Quantification of dose nonuniformities by voxel-based dosimetry in patients receiving 90Y-ibritumomab-tiuxetan.

OBJECTIVE: To assess the impact of nonuniform dose distribution within lesions and tumor-involved organs of patients receiving Zevalin, and to discuss possible implications of equivalent uniform biological effective doses (EU-BED) on treatment efficacy and toxicity. MATLAB? -based software for voxel-based dosimetry was adopted for this purpose. METHODS: Eleven lesions from seven patients with either indolent or aggressive non-Hodgkin lymphoma were analyzed, along with four organs with disease. Absorbed doses were estimated by a direct integration of single-voxel kinetic data from serial tomographic images. After proper corrections, differential BED distributions and surviving cell fractions were estimated, allowing for the calculation of EU-BED. To quantify dose uniformity in each target area, a heterogeneity index was defined. RESULTS: Average doses were below those prescribed by conventional radiotherapy to eradicate lymphoma lesions. Dose heterogeneity and effect on tumor control varied among lesions, with no apparent relation to tumor mass. Although radiation doses to involved organs were safe, unexpected liver toxicity occurred in one patient who presented with a pattern of diffuse infiltration. CONCLUSION: Voxel-based dosimetry and radiobiologic modeling can be successfully applied to lesions and tumor-involved organs, representing a methodological advance over estimation of mean absorbed doses. However, effects on tumor control and organ toxicity still cannot be easily predicted.

Thermomechanical analysis of strain localization in a ductile detachment zone

At the latitude of the Thor-Odin dome (British Columbia) the Columbia River Detachment defines the eastern margin of the Shuswap metamorphic core complex and localizes in a 1 km thick muscovite-bearing quartzite mylonite. We present a combined Ar-40/Ar-39, (micro) structural, and oxygen isotope study of the deformation history in the detachment and evaluate the spatial and temporal relationships between microstructure formation and localization of strain. High-precision Ar-40/Ar-39 geochronology from different levels in the mylonite delineates a pattern of increasingly younger (49.0 to 47.9 Ma) deformation ages in deeper levels of the mylonitic footwall. The correlation of Ar-40/Ar-39 ages with decreasing deformation temperatures (similar to 550 degrees-400 degrees C) in the top 200 m of the mylonite indicates that deformation migrated downward from the contact with the hanging wall. Strain localization was diachronous in progressively deeper levels of the footwall and was likely controlled by fluid-assisted strain hardening due to advective heat removal and contemporaneous reaction weakening due to dissolution-reprecipitation of white mica. The observed constant high-stress microstructures across the entire detachment indicate that flow stress was buffered by the interplay of strain rate and temperature, where high strain rates at elevated temperature produced the same microstructure as lower strain rates under decreasing temperature conditions. The combined data suggest that the complex interplay among temporally nonuniform rates of footwall exhumation, heat advection, and embrittlement by meteoric fluids strongly determines the thermomechanical behavior of extensional detachments.

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

B1-insensitive T2 preparation for improved coronary magnetic resonance angiography at 3 T.

At 3 T, the effective wavelength of the RF field is comparable to the dimension of the human body, resulting in B1 standing wave effects and extra variations in phase. This effect is accompanied by an increase in B0 field inhomogeneity compared to 1.5 T. This combination results in nonuniform magnetization preparation by the composite MLEV weighted T2 preparation (T2 Prep) sequence used for coronary magnetic resonance angiography (MRA). A new adiabatic refocusing T2 Prep sequence is presented in which the magnetization is tipped into the transverse plane with a hard RF pulse and refocused using a pair of adiabatic fast-passage RF pulses. The isochromats are subsequently returned to the longitudinal axis using a hard RF pulse. Numerical simulations predict an excellent suppression of artifacts originating from B1 inhomogeneity while achieving good contrast enhancement between coronary arteries and surrounding tissue. This was confirmed by an in vivo study, in which coronary MR angiograms were obtained without a T2 Prep, with an MLEV weighted T2 Prep and the proposed adiabatic T2 Prep. Improved quantitative and qualitative coronary MRA image measurement was achieved using the adiabatic T2 Prep at 3 T.

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.