Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Low cytosine triphosphate synthase 2 expression renders resistance to 5-fluorouracil in colorectal cancer

Understanding the determinants of resistance of 5-fluorouracil (5FU) is of significant value to optimizing administration of the drug, and introducing novel agents and treatment strategies. Here, the expression of 92 genes involved in 5FU transport, metabolism, co-factor (folate) metabolism and downstream effects was measured by real-time PCR low density arrays in 14 patient-derived colorectal cancer xenografts characterized for 5FU resistance. Candidate gene function was tested by siRNA and uridine modulation, and immunoblotting, apoptosis and cell cycle analysis. Predictive significance was tested by immunohistochemistry of tumors from 125 stage III colorectal cancer patients treated with and without 5FU. Of 8 genes significantly differentially expressed between 5FU sensitive and resistant xenograft tumors, CTPS2 was the gene with the highest probability of differential expression (p = 0.008). Reduction of CTPS2 expression by siRNA increased the resistance of colorectal cancer cell lines DLD1 and LS174T to 5FU and its analog, FUDR. CTPS2 siRNA significantly reduced cell S-phase accumulation and apoptosis following 5FU treatment. Exposure of cells to uridine, a precursor to the CTPS2 substrate uridine triphosphate, also increased 5FU resistance. Patients with low CTPS2 did not gain a survival benefit from 5FU treatment (p = 0.072), while those with high expression did (p = 0.003). Low CTPS2 expression may be a rationally-based determinant of 5FU resistance.

Out-of-field cell survival following exposure to intensity-modulated radiation fields

PURPOSE:
To determine the in-field and out-of-field cell survival of cells irradiated with either primary field or scattered radiation in the presence and absence of intercellular communication.
METHODS AND MATERIALS:
Cell survival was determined by clonogenic assay in human prostate cancer (DU145) and primary fibroblast (AGO1552) cells following exposure to different field configurations delivered using a 6-MV photon beam produced with a Varian linear accelerator.
RESULTS:
Nonuniform dose distributions were delivered using a multileaf collimator (MLC) in which half of the cell population was shielded. Clonogenic survival in the shielded region was significantly lower than that predicted from the linear quadratic model. In both cell lines, the out-of-field responses appeared to saturate at 40%-50% survival at a scattered dose of 0.70 Gy in DU-145 cells and 0.24 Gy in AGO1522 cells. There was an approximately eightfold difference in the initial slopes of the out-of-field response compared with the a-component of the uniform field response. In contrast, cells in the exposed part of the field showed increased survival. These observations were abrogated by direct physical inhibition of cellular communication and by the addition of the inducible nitric oxide synthase inhibitor aminoguanidine known to inhibit intercellular bystander effects. Additional studies showed the proportion of cells irradiated and dose delivered to the shielded and exposed regions of the field to impact on response.
CONCLUSIONS:
These data demonstrate out-of-field effects as important determinants of cell survival following exposure to modulated irradiation fields with cellular communication between differentially irradiated cell populations playing an important role. Validation of these observations in additional cell models may facilitate the refinement of existing radiobiological models and the observations considered important determinants of cell survival.

Temporal characterization and in vitro comparison of cell survival following the delivery of 3D-conformal, intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT)

A phantom was designed and implemented for the delivery of treatment plans to cells in vitro. Single beam, 3D-conformal radiotherapy (3D-CRT) plans, inverse planned five-field intensity-modulated radiation therapy (IMRT), nine-field IMRT, single-arc volumetric modulated arc therapy (VMAT) and dual-arc VMAT plans were created on a CT scan of the phantom to deliver 3 Gy to the cell layer and verified using a Farmer chamber, 2D ionization chamber array and gafchromic film. Each plan was delivered to a 2D ionization chamber array to assess the temporal characteristics of the plan including delivery time and 'cell's eye view' for the central ionization chamber. The effective fraction time, defined as the percentage of the fraction time where any dose is delivered to each point examined, was also assessed across 120 ionization chambers. Each plan was delivered to human prostate cancer DU-145 cells and normal primary AGO-1522b fibroblast cells. Uniform beams were delivered to each cell line with the delivery time varying from 0.5 to 20.54 min. Effective fraction time was found to increase with a decreasing number of beams or arcs. For a uniform beam delivery, AGO-1552b cells exhibited a statistically significant trend towards increased survival with increased delivery time. This trend was not repeated when the different modulated clinical delivery methods were used. Less sensitive DU-145 cells did not exhibit a significant trend towards increased survival with increased delivery time for either the uniform or clinical deliveries. These results confirm that dose rate effects are most prevalent in more radiosensitive cells. Cell survival data generated from uniform beam deliveries over a range of dose rates and delivery times may not always be accurate in predicting response to more complex delivery techniques, such as IMRT and VMAT.