PO83

Purpose In order to develop a robust universal model which can accurately predict tumor control probability (TCP), it is necessary to first explore the sensitivity of the model on its input radiobiological parameters. We propose a methodology to derive population-averaged values of TCP based on a computational “clinical trial” with an enrollment of virtual patients orders of magnitude larger than physically-achievable cohort sizes (∼1 million), each with precisely-known radiobiological parameter values. Materials and Methods Each virtual patient was randomly assigned α and α/β values following a randomized distribution based on a previous study by Wang et al, endorsed by AAPM TG137 and TG265: α to a log-normal distribution function with mean (µ) of 0.15 Gy-1 and standard deviation (σ) of 0.04 Gy-1; α/β to a Gaussian function with µ=3.1 Gy and σ= 0.5 Gy; the initial clonogenic population was a fixed value of 1.6 x 106 (low-risk patient cohort). Next, after establishing the cohort, the TCP was calculated for each patient using the linear-quadratic (LQ) model assuming Poisson statistics for a range of doses from 0 to 140 Gy. The fractional TCP value was compared against a random number generator value to ultimately determine the binary patient outcome (i.e. TCP or fail). This process was repeated for each patient in the trial and the final population-based TCP was calculated by the ratio of successes to the number of patients in the trial. A series of new trials was created with one million patients to test α and α/β dependence with intentional variations in α or α/β values for α values from 0.7 to 0.23 Gy-1 and α/β values from 1.5 to 5.0 Gy. Results A series of 11 TCP curves was generated. For each curve, one million patients were created and assigned values of α, α/β. For the reference cohort using both the Gaussian and log-normal functions, the TCP90% and TCP50% were 89.4 and 68.9 Gy. With only a fixed log-normal α function, TCP90% was 70.3, 84.3, 89.4, 93.1, 101 Gy and TCP50% was 56.4, 65.9, 69.6, 71.8, 77.7 Gy for α/β=1.5, 2.6, 3.1, 3.6, 5 Gy, respectively. With only a fixed Gaussian α/β function, TCP90% was 126.1, 92.3, 74.0, 62.3 53.5 and TCP50% was 114.3, 89.8, 67.4, 56.4, 48.3 Gy for α=0.07, 0.11, 0.15, 0.19, 0.23 Gy-1, respectively. As illustrated in the Figure, larger values of α or smaller α/β ratios shift the TCP curve to lower TCP90% and TCP50%. Additionally, choosing a distribution of α values centered on 0.15 Gy-1 rather than a fixed α=0.15 Gy-1 significantly flattens the slope of the TCP curve, while using a distribution of α/β values produced indistinguishable TCP curves. Conclusions By leveraging the Law of Large Numbers and raw computing power, we were able to create multiple heterogeneous cohorts each containing 1 million virtual patients to generate realistic TCP curves based on previously published distributions of plausible α and α/β values, such as those endorsed by AAPM TG137 and TG265. This virtual clinical trial was able to extract a population-averaged fractional TCP. This framework can be used to test the sensitivity of the TCP model by systematically varying the input model parameters. This methodology is especially promising because it can simultaneously handle many more radiobiological parameters so long as the patient cohort size is increased enough to satisfy statistical requirements. In order to develop a robust universal model which can accurately predict tumor control probability (TCP), it is necessary to first explore the sensitivity of the model on its input radiobiological parameters. We propose a methodology to derive population-averaged values of TCP based on a computational “clinical trial” with an enrollment of virtual patients orders of magnitude larger than physically-achievable cohort sizes (∼1 million), each with precisely-known radiobiological parameter values. Each virtual patient was randomly assigned α and α/β values following a randomized distribution based on a previous study by Wang et al, endorsed by AAPM TG137 and TG265: α to a log-normal distribution function with mean (µ) of 0.15 Gy-1 and standard deviation (σ) of 0.04 Gy-1; α/β to a Gaussian function with µ=3.1 Gy and σ= 0.5 Gy; the initial clonogenic population was a fixed value of 1.6 x 106 (low-risk patient cohort). Next, after establishing the cohort, the TCP was calculated for each patient using the linear-quadratic (LQ) model assuming Poisson statistics for a range of doses from 0 to 140 Gy. The fractional TCP value was compared against a random number generator value to ultimately determine the binary patient outcome (i.e. TCP or fail). This process was repeated for each patient in the trial and the final population-based TCP was calculated by the ratio of successes to the number of patients in the trial. A series of new trials was created with one million patients to test α and α/β dependence with intentional variations in α or α/β values for α values from 0.7 to 0.23 Gy-1 and α/β values from 1.5 to 5.0 Gy. A series of 11 TCP curves was generated. For each curve, one million patients were created and assigned values of α, α/β. For the reference cohort using both the Gaussian and log-normal functions, the TCP90% and TCP50% were 89.4 and 68.9 Gy. With only a fixed log-normal α function, TCP90% was 70.3, 84.3, 89.4, 93.1, 101 Gy and TCP50% was 56.4, 65.9, 69.6, 71.8, 77.7 Gy for α/β=1.5, 2.6, 3.1, 3.6, 5 Gy, respectively. With only a fixed Gaussian α/β function, TCP90% was 126.1, 92.3, 74.0, 62.3 53.5 and TCP50% was 114.3, 89.8, 67.4, 56.4, 48.3 Gy for α=0.07, 0.11, 0.15, 0.19, 0.23 Gy-1, respectively. As illustrated in the Figure, larger values of α or smaller α/β ratios shift the TCP curve to lower TCP90% and TCP50%. Additionally, choosing a distribution of α values centered on 0.15 Gy-1 rather than a fixed α=0.15 Gy-1 significantly flattens the slope of the TCP curve, while using a distribution of α/β values produced indistinguishable TCP curves. By leveraging the Law of Large Numbers and raw computing power, we were able to create multiple heterogeneous cohorts each containing 1 million virtual patients to generate realistic TCP curves based on previously published distributions of plausible α and α/β values, such as those endorsed by AAPM TG137 and TG265. This virtual clinical trial was able to extract a population-averaged fractional TCP. This framework can be used to test the sensitivity of the TCP model by systematically varying the input model parameters. This methodology is especially promising because it can simultaneously handle many more radiobiological parameters so long as the patient cohort size is increased enough to satisfy statistical requirements.