Computational Models of Vascularization and Therapy in Tumor Growth - Mechanical and Chemical Signaling in Angiogenesis - page 225

Translation of those modeling attempts into clinical oncology have been limited
so far mainly due to the lack of longitudinal data associated with clinical trials of
new drugs in oncology. In particular, it is often not possible, due to ethical reasons,
to find data for untreated patients. Nevertheless, very recently, models have been
proposed to analyze tumor size dynamics in patients.
The analysis of longitudinal tumor size in non-small cell lung cancer (NSCLC)
led to the development of a simple model combining linear growth and expo-
nential decay as a function of drug concentration [ 11 ]. The model was successfully
applied to four randomized clinical trials for NSCLC treatments that were sub-
mitted for registration: bevacizumab, docetaxel, elotinib and pemetrexed. One of
the main results of this study was that the change in tumor size observed 7 weeks
after treatment initiation was a better parameter to predict survival than the
classical RECIST criteria. This study clearly demonstrates the interest of using a
dynamic approach for evaluating the efficacy of anticancer drugs; and the potential
benefit for forthcoming clinical trials is relatively similar to the results obtained
with the model for myelosuppression [ 1 ]. To illustrate however, the issue of data
availability previously mentioned, the analysis in [ 11 ] was carried out on more
than 2,000 patients and still, to model tumor growth, a linear model (one
parameter) was used. Other similar examples have been published. The reader can
refer in particular to [ 12 ] and [ 13 ]. The last reference deals with tumor dynamic
analysis in colorectal cancer patients.
Finally, it is worthwhile to mention a similar work where the objective was to
analyze tumor growth kinetics in patients with metastatic renal cancer (mRCC)
and gastrointestinal stromal tumors (GIST) treated by the anti-angiogenic com-
pound Sunitinib [ 14 ].
So far, we have discussed models based on ordinary differential equations
where the only considered variable of the system is time. It is worthwhile to
mention here that several models have been proposed to integrate time together
with space in the description of brain tumor growth and treatment. The proposed
models describe the spatio-temporal evolution of tumor cells in the brain as
''traveling waves'' driven by two processes: uncontrolled proliferation and tissue
invasion [ 15 ]. This proliferation-invasion description led to the suggestion that
tumor diameter grows linearly over time with a velocity given by a combination of
the two model parameters [ 16 ]. Swanson and colleagues showed the relevance of
such a model for prediction of untreated glioma growth kinetics, specifically
estimating net rates of proliferation and invasion for individual patients in vivo
[ 17 , 18 ]. These parameters were shown to be significant prognostic factors of
therapy efficacy [ 19 ] and durations of survival [ 20 , 21 ]. Mandonnet and colleagues
studied the reliability of this model in determining low-grade gliomas dynamics
[ 22 - 25 ] and showed it to be in agreement with the linear evolution of the mean
tumor diameter observed in these tumors before transformation towards a higher
grade of malignancy. The same model has been recently extended to integrate the
process of angiogenesis for high grade gliomas [ 26 ].
In the following years, more and more models will continue to be developed
addressing different cancer indications and different treatments such as targeted