Determination of optical properties in heterogeneous turbid media using a cylindrical diffusing fiber

For interstitial photodynamic therapy (PDT), cylindrical diffusing fibers (CDFs) are often used to deliver light. This study examines the feasibility and accuracy of using CDFs to characterize the absorption (μ(a)) and reduced scattering (μ'(s)) coefficients of heterogeneous turbid media. Measurements were performed in tissue-simulating phantoms with μ(a)?between 0.1 and 1?cm(-1)?and μ'(s) between 3 and 10?cm(-1)?with CDFs 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 μ(a)?using a value of μ'(s) determined a priori (uniform fit) or μ'(s) 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 μ'(s), thus requiring a complementary method such as using a point source for determination of μ'(s). The error for determining μ(a)?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?s. This method can result in dramatically improved accuracy of light fluence rate calculation for CDFs for prostate PDT in vivo when the same model and geometry is used for forward calculations using the extrapolated tissue optical properties.     

Determination of in vivo light fluence distribution in a heterogeneous prostate during photodynamic therapy

Light fluence delivered to the tumor volume is an important dosimetry quantity in photodynamic therapy (PDT). The in vivo measurements in four 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 cm(-2) and from 45 to 385 mW cm(-2), respectively, among 13 quadrants of four 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 four patients were 23% and 4%, respectively. The kernel model, which is based on an analytic expression of a point source in a spherically symmetrical heterogeneity, has the advantage of fast calculation and is suitable for real-time PDT treatment planning.     

Light dosimetry for multiple cylindrical diffusing sources for use in photodynamic therapy

Since prostatic carcinoma is usually multifocal within the prostate, effective photodynamic therapy (PDT) of prostatic carcinoma is expected to require the photochemical destruction of the entire organ. Accurate light dosimetry will be essential to avoid damage to proximal sensitive tissue such as the rectum. The prostate will be illuminated using interstitial cylindrical fibreoptic light sources and, because of the limited transparency of prostate tissue, these sources will be mounted in a parallel array analogous to the source array used in brachytherapy. Both source spacing and the light delivered to each source will control light dosimetry from a parallel array of fibreoptic sources implanted into tissue. Clinical PDT will require dose planning in order to determine the position and illumination of each source prior to treatment, but unfortunately few methods of predicting light fluence from cylindrical interstitial sources currently exist. In this paper, a novel light fluence model is used to predict tissue transillumination resulting from cylindrical interstitial sources. The cylindrical source is modelled as a finite array of infinitesimal small sources using Christian Huygens' famous single-slit diffraction model. We show that this source model when combined with a robust derivation of fluence in a spherical geometry using diffusion theory, accurately predicts fluence levels from a single cylindrical source in a variety of media. This method is found to retain its accuracy near the sources. With a simple extension, this fluence model is used to predict the light fluence levels from an array of three sources and the predicted fluence is found to compare favourably with experimental data.     

Dosimetric IMRT verification with a flat-panel EPID

A convolution-based calibration procedure has been developed to use an amorphous silicon flat-panel electronic portal imaging device (EPID) for accurate dosimetric verification of intensity-modulated radiotherapy (IMRT) treatments. Raw EPID images were deconvolved to accurate, high-resolution 2-D distributions of primary fluence using a scatter kernel composed of two elements: a Monte Carlo generated kernel describing dose deposition in the EPID phosphor, and an empirically derived kernel describing optical photon spreading. Relative fluence profiles measured with the EPID are in very good agreement with those measured with a diamond detector, and exhibit excellent spatial resolution required for IMRT verification. For dosimetric verification, the EPID-measured primary fluences are convolved with a Monte Carlo kernel describing dose deposition in a solid water phantom, and cross-calibrated with ion chamber measurements. Dose distributions measured using the EPID agree to within 2.1% with those measured with film for open fields of 2 x 2 cm2 and 10 x 10 cm2. Predictions of the EPID phantom scattering factors (SPE) based on our scatter kernels are within 1% of the SPE measured for open field sizes of up to 16 x 16 cm2. Pretreatment verifications of step-and-shoot IMRT treatments using the EPID are in good agreement with those performed with film, with a mean percent difference of 0.2 +/- 1.0% for three IMRT treatments (24 fields).     

Immune response against angiosarcoma following lower fluence rate clinical photodynamic therapy.

Tumor response to photodynamic therapy (PDT) is dependent on treatment parameters used. In particular, the light fluence rate may be an important determinant of the treatment outcome. In this clinical case report, we describe the response of angiosarcoma to PDT carried out using different fluence rates and drug and light doses. A patient with recurrent multifocal angiosarcoma of the head and neck was recruited for PDT. A new generation chlorin-based photosensitizer, Fotolon, was administered at a dose of 2.0 to 5.7 mg/kg. The lesions were irradiated with 665 nm laser light for a light dose of 65 to 200 J/cm2 delivered at a fluence rate of 80 or 150 mW/cm2. High dose PDT carried out at a high fluence rate resulted in local control of the disease for up to a year; however, the disease recurred and PDT had to be repeated. PDT of new lesions carried out at a lower fluence rate resulted in tumor eradication. More significantly, it also resulted in spontaneous remission of neighboring and distant untreated lesions. Repeat PDT carried out on a recurrent lesion at a lower fluence rate resulted in eradication of both treated and untreated lesions despite the lower total light dose delivered. Immunohistochemical examination of biopsy samples implies that PDT could have activated a cell-mediated immune response against untreated lesions. Subsequent histopathological examination of the lesion sites showed negative for disease. Our clinical observations show that lower fluence rate PDT results in better outcome and also indicate that the fluence rate, rather than the total light dose, is a more crucial determinant of the treatment outcome. Specifically, lower fluence rate PDT appears to activate the body's immune response against untreated lesions.     

Photon field quantities and units for kernel based radiation therapy planning and treatment optimization.

The problem of choosing radiation quantities and units for energy deposition kernels and their associated kernel densities is treated with the aim of making them consistent with related classical radiation quantities and units such as restricted mass stopping powers and mass attenuation coefficients. It is shown that it is very useful to define the kernels h(r), in terms of the quotient of the mean specific energy imparted to the medium by the radiant energy incident on a volume element centred at the origin of the kernel. The basic building block used to generate these kernels is the point energy deposition kernel, h(p), describing the spatial distribution of the energy imparted by a photon interacting at a point in a medium. This will allow the kernels to be regarded as generalizations of the traditional mass stopping and attenuation coefficients, which in detail describe the spatial distribution of the mean energy deposition around an interaction site. As a consequence, the irradiation or kernel density, f(r) should be expressed in terms of the radiant energy incident per unit volume of the medium. It is shown that the kernel density is equal to minus the divergence of the incident unattenuated vectorial energy fluence, and it therefore acts as an irradiation density for the incident vectorial energy fluence. The microscopic kernels or the irradiation density may thus be viewed as a perfect 'sink' distribution to the required incident photon energy fluence which is totally absorbed at f(r), and instead replaced by the kernels which describe the detailed energy deposition in the medium in coordinates centred at the sinks. From these definitions the required incident energy fluence from an external radiation source used for treatment realization can be determined directly by projecting the irradiation density on the relevant positions of the radiation source. This procedure has the valuable property that maximal calculational accuracy is achieved in the tumour because the irradiation density has non-zero values only in the tumour, and the accuracy of the kernel is highest at its origin.     

Integrating sphere effect in whole bladder wall photodynamic therapy: I. 532 nm versus 630 nm optical irradiation

The optical absorption, scattering and anisotropy coefficients of piglet bladder, with and without Photofrin, and of diseased human bladder were determined in vitro with a double integrating sphere set-up in the wavelength range 450-800 nm. Monte Carlo simulations were performed in a spherical geometry, representing the bladder, using the optical properties at 532 nm and 630 nm determined in vitro. The calculated fluence rates support the fluence rates that were measured at the bladder wall of a piglet during an in vivo whole bladder wall (WBW) irradiation at 532 nm and 630 nm. Fluence rates calculated and measured in vivo at 630 nm are in agreement with those measured previously in clinical photodynamic therapy (PDT) at 630 nm. WBW-PDT with red light (630 nm) will be technically more advantageous than with green light (532 nm) because of a stronger integrating sphere effect, which reduces the variations of the fluence rate at the bladder wall when the isotropic light source is moved away from the centre of the bladder. Since the optical properties show considerable variations from bladder to bladder, and since as a result the light fluence rate at the bladder wall can vary by a factor of 3 to 4 for the same non-scattered light fluence rate, we conclude that in situ light dosimetry during clinical WBW-PDT is a necessity.     

Influence of uterine cervix shape on photodynamic therapy efficiency

The goal of practical photodynamic therapy (PDT) dosimetry is to optimize the distribution of a light dose delivered to tissue by selecting the irradiation time and geometry to match the geometry and optical properties of the tumor and surrounding tissue. Homogeneous irradiation is among one of the sources of correct PDT dosimetry. The goal of this study is to model and predict the influence of the shape of a treated organ in need of light dose correction. Thus efficiency of light delivery to the tissue volume is defined and calculated with shape factors of the uterine cervix as parameters. Two cases (parallel and divergent beam) of enlightening configuration are investigated. The calculations presented extend PDT dosimetry with the influence of the shape of the uterine cervix on PDT necrosis depth. This allows for photodynamic excitation light dose correction for more reliable treatments.     

A pencil beam model for photon dose calculation.

A method for photon dose calculation in radio therapy planning using pencil beam energy deposition kernels is presented. It is designed to meet the requirements of an algorithm for 3-D treatment planning that is general enough to handle irregularly shaped radiation fields incident on a heterogeneous patient. It is point oriented and thus faster than a full 3-D convolution algorithm and uses the same physical data base to characterize a clinical beam as a full 3-D convolution algorithm. It is shown that photon therapy beams can be characterized with great accuracy from a combination of precalculated Monte Carlo energy deposition kernels and dose distributions measured in a water phantom. The data are used to derive analytical pencil beam kernels that are approximately partitionated into the dose from (i) primary released electrons and positrons, (ii) scattered, bremsstrahlung, and annihilation photons, (iii) contaminating photons, and (iv) charged particles from the collimator head. A semianalytical integration method, based on triangulation of the field, is developed for dose calculation using the analytical kernels. Dose is calculated in units normalized to the incident energy fluence which facilitates output factor calculation. For application in heterogeneous media, a scatter correction factor is derived using monodirectional convolution along the ray path. In homogeneous media results are compared with measurements and in heterogeneous media with Monte Carlo calculations and the Batho method.     

A two-step algorithm for predicting portal dose images in arbitrary detectors

Recently, portal imaging systems have been successfully demonstrated in dosimetric treatment verification applications, where measured and predicted images are quantitatively compared. To advance this approach to dosimetric verification, a two-step model which predicts dose deposition in arbitrary portal image detectors is presented. The algorithm requires patient CT data, source-detector distance, and knowledge of the incident beam fluence. The first step predicts the fluence entering a portal imaging detector located behind the patient. Primary fluence is obtained through ray-tracing techniques, while scatter fluence prediction requires a library of Monte Carlo-generated scatter fluence kernels. These kernels allow prediction of basic radiation transport parameters characterizing the scattered photons, including fluence and mean energy. The second step of the algorithm involves a superposition of Monte Carlo-generated pencil beam kernels, describing dose deposition in a specific detector, with the predicted incident fluence. This process is performed separately for primary and scatter fluence, and yields a predicted dose image. A small but noticeable improvement in prediction is obtained by explicitly modeling the off-axis energy spectrum softening due to the flattening filter. The algorithm is tested on a slab phantom and a simple lung phantom (6 MV). Furthermore, an anthropomorphic phantom is utilized for a simulated lung treatment (6 MV), and simulated pelvis treatment (23 MV). Data were collected over a range of air gaps (10-80 cm). Detectors incorporating both low and high atomic number buildup are used to measure portal image profiles. Agreement between predicted and measured portal dose is better than 3% in areas of low dose gradient (<30%/cm) for all phantoms, air gaps, beam energies, and detector configurations tested here. It is concluded that this portal dose prediction algorithm is fast, accurate, allows separation of primary and scatter dose, and can model arbitrary detectors.     

Monte Carlo evaluation of a photon pencil kernel algorithm applied to fast neutron therapy treatment planning

When dedicated software is lacking, treatment planning for fast neutron therapy is sometimes performed using dose calculation algorithms designed for photon beam therapy. In this work Monte Carlo derived neutron pencil kernels in water were parametrized using the photon dose algorithm implemented in the Nucletron TMS (treatment management system) treatment planning system. A rectangular fast-neutron fluence spectrum with energies 0-40 MeV (resembling a polyethylene filtered p(41)+Be spectrum) was used. Central axis depth doses and lateral dose distributions were calculated and compared with the corresponding dose distributions from Monte Carlo calculations for homogeneous water and heterogeneous slab phantoms. All absorbed doses were normalized to the reference dose at 10 cm depth for a field of radius 5.6 cm in a 30 x 40 x 20 cm3 water test phantom. Agreement to within 7% was found in both the lateral and the depth dose distributions. The deviations could be explained as due to differences in size between the test phantom and that used in deriving the pencil kernel (radius 200 cm, thickness 50 cm). In the heterogeneous phantom, the TMS, with a directly applied neutron pencil kernel, and Monte Carlo calculated absorbed doses agree approximately for muscle but show large deviations for media such as adipose or bone. For the latter media, agreement was substantially improved by correcting the absorbed doses calculated in TMS with the neutron kerma factor ratio and the stopping power ratio between tissue and water. The multipurpose Monte Carlo code FLUKA was used both in calculating the pencil kernel and in direct calculations of absorbed dose in the phantom.     

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.     

Fluence-convolution broad-beam (FCBB) dose calculation

IMRT optimization requires a fast yet relatively accurate algorithm to calculate the iteration dose with small memory demand. In this paper, we present a dose calculation algorithm that approaches these goals. By decomposing the infinitesimal pencil beam (IPB) kernel into the central axis (CAX) component and lateral spread function (LSF) and taking the beam's eye view (BEV), we established a non-voxel and non-beamlet-based dose calculation formula. Both LSF and CAX are determined by a commissioning procedure using the collapsed-cone convolution/superposition (CCCS) method as the standard dose engine. The proposed dose calculation involves a 2D convolution of a fluence map with LSF followed by ray tracing based on the CAX lookup table with radiological distance and divergence correction, resulting in complexity of O(N(3)) both spatially and temporally. This simple algorithm is orders of magnitude faster than the CCCS method. Without pre-calculation of beamlets, its implementation is also orders of magnitude smaller than the conventional voxel-based beamlet-superposition (VBS) approach. We compared the presented algorithm with the CCCS method using simulated and clinical cases. The agreement was generally within 3% for a homogeneous phantom and 5% for heterogeneous and clinical cases. Combined with the 'adaptive full dose correction', the algorithm is well suitable for calculating the iteration dose during IMRT optimization.     

Slit x-ray beam primary dose profiles determined by analytical transport of Compton recoil electrons

Accurate measurement of radiation beam penumbras is essential for conformal radiotherapy. For this purpose a detailed knowledge of the dosimeter's spatial response is required. However, experimental determination of detector spatial response is cumbersome and restricted to the specific detector type and beam spectrum used. A model has therefore been developed to calculate in slit beam geometry both dose profiles and detector response profiles. Summations over representative photon beam spectra yield profiles for polyenergetic beams. In the present study the model is described and resulting dose profiles verified. The model combines Compton scattering of incident photons, transport of resulting electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. This analytic model thus yields line spread kernels of primary dose in a water phantom. It is shown that the spatial response of an ideal point detector to a primary photon beam can be well described by the model; the calculations are verified by measurements with a diamond detector in a telescopic slit geometry in which all dose contributions except for the primary dose can be excluded. Effects of photon detector behavior, source size of the linear accelerator (linac) and detector size are studied. Measurements show that slit dose profiles calculated by means of the kernel are accurate within 0.1 mm of the full-width at half-maximum. For a theoretical point source and point detector combined with a 0.2 mm wide slit, the full-width half-maximum values of the slit beam dose profiles are calculated as 0.37 mm and 0.42 mm in a 6 MV and 25 MV x-ray beam, respectively. The present study shows that the model is adequate to calculate local dose effects that are dominated by approximately mono-directional, primary photon fluence. The analytic model further provides directional electron fluence information and is designed to be applied to various detectors and linac beam spectra.     

Evaluation of smoothing in an iterative lp-norm minimization algorithm for surface-based source localization of MEG

The imaging of neural sources of magnetoencephalographic data based on distributed source models requires additional constraints on the source distribution in order to overcome ill-posedness and obtain a plausible solution. The minimum l(p) norm (0 < p < or = 1) constraint is known to be appropriate for reconstructing focal sources distributed in several regions. A well-known recursive method for solving the l(p)-norm minimization problem, for example, is the focal underdetermined system solver (FOCUSS). However, this iterative algorithm tends to give spurious sources when the noise level is high. In this study, we present an algorithm to incorporate a smoothing technique into the FOCUSS algorithm and test different smoothing kernels in a surface-based cortical source space. Simulations with cortical source patches assumed in auditory areas show that the incorporation of the smoothing procedure improves the performance of the FOCUSS algorithm, and that using the geodesic distance for constructing a smoothing kernel is a better choice than using the Euclidean one, particularly when employing a cortical source space. We also apply these methods to a real data set obtained from an auditory experiment and illustrate their applicability to realistic data by presenting the reconstructed source images localized in the superior temporal gyrus.     

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.     

基于笔射束核阵列的三维适形剂量计算

目的:介绍一种基于笔射束核阵列的方法在剂量计算中的应用。方法:通过对由测量数据反解卷积获取的笔射束核阵列做进一步处理,得到拟合笔射束核。利用光通分布与笔射束核卷积得到射野剂量的分布,将拟合核和标准核计算的目标射野的剂量值与测量值进行比较。结果:与常规笔射束核相比,改进后的笔射束核应用于卷积模型中计算剂量分布,对模型的计算准确度有较大的提高。结论:改进后的笔射束核能够有效的提高卷积模型的计算精度,更为精确的预测射野的剂量分布。     

Accurate convolution/superposition for multi-resolution dose calculation using cumulative tabulated kernels

Convolution/superposition (C/S) is regarded as the standard dose calculation method in most modern radiotherapy treatment planning systems. Different implementations of C/S could result in significantly different dose distributions. This paper addresses two major implementation issues associated with collapsed cone C/S: one is how to utilize the tabulated kernels instead of analytical parametrizations and the other is how to deal with voxel size effects. Three methods that utilize the tabulated kernels are presented in this paper. These methods differ in the effective kernels used: the differential kernel (DK), the cumulative kernel (CK) or the cumulative-cumulative kernel (CCK). They result in slightly different computation times but significantly different voxel size effects. Both simulated and real multi-resolution dose calculations are presented. For simulation tests, we use arbitrary kernels and various voxel sizes with a homogeneous phantom, and assume forward energy transportation only. Simulations with voxel size up to 1 cm show that the CCK algorithm has errors within 0.1% of the maximum gold standard dose. Real dose calculations use a heterogeneous slab phantom, both the 'broad' (5 x 5 cm2) and the 'narrow' (1.2 x 1.2 cm2) tomotherapy beams. Various voxel sizes (0.5 mm, 1 mm, 2 mm, 4 mm and 8 mm) are used for dose calculations. The results show that all three algorithms have negligible difference (0.1%) for the dose calculation in the fine resolution (0.5 mm voxels). But differences become significant when the voxel size increases. As for the DK or CK algorithm in the broad (narrow) beam dose calculation, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 10% (7%) of the maximum dose. As for the broad (narrow) beam dose calculation using the CCK algorithm, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 1% of the maximum dose. Among all three methods, the CCK algorithm is demonstrated to be the most accurate one for multi-resolution dose calculations.     

Predicting colorectal surgical complications using heterogeneous clinical data and kernel methods

ObjectiveIn this work, we have developed a learning system capable of exploiting information conveyed by longitudinal Electronic Health Records (EHRs) for the prediction of a common postoperative complication, Anastomosis Leakage (AL), in a data-driven way and by fusing temporal population data from different and heterogeneous sources in the EHRs.Material and methodsWe used linear and non-linear kernel methods individually for each data source, and leveraging the powerful multiple kernels for their effective combination. To validate the system, we used data from the EHR of the gastrointestinal department at a university hospital.ResultsWe first investigated the early prediction performance from each data source separately, by computing Area Under the Curve values for processed free text (0.83), blood tests (0.74), and vital signs (0.65), respectively. When exploiting the heterogeneous data sources combined using the composite kernel framework, the prediction capabilities increased considerably (0.92). Finally, posterior probabilities were evaluated for risk assessment of patients as an aid for clinicians to raise alertness at an early stage, in order to act promptly for avoiding AL complications.DiscussionMachine-learning statistical model from EHR data can be useful to predict surgical complications. The combination of EHR extracted free text, blood samples values, and patient vital signs, improves the model performance. These results can be used as a framework for preoperative clinical decision support.