Woodward D E, Cook J, Tracqui P, Cruywagen G C, Murray J D, Alvord E C
Department of Mathematics, Southern Methodist University, Dallas, TX, 75275, USA.
Cell Prolif. 1996 Jun;29(6):269-88. doi: 10.1111/j.1365-2184.1996.tb01580.x.
We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.
我们基于肿瘤细胞的增殖和浸润建立了一个数学模型，该模型能够对各级恶性胶质瘤在不同程度手术切除后的预期寿命进行预测。关键的模型参数是生长速率和扩散速率。这些速率最初源自对一例接受化疗的复发性间变性星形细胞瘤病例的分析。数值模拟使我们能够估计，如果采用不同程度的手术切除而非化疗，该患者会发生什么情况。在每种情况下，“全切”甚至最大程度切除后残留的浸润性肿瘤外壳会继续生长，并能非常迅速地再生肿瘤块。通过建立一个模型，该模型能依据生长和扩散速率确定诊断时细胞的分布，然后将这些速率改变约50%，我们创建了一个假设的肿瘤患者群体，其生存时间与克雷思最近报道的胶质母细胞瘤治疗结果吻合良好。生长速率和扩散速率降低十倍则模拟了许多其他研究者报道的生长较慢的胶质瘤的结果。因此，该模型从数量上支持了以下观点：（i）胶质瘤浸润非常广泛，无论手术或放射切除范围多大，仅靠切除都无法治愈；（ii）切除范围越广，无论胶质瘤的恶性程度如何，预期寿命就越长；（iii）生长速率和扩散速率的测量可能比目前对胶质瘤类型和级别的组织学估计更能预测生存率。
