A TCP model incorporating setup uncertainty and tumor cell density variation in microscopic extension to guide treatment planning

Purpose: Tumor control probability (TCP) models have been proposed to evaluate and guide treatment planning. However, they are usually based on the dose volume histograms (DVHs) of the planning target volume (PTV) and may not properly reflect the substantial variation in tumor burden from the gross tumor volume (GTV) to the microscopic extension (ME) and to the margin of PTV. In this study, the authors propose a TCP model that can account for the effects of setup uncertainties and tumor cell density decay in the ME region. Methods: The proposed TCP model is based on the total surviving clonogenic tumor cells (CTCs) after irradiation of a known dose distribution to a region with a CTC distribution. The CTC density was considered to be homogeneous within the GTV, while decreasing exponentially in the ME region. The effect of random setup uncertainty was modeled by convolving the dose distribution with a Gaussian probability density function, represented by a standard deviation, σ. The effect of systematic setup uncertainty was modeled by summing each calculated TCP for all potential offsets in a Gaussian probability, represented by ∑. The model was then applied to simplified cases to demonstrate the concept. TCP dose responses were calculated for various GTV volumes, DVH shapes, CTC density decay coefficients, probabilities of lymph node metastasis, and random and systematic errors. The slopes of the dose falloff to cover the CTC density decay in the ME region and the margins to compensate setup errors were also analyzed in generalized cases. Results: The sigmoid TCP dose response curve shifted to the right substantially for a larger GTV, while modestly for cold spots in DVH. A dose distribution with a uniform dose within the GTV, and a linear dose falloff in the ME region, tended to cause a minimal TCP deterioration if a proper dose falloff slope was used. When the dose falloff slope was less steep than a critical slope represented by k_T, the D50, which is the prescription dose at TCP=50%, and 50, which is the TCP slope at TCP=50%, varied little with different dose falloff slopes. However, both D50 and 50 deteriorated fast when the slopes were steeper than k_T. The random setup error tended to shift the TCP curve to the right, while the systematic error tended to compress the curve downward. For combined random and systematic errors, we demonstrated that based on the model, a margin of √(0.75σ) ² + (1.15∑)² added to the GTV was found to cause a TCP change corresponding to 2% drop at TCP=90%, or 0.5 Gy shift in D50. Conclusions: This study conceptually demonstrated that a TCP model incorporating the effects of tumor cell density variation and setup uncertainty may be used to guide radiation treatment planning.