Simulation analysis for tumor radiotherapy based on three-component mathematical models

Assessing tumor volumetric reduction with consideration for setup errors based on mathematical tumor model and microdosimetric kinetic model in single-isocenter VMAT for brain metastases

The volumetric reduction rate (VRR) was evaluated with consideration for six degrees-of-freedom (6DoF) patient setup errors based on a mathematical tumor model in single-isocenter volumetric modulated arc therapy (SI-VMAT) for brain metastases. Simulated gross tumor volumes (GTV) of 1.0 cm and dose distribution were created (27 Gy/3 fractions). The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was translated within 0-1.0 mm (Trans) and rotated within 0-1.0° (Rot) in the three axis directions using affine transformation. The tumor growth volume was calculated using a multicomponent mathematical model (MCTM), and lethal effects of irradiation and repair from damage during irradiation were calculated by a microdosimetric kinetic model (MKM) for non-small cell lung cancer (NSCLC) A549 and NCI-H460 (H460) cells. The VRRs were calculated 5 days after the end of irradiation using the physical dose to the GTV for varying d and 6DoF setup errors. The tolerance value of VRR, the GTV volume reduction rate, was set at 5%, based on the pre-irradiation GTV volume. With the exception of the only one A549 condition where (Trans, Rot) = (1.0 mm, 1.0°) was repeated for 3 fractions, all conditions met all the tolerance VRR values for A549 and H460 cells with varying d from 0 to 10 cm. Evaluation based on the mathematical tumor model suggested that if the 6DoF setup errors at each irradiation could be kept within 1.0 mm and 1.0°, there would be little effect on tumor volume regardless of the distance from the isocenter in SI-VMAT.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

Model Calibration of Pharmacokinetic-Pharmacodynamic Lung Tumour Dynamics for Anticancer Therapies

Individual curves for tumor growth can be expressed as mathematical models. Herein we exploited a pharmacokinetic-pharmacodynamic (PKPD) model to accurately predict the lung growth curves when using data from a clinical study. Our analysis included 19 patients with non-small cell lung cancer treated with specific hypofractionated regimens, defined as stereotactic body radiation therapy (SBRT). The results exhibited the utility of the PKPD model for testing growth hypotheses of the lung tumor against clinical data. The model fitted the observed progression behavior of the lung tumors expressed by measuring the tumor volume of the patients before and after treatment from CT screening. The changes in dynamics were best captured by the parameter identified as the patients’ response to treatment. Median follow-up times for the tumor volume after SBRT were 126 days. These results have proven the use of mathematical modeling in preclinical anticancer investigations as a potential prognostic tool.

Exposure-response modeling improves selection of radiation and radiosensitizer combinations

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate.

Lung Cancer Radiotherapy: Simulation and Analysis Based on a Multicomponent Mathematical Model

Background

Lung cancer has been one of the most deadly illnesses all over the world, and radiotherapy can be an effective approach for treating lung cancer. Now, mathematical model has been extended to many biomedical fields to give a hand for analysis, evaluation, prediction, and optimization.

Methods

In this paper, we propose a multicomponent mathematical model for simulating the lung cancer growth as well as radiotherapy treatment for lung cancer. The model is digitalized and coded for computer simulation, and the model parameters are fitted with many research and clinical data to provide accordant results along with the growth of lung cancer cells in vitro.

Results

Some typical radiotherapy plans such as stereotactic body radiotherapy, conventional fractional radiotherapy, and accelerated hypofractionated radiotherapy are simulated, analyzed, and discussed. The results show that our mathematical model can perform the basic work for analysis and evaluation of the radiotherapy plan.

Conclusion

It will be expected that in the near future, mathematical model will be a valuable tool for optimization in personalized medical treatment.