The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting approach is that of obtaining LQ-like behavior from kinetic models, systems of differential equations that model the induction and repair of damage. Development of such kinetic models is particularly interesting for application to continuous dose rate therapies, such as molecular radiotherapy or brachytherapy. In this work, we present a simple kinetic model that describes the kinetics of populations of tumor cells, rather than lethal/sub-lethal lesions, which may be especially useful for application to continuous dose rate therapies, as in molecular radiotherapy. The multi-compartment model consists of a set of three differential equations. The model incorporates in an easy way different cross-interacting compartments of cells forming a tumor, and may be of especial interest for studying dynamics of treated tumors. In the fast dose delivery limit, the model can be analytically solved, obtaining a simple closed-form expression. Fitting of several surviving curves with both this solution and the LQ model shows that they produce similar fits, despite being functionally different. We have also investigated the operation of the model in the continuous dose rate scenario, firstly by fitting pre-clinical data of tumor response to ¹³¹I-CLR1404 therapy, and secondly by showing how damage repair and proliferation rates can cause a treatment to achieve control or not. Kinetic models like the one presented in this work may be of special interest when modeling response to molecular radiotherapy.

描述辐射细胞存活的线性二次方程（LQ）模型可能是放疗中最常用的生物数学模型。关于LQ模型的机械起源一直有激烈的争论。一种有趣的方法是从动力学模型（模型化损伤的诱导和修复的微分方程系统）获得类似LQ的行为。此类动力学模型的开发对于应用于连续剂量率疗法（例如分子放射疗法或近距离疗法）特别感兴趣。在这项工作中，我们提出了一个简单的动力学模型，该模型描述了肿瘤细胞群体的动力学，而不是致死/亚致死性病变，这对于连续剂量率的应用可能特别有用。疗法，如分子放射疗法。多隔室模型由一组三个微分方程组成。该模型以简单的方式并入了形成肿瘤的细胞的不同交叉相互作用的区室，并且对于研究所治疗​​的肿瘤的动力学可能特别有意义。在快速给药极限内，可以解析模型，获得简单的闭合形式表达式。使用此解决方案和LQ模型对多条尚存的曲线进行拟合显示，尽管它们在功能上有所不同，但它们仍产生相似的拟合。我们还研究了在连续剂量率情况下该模型的运行情况，首先通过对¹³¹种肿瘤反应的临床前数据进行拟合I-CLR1404治疗，其次通过显示损伤修复和增殖率如何导致治疗获得控制或不控制。在对分子放射治疗的响应建模时，可能需要特别关注本工作中提出的动力学模型。