Eikenberry S E, Sankar T, Preul M C, Kostelich E J, Thalhauser C J, Kuang Y
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA.
Cell Prolif. 2009 Aug;42(4):511-28. doi: 10.1111/j.1365-2184.2009.00613.x. Epub 2009 May 29.
Glioblastomas are aggressive primary brain cancers that are characterized by extensive infiltration into the brain and are highly resistant to treatment. Through mathematical modelling, we model the process of invasion and predict the relative importance of mechanisms contributing to malignant invasion. Clinically, we predict patterns of tumour recurrence following various modes of therapeutic intervention.
Our mathematical model uses a realistic three-dimensional brain geometry and considers migrating and proliferating cells as separate classes. Several mechanisms for infiltrative migration are considered. Methods are developed for simulating surgical resection, radiotherapy and chemotherapy.
The model provides clinically realistic predictions of tumour growth and recurrence following therapeutic intervention. Specific results include (i) invasiveness is governed largely by the ability of glioblastoma cells to degrade and migrate through the extracellular matrix and the ability of single migrating cells to form colonies; (ii) tumours originating deeper in the brain generally grow more quickly than those of superficial origin; (iii) upon surgery, the margins and geometry of resection significantly determine the extent and pattern of postoperative recurrence; (iv) radiotherapy works synergistically with greater resection margins to reduce recurrence; (v) simulations in both two- and three-dimensional geometries give qualitatively similar results; and (vi) in an actual clinical case comprising several surgical interventions, the model provides good qualitative agreement between the simulated and observed course of the disease.
The model provides a useful initial framework by which biological mechanisms of invasion and efficacy of potential treatment regimens may be assessed.
胶质母细胞瘤是侵袭性原发性脑癌，其特征是广泛浸润大脑且对治疗具有高度抗性。通过数学建模，我们对侵袭过程进行建模，并预测促成恶性侵袭的各种机制的相对重要性。在临床上，我们预测各种治疗干预模式后的肿瘤复发模式。
我们的数学模型采用逼真的三维脑几何结构，并将迁移和增殖细胞视为不同类别。考虑了几种浸润性迁移机制。开发了用于模拟手术切除、放疗和化疗的方法。
该模型为治疗干预后的肿瘤生长和复发提供了符合临床实际的预测。具体结果包括：（i）侵袭性主要由胶质母细胞瘤细胞降解并穿过细胞外基质的能力以及单个迁移细胞形成集落的能力决定；（ii）起源于脑深部的肿瘤通常比起源于浅表的肿瘤生长更快；（iii）手术时，切除边缘和几何形状显著决定术后复发的范围和模式；（iv）放疗与更大的切除边缘协同作用以减少复发；（v）二维和三维几何结构中的模拟给出定性相似的结果；（vi）在一个包含多次手术干预的实际临床病例中，该模型在模拟和观察到的疾病病程之间提供了良好的定性一致性。
该模型提供了一个有用的初始框架，通过它可以评估侵袭的生物学机制和潜在治疗方案的疗效。
