Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", CNR, Rome, Italy.
Bull Math Biol. 2010 Jul;72(5):1069-91. doi: 10.1007/s11538-009-9482-y. Epub 2009 Nov 14.
We propose a spatially distributed continuous model for the spheroid response to radiation, in which the oxygen distribution is represented by means of a diffusion-consumption equation and the radiosensitivity parameters depend on the oxygen concentration. The induction of lethally damaged cells by a pulse of radiation, their death, and the degradation of dead cells are included. The compartments of lethally damaged cells and of dead cells are subdivided into different subcompartments to simulate the delays that occur in cell death and cell degradation, with a gain in model flexibility. It is shown that, for a single irradiation and under the hypothesis of a sufficiently small spheroid radius, the model can be reformulated as a linear stationary ordinary differential equation system. For this system, the parameter identifiability has been investigated, showing that the set of unknown parameters can be univocally identified by exploiting the response of the model to at least two different radiation doses. Experimental data from spheroids originated from different cell lines are used to identify the unknown parameters and to test the predictive capability of the model with satisfactory results.
我们提出了一种用于球形物对辐射响应的空间分布连续模型，其中氧分布通过扩散-消耗方程表示，而放射敏感性参数取决于氧浓度。我们还包括了由辐射脉冲诱导的致死性损伤细胞、它们的死亡以及死亡细胞的降解。致死性损伤细胞和死亡细胞的隔室被细分为不同的亚隔室，以模拟细胞死亡和细胞降解过程中的延迟，从而提高模型的灵活性。结果表明，对于单次照射，并且假设球形物半径足够小，该模型可以重新表述为线性定常常微分方程组。对于该系统，我们研究了参数的可识别性，结果表明，可以通过利用模型对至少两种不同辐射剂量的响应来唯一确定未知参数集。来自不同细胞系的球形物的实验数据被用于识别未知参数，并以令人满意的结果测试了模型的预测能力。
