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This paper presents an improved numerical simulation and optimization of radiotherapy cancer treatments. The model used was obtained by integrating the Caputo fractional derivative and the linear-quadratic with the repopulation model into the previous radiotherapy cancer treatment model. Taking advantage of the existing model factors and parameters, especially the clinical data of six cancer patients treated with radiotherapy, the resulting model equationswere simulated inMATLAB. The Caputo fractional derivativeswere evaluated by using the fractional differential equation code (FDE12.m). The biologically effective dose formula was used to obtain six regression equations thatwere used for determining the appropriate fractional-order for each radiation protocol. Thereafter, the simulations were done in four cases. First, the fractionated doses of six patients were varied from 1.0 Gy to 6.0 Gy. Secondly, the fractionated doses were also varied from 1.0 Gy and 6.0 Gy but with 20 fractions. Thirdly, the doses of the six patients were unaltered but the number of fractions was varied from 25 to 35 fractions. Finally, a single regression equation was used to simulate the six patients' cancer treatment. The simulations had minimal errors and it was concluded that the simulated results are better predictions of the different radiation protocols. [ABSTRACT FROM AUTHOR]

Background This paper presents a numerical simulation of normal and cancer cells' population dynamics during radiotherapy. The model used for the simulation was the improved cancer treatment model with radiotherapy. The model simulated the population changes during a fractionated cancer treatment process. The results gave the final populations of the cells, which provided the final volumes of the tumor and normal cells. Method The improved model was obtained by integrating the previous cancer treatment model with the Caputo fractional derivative. In addition, the cells' population decay due to radiation was accounted for by coupling the linear-quadratic model into the improved model. The simulation of the treatment process was done with numerical variables, numerical parameters, and radiation parameters. The numerical variables include the populations of the cells and the time of treatment. The numerical parameters were the model factors which included the proliferation rates of cells, competition coefficients of cells, and perturbation constant for normal cells. The radiation parameters were clinical data based on the treatment procedure. The numerical parameters were obtained from the previous literature while the numerical variables and radiation parameters, which were clinical data, were obtained from reported data of four cancer patients treated with radiotherapy. The four cancer patients had tumor volumes of 28.4 cm 3 , 18.8 cm 3 , 30.6 cm 3 , and 12.6 cm 3 and were treated with different treatment plans and a fractionated dose of 1.8 Gy each. The initial populations of cells were obtained by using the tumor volumes. The computer simulations were done with MATLAB. Results The final volumes of the tumors, from the results of the simulations, were 5.67 cm 3 , 4.36 cm 3 , 5.74 cm 3 , and 6.15 cm 3 while the normal cells' volumes were 28.17 cm 3 , 18.68 cm 3 , 30.34 cm 3 , and 12.54 cm 3 . The powers of the derivatives were 0.16774, 0.16557, 0.16835, and 0.16. A variance-based sensitivity analysis was done to corroborate the model with the clinical data. The result showed that the most sensitive factors were the power of the derivative and the cancer cells' proliferation rate. Conclusion The model provided information concerning the status of treatments and can also predict outcomes of other treatment plans., (Copyright © 2019 Elsevier B.V. All rights reserved.)

A bleeding pseudoaneurysm of the peripancreatic artery can present with massive upper gastrointestinal hemorrhage. History of pancreatitis and urgent imaging are crucial in the making of the diagnosis. Here, we report a patient with alcoholic chronic pancreatitis presented with ruptured pseudoaneurysm of gastroduodenal artery (GDA). He was treated with percutaneous angiographic embolisation.