Camacho Ariel, Jerez Silvia
CIMAT, 36000, Guanajuato, Gto., Mexico.
J Math Biol. 2019 Jan;78(1-2):497-526. doi: 10.1007/s00285-018-1281-3. Epub 2018 Aug 21.
Metastatic disease is a lethal stage of cancer progression. It is characterized by the spread of aberrant cells from a primary tumor to distant tissues like the bone. Several treatments are used to deal with bone metastases formation, but they are palliative since the disease is considered incurable. Computational and mathematical models are used to understand the underlying mechanisms of how bone metastasis evolves. In this way, new therapies aiming to reduce or eliminate the metastatic burden in the bone tissue may be proposed. We present an optimal control approach to analyze some common treatments for bone metastasis. In particular, we focus on denosumab treatment, an anti-resorptive therapy, and radiotherapy treatment which has a cell killing action. We base our work in a variant of an existing model introduced by Komarova. The new model incorporates a logistic equation in order to describe the bone metastasis evolution. We provide proofs of existence and uniqueness of solutions to the corresponding optimal control problems for each treatment. Moreover, we present some numerical simulations to analyze the effectiveness of both treatments when different interactions between cancer and bone cells occur. A discussion of the obtained results is provided.
转移性疾病是癌症进展的致命阶段。其特征是异常细胞从原发性肿瘤扩散到远处组织，如骨骼。有几种治疗方法用于应对骨转移的形成，但由于该疾病被认为无法治愈，这些治疗都是姑息性的。计算和数学模型被用于理解骨转移如何演变的潜在机制。通过这种方式，可能会提出旨在减轻或消除骨组织中转移负担的新疗法。我们提出一种最优控制方法来分析一些常见的骨转移治疗方法。特别地，我们关注地诺单抗治疗（一种抗吸收疗法）和具有细胞杀伤作用的放射治疗。我们的工作基于Komarova引入的一个现有模型的变体。新模型纳入了一个逻辑方程以描述骨转移的演变。我们为每种治疗的相应最优控制问题提供了解的存在性和唯一性证明。此外，我们进行了一些数值模拟，以分析当癌细胞与骨细胞之间发生不同相互作用时两种治疗方法的有效性。并对所得结果进行了讨论。
