Development of a Compartmental Pharmacokinetic Model for Molecular Radiotherapy with 131I-CLR1404.

Pharmacokinetic modeling of the radiopharmaceuticals used in molecular radiotherapy is an important step towards accurate radiation dosimetry of such therapies. In this paper, we present a pharmacokinetic model for CLR1404, a phospholipid ether analog that, labeled with 124I/131I, has emerged as a promising theranostic agent. We follow a systematic approach for the model construction based on a decoupling process applied to previously published experimental data, and using the goodness-of-fit, Sobol's sensitivity analysis, and the Akaike Information Criterion to construct the optimal form of the model, investigate potential simplifications, and study factor prioritization. This methodology was applied to previously published experimental human time-activity curves for 9 organs. The resulting model consists of 17 compartments involved in the CLR1404 metabolism. Activity dynamics in most tissues are well described by a blood contribution plus a two-compartment system, describing fast and slow uptakes. The model can fit both clinical and pre-clinical kinetic data of 124I/131I. In addition, we have investigated how simple fits (exponential and biexponential) differ from the complete model. Such fits, despite providing a less accurate description of time-activity curves, may be a viable alternative when limited data is available in a practical case.

Quantification of internal dosimetry in PET patients II: Individualized Monte Carlo-based dosimetry for [18F]fluorocholine PET.

PURPOSE: To obtain individualized internal doses with a Monte Carlo (MC) method in patients undergoing diagnostic [18F]FCH-PET studies and to compare such doses with the MIRD method calculations. METHODS: A patient cohort of 17 males were imaged after intravenous administration of a mean [18F]FCH activity of 244.3 MBq. The resulting PET/CT images were processed in order to generate individualized input source and geometry files for dose computation with the MC tool GATE. The resulting dose estimates were studied and compared to the MIRD method with two different computational phantoms. Mass correction of the S-factors was applied when possible. Potential sources of uncertainty were closely examined: the effect of partial body images, urinary bladder emptying, and biokinetic modeling. RESULTS: Large differences in doses between our methodology and the MIRD method were found, generally in the range ±25%, and up to ±120% for some cases. The mass scaling showed improvements, especially for non-walled and high-uptake tissues. Simulations of the urinary bladder emptying showed negligible effects on doses to other organs, with the exception of the prostate. Dosimetry based on partial PET/CT images (excluding the legs) resulted in an overestimation of mean doses to bone, skin, and remaining tissues, and minor differences in other organs/tissues. Estimated uncertainties associated with the biokinetics of FCH introduce variations of cumulated activities in the range of ±10% in the high-uptake organs. CONCLUSIONS: The MC methodology allows for a higher degree of dosimetry individualization than the MIRD methodology, which in some cases leads to important differences in dose values. Dosimetry of FCH-PET based on a single partial PET study seems viable due to the particular biokinetics of FCH, even though some correction factors may need to be applied to estimate mean skin/bone doses.

A kinetic model of continuous radiation damage to populations of cells: comparison to the LQ model and application to molecular radiotherapy.

The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting approach is that of obtaining LQ-like behavior from kinetic models, systems of differential equations that model the induction and repair of damage. Development of such kinetic models is particularly interesting for application to continuous dose rate therapies, such as molecular radiotherapy or brachytherapy. In this work, we present a simple kinetic model that describes the kinetics of populations of tumor cells, rather than lethal/sub-lethal lesions, which may be especially useful for application to continuous dose rate therapies, as in molecular radiotherapy. The multi-compartment model consists of a set of three differential equations. The model incorporates in an easy way different cross-interacting compartments of cells forming a tumor, and may be of especial interest for studying dynamics of treated tumors. In the fast dose delivery limit, the model can be analytically solved, obtaining a simple closed-form expression. Fitting of several surviving curves with both this solution and the LQ model shows that they produce similar fits, despite being functionally different. We have also investigated the operation of the model in the continuous dose rate scenario, firstly by fitting pre-clinical data of tumor response to 131I-CLR1404 therapy, and secondly by showing how damage repair and proliferation rates can cause a treatment to achieve control or not. Kinetic models like the one presented in this work may be of special interest when modeling response to molecular radiotherapy.

Quantification of internal dosimetry in PET patients: individualized Monte Carlo vs generic phantom-based calculations.

PURPOSE: The purpose of this work is to calculate individualized dose distributions in patients undergoing 18 F-FDG PET/CT studies through a methodology based on full Monte Carlo (MC) simulations and PET/CT patient images, and to compare such values with those obtained by employing nonindividualized phantom-based methods. METHODS: We developed a MC-based methodology for individualized internal dose calculations, which relies on CT images (for organ segmentation and dose deposition), PET images (for organ segmentation and distributions of activities), and a biokinetic model (which works with information provided by PET and CT images) to obtain cumulated activities. The software vGATE version 8.1. was employed to carry out the Monte Carlo calculations. We also calculated deposited doses with nonindividualized phantom-based methods (Cristy-Eckerman, Stabin, and ICRP-133). RESULTS: Median MC-calculated dose/activity values are within 0.01-0.03 mGy/MBq for most organs, with higher doses delivered especially to the bladder wall, major vessels, and brain (medians of 0.058, 0.060, 0.066 mGy/MBq, respectively). Comparison with values obtained with nonindividualized phantom-based methods has shown important differences in many cases (ranging from -80% to + 260%). These differences are significant (p < 0.05) for several organs/tissues, namely, remaining tissues, adrenals, bladder wall, bones, upper large intestine, heart, pancreas, skin, and stomach wall. CONCLUSIONS: The methodology presented in this work is a viable and useful method to calculate internal dose distributions in patients undergoing medical procedures involving radiopharmaceuticals, individually, with higher accuracy than phantom-based methods, fulfilling the guidelines provided by the European Council directive 2013/59/Euratom.

A Model of Indirect Cell Death Caused by Tumor Vascular Damage after High-Dose Radiotherapy.

There is increasing evidence that high doses of radiotherapy, like those delivered in stereotactic body radiotherapy (SBRT), trigger indirect mechanisms of cell death. Such effect seems to be two-fold. High doses may trigger an immune response and may cause vascular damage, leading to cell starvation and death. Development of mathematical response models, including indirect death, may help clinicians to design SBRT optimal schedules. Despite increasing experimental literature on indirect tumor cell death caused by vascular damage, efforts on modeling this effect have been limited. In this work, we present a biomathematical model of this effect. In our model, tumor oxygenation is obtained by solving the reaction-diffusion equation; radiotherapy kills tumor cells according to the linear-quadratic model, and also endothelial cells (EC), which can trigger loss of functionality of capillaries. Capillary death will affect tumor oxygenation, driving nearby tumor cells into severe hypoxia. Capillaries can recover functionality due to EC proliferation. Tumor cells entering a predetermined severe hypoxia status die according to a hypoxia-death model. This model fits recently published experimental data showing the effect of vascular damage on surviving fractions. It fits surviving fraction curves and qualitatively reproduces experimental values of percentages of functional capillaries 48 hours postirradiation, and hypoxic cells pre- and 48 hours postirradiation. This model is useful for exploring aspects of tumor and EC response to radiotherapy and constitutes a stepping stone toward modeling indirect tumor cell death caused by vascular damage and accounting for this effect during SBRT planning. SIGNIFICANCE: A novel biomathematical model of indirect tumor cell death caused by vascular radiation damage could potentially help clinicians interpret experimental data and design better radiotherapy schedules.

Adaptive biokinetic modelling of iodine-131 in thyroid cancer treatments: implications on individualised internal dosimetry.

Nowadays therapies involving radioiodine (I-131) represent 84% of the total metabolic treatments in Europe, according to the last report of the European Association of Nuclear Medicine in relation to treatment planning for molecular radiotherapy. Last recommendations of the European Council, i.e. 2013/59/Euroatom, mandates that metabolic treatments should be planned according to the radiation doses delivered to individual patients, analogous to external beam radiotherapy. In this work, we present a novel biokinetic model for I-131 that allows on to obtain realistic activity distributions for particular patients with thyroid cancer in absence of metastasis. Other models existing in the literature present either a too simple metabolic description to obtain realistic results or a too complex one for adapting the model to individual patients, and many of these models are not indicated for metabolic treatments. The individualisation of activity distribution is obtained by an optimisation method that adjusts our model to a set of experimental measurements. Significant differences in terms of absorbed doses are observed between our model and the standard generalist models, especially in terms of red marrow absorbed dose.

Development and clinical characterization of a novel 2041 liquid-filled ionization chambers array for high-resolution verification of radiotherapy treatments.

PURPOSE: The aim of this study was to present a novel 2041 liquid-filled ionization chamber array for high-resolution verification of radiotherapy treatments. MATERIALS AND METHODS: The prototype has 2041 ionization chambers of 2.5 × 2.5 mm2 area filled with isooctane. The detection elements are arranged in a central square grid of 43 × 43, totally covering an area of 107.5 × 107.5 mm2 . The central inline and cross-line are extended to 227 mm and the diagonals to 321 mm to be able to perform profile measurements of large fields. We have studied stability, pixel response uniformity, dose rate dependence, depth and field size dependence and anisotropy. We present results for output factors, tongue-and-groove, garden fence, small field profiles, irregular fields, and verification of dose planes of patient treatments. RESULTS: Comparison with other detectors used for small field dosimetry (SFD, CC13, microDiamond) has shown good agreement. Output factors measured with the device for square fields ranging from 10 × 10 to 100 × 100 mm2 showed relative differences within 1%. The response of the detector shows a strong dependence on the angle of incident radiation that needs to be corrected for. On the other hand, inter-pixel relative response variations in the 0.95-1.08 range have been found and corrected for. The application of the device for the verification of dose planes of several treatments has shown gamma passing rates above 97% for tolerances of 2% and 2 mm. The verification of other clinical fields, like small fields and irregular fields used in the commissioning of the TPS, also showed large passing rates. The verification of garden fence and tongue-and-groove fields was affected by volume-averaging effects. CONCLUSIONS: The results show that the liquid filled ionization chamber prototype here presented is appropriate for the verification of radiotherapy treatments with high spatial resolution. Recombination effects do not affect very much the verification of relative dose distributions. However, verification of absolute dose distributions may require normalization to a radiation field which is representative of the dose rate of the treatment delivered.

Characterising endourologist learning curve during percutaneous nephrolithotomy: implications on occupational dose and patients.

In this study we have characterised the learning curve for percutaneous nephrolithotomy procedures over 301 cases for six years. Different surrogate parameters of clinical expertise have been used, such as dose area product, total procedure time, fluoroscopy time and personal equivalent doses. In addition, two different endourologists have been monitored; one of whom had specific Radiation Protection training (ICRP 85). Eye lens dose was estimated from thermoluminescent dosimeters. Significant differences were observed between both endourologists, especially in the fluoroscopy time. Finally, both entrance skin dose and effective doses of patients have been determined.

Characterizing endourologist learning curve during percutaneous nephrolithotomy: implications on occupational dose and patients.

In this study we have characterized the learning curve of percutaneous nephrolithotomy procedures over 301 cases for six years. Different surrogate parameters of clinical expertise have been used, such as dose area product, total procedure time, fluoroscopy time and personal equivalent doses. In addition, two different endourologists have been monitored; one of whom was subjected to a specific Radiation Protection training (ICRP 85). Eye lens dose is estimated from thermoluminescent dosimeters. Significant differences are observed between both endourologists, especially in the fluoroscopy time. Finally, both entrance skin dose and effective doses of patients have been determined.

Social media enhances languages differentiation: a mathematical description.

Understanding and predicting the evolution of competing languages is a topic of high interest in a world with more than 6000 languages competing in a highly connected environment. We consider a reasonable mathematical model describing a situation of competition between two languages and analyse the effect of the speakers' connectivity (i.e. social networks). Surprisingly, instead of homogenizing the system, a high degree of connectivity helps to introduce differentiation for the appropriate parameters.

Evaluation and optimization of occupational eye lens dosimetry during positron emission tomography (PET) procedures.

The last recommendations of the International Commission on Radiological Protection for eye lens dose suggest an important reduction on the radiation limits associated with early and late tissue reactions. The aim of this work is to quantify and optimize the eye lens dose associated to nurse staff during positron emission tomography (PET) procedures. PET is one of the most important diagnostic methods of oncological and neurological cancer disease involving an important number of workers exposed to the high energy isotope F-18. We characterize the relevant stages as preparation and administration of monodose syringes in terms of occupational dose. A direct reading silicon dosimeter was used to measure the lens dose to staff. The highest dose of radiation was observed during preparation of the fluorodesoxyglucose (FDG) syringes. By optimizing a suitable vials' distribution of FDG we find an important reduction in occupational doses. Extrapolation of our data to other clinical scenarios indicates that, depending on the work load and/or syringes activity, safety limits of the dose might be exceeded.

Externally controlled anisotropy in pattern-forming reaction-diffusion systems.

The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.

Influence of oscillatory centrifugal forces on the mechanism of Turing pattern formation.

Constantly acting centrifugal forces on Turing pattern forming systems have been observed to induce orientation and wavelength changes on Turing structures. Here, we will consider a periodic modulation of such centrifugal forces and their effects on pattern formation. Depending on the oscillation period the system exhibits a wide variety of stationary (stripes, H(0), etc.) or nonstationary patterns (black eyes, etc.), as well as transitions and instabilities such as Eckhaus, zigzag, etc. In this paper, a detailed description of the different patterns and patterning mechanisms will be described and understood within the previous context. The system considered is the Belousov-Zhabotinsky reaction encapsulated in AOT micelles modeled by the adapted version of the Oregonator model.

Characterizing topological transitions in a Turing-pattern-forming reaction-diffusion system.

Turing structures appear naturally and they are demonstrated under different spatial configurations such as stripes and spots as well as mixed states. The traditional tool to characterize these patterns is the Fourier transformation, which accounts for the spatial wavelength, but it fails to discriminate among different spatial configurations or mixed states. In this paper, we propose a parameter that clearly differentiates the different spatial configurations. As an application, we considered the transitions induced by an external forcing in a reaction-diffusion system although the results are straightforwardly extended to different problems with similar topologies. The method was also successfully tested on a temporally evolving pattern.

Modulation of volume fraction results in different kinetic effects in Belousov-Zhabotinsky reaction confined in AOT-reverse microemulsion.

The effects of volume fraction modulations on a Belousov-Zhabotinsky reaction catalyzed by the photosensitive Ru(bpy)(3)(+2) confined in an AOT microemulsion system are analyzed. Kinetic observables such as the induction time or the initial oscillation period demonstrate two different types of correlation with the volume fraction depending on whether the system is below or above the microemulsion percolation threshold. Temporal evolution also demonstrates an exponential growth of the period with the number of oscillations independent of the volume fraction of the system.

Manipulation of diffusion coefficients via periodic vertical forcing controls the mechanism of Turing pattern formation.

We study, theoretically and experimentally, the dynamical response of macroscopic Turing patterns to a mechanical periodic forcing which implies a sinusoidal modulation of gravity. Theoretical predictions indicate that the extra energy, due to the forcing, modifies the diffusion coefficient at a microscopic level, producing changes in the Turing domain and in the pattern characteristics, in particular its wavelength. To check the theoretical analysis, we perform numerical simulations with standard models. Experiments were also performed in the closed Belousov-Zhabotinsky reaction confined in AOT microemulsion (BZ-AOT system). Experiments as well as numerical and theoretical results show good agreement.