate. In the present report we consider 1) regional differences in hypoxia, vascular response, and cell kill as a function of tumor depth and 2) the role of fluence rate as a mediator of depth-dependent regional intratumor heterogeneity. Intradermal RIF murine tumors were treated with Photofrin-PDT using surface illumination at an irradiance of 75 or 38 mW/cm2. Regional heterogeneity in tumor response was examined through comparison of effects in the surface vs. base of tumors, i.e. along a plane parallel to the skin surface and perpendicular to the incident illumination. 75 mW/cm2-PDT created significantly greater hypoxia in tumor bases relative to their surfaces. Increased hypoxia in the tumor base could not be attributed to regional differences in Photofrin concentration nor effects of fluence rate distribution on photochemical oxygen consumption, but significant depth-dependent heterogeneity in vascular responses and cytotoxic response were detected. At a lower fluence rate of 38 mW/cm2, no detectable regional differences in hypoxia or cytotoxic responses were apparent, and heterogeneity in vascular response was significantly less than that during 75 mW/cm2-PDT. This research suggests that the benefits of low-fluence-rate-PDT are mediated in part by a reduction in intratumor heterogeneity in hypoxic, vascular and cytotoxic responses.
doi:10.1039/b9pp00004f
PMCID: PMC2834171  PMID: 20024165
photodynamic therapy; fluence rate; hypoxia; EF3; blood flow
8.  Motexafin lutetium-photodynamic therapy of prostate cancer: Short and long term effects on PSA 
Purpose:
The time course of serum PSA response to photodynamic therapy (PDT) of prostate cancer was measured.
Experimental Design:
Seventeen patients were treated in a Phase I trial of motexafin lutetium-PDT. PDT dose was calculated in each patient as the product of the ex vivo-measured pre-PDT photosensitizer level and the in situ-measured light dose. Serum PSA level was measured within two months prior to PDT (baseline), and at day 1; weeks 1-3; months 1, 2 and 3; months 4-6 and months 7-11 after PDT.
Results:
At 24h after PDT, serum PSA increased by 98±36% (mean ± SE) relative to baseline levels (p=0.007). When patients were dichotomized based on median PDT dose, those who received high PDT dose demonstrated a 119±52% increase in PSA compared to a 54±27% increase in patients treated at low PDT dose. Patients treated with high vs. low PDT dose demonstrated a median biochemical delay of 82 vs. 43 days (p=0.024), with biochemical delay defined as the length of time between PDT and a nonreversible increase in PSA to a value ≥baseline.
Conclusions:
Results show PDT to induce large, transient increases in serum PSA levels. Patients who experienced high PDT dose demonstrated greater short-term increase in PSA and a significantly more durable PSA response (biochemical delay). These data strongly promote the need for individualized delivery of PDT dose and assessment of treatment effect in PDT of prostate cancer. Information gained from such patient-specific measurements could facilitate the introduction of multiple PDT sessions in patients who would benefit.
doi:10.1158/1078-0432.CCR-08-0317
PMCID: PMC2680073  PMID: 18676760
motexafin lutetium; prostate; PSA; PDT dose; photosensitizer concentration

Results 1-8 (8)