Dynamics of glioma growth and invasionGliomas are brain tumors that differ from most other tumors by their aggressive diffuse invasion of the surrounding normal tissue. This invasive nature contributes to the dismal 6 to 12 months prognosis for the highest grade glioma known as glioblastoma. The remarkable continuing development of medical imaging has increased the ability to detect gliomas, but has not been able to sufficiently define the extent of invasion of the tumor cells peripheral to the bulk tumor mass. For this reason, only the "tip of the iceberg" of the full lesion is visible by standard imaging tools (MRI, CT, PET). Thus, it is not surprising that even extensive surgical resection or local irradiation of the portion of the lesion detectable on imaging is followed by tumorous recurrence at or near the edge of the treatment region. Our goal is to use mathematical modeling to predict the true extent of the tumor given the limited information provided by standard clinical imaging.
The following 3 scenarios illustrate the kind of questions that our model can help answer.
1) Imagine that you are patient with a low-grade glioma. Would you want to know how long you will live without treatment, following surgery, following x-irradiation, following chemo-therapy? When will the tumor "progress" to a higher grade? We have a definitive answer to the first question but only preliminary data and partial answers to the other two.
2) Imagine that you have just invented a new drug designed to bypass the normal blood-brain barrier and kill glioma cells. You personally, not "the company", will pay all expenses involved in testing the drug in humans. You receive a sequence of MR images showing the progression of the tumor during and after treatment. Can you interpret the treatment effect? Without our model you probably cannot.
3) Imagine that you are directing a study in humans comparing two treatments of glioblastoma. How will you distinguish the non-responders from those "naturally" growing faster, the responders from those "naturally" growing slower? Would you like to compare each patient with his/her "virtual control" matched for rates of proliferation and migration and size of tumor?
Our model provides for this scenario and has already demonstrated the significance of size.
Answering the questions implied by these scenarios form the basis of this research proposal.
Our mathematical model of gliomas has reached what we believe to be "proof of principle" in that all of the patients that we have analyzed so far fit the prediction, quantifying the spatio-temporal proliferation and invasion dynamics of gliomas within anatomically accurate heterogeneous brain tissue in three spatial dimensions. The implications of this type of modeling would be of considerable interest to neurooncologists attempting to improve the treatment of gliomas by designing drugs specifically to bypass the normal blood brain barrier in order to kill the glioma cells invading the normal-appearing tissue.
It is clear to us that truly revolutionary research to improve the humbling prognosis of gliomas cannot proceed without knowledge of the interactions of the two most salient features of their progression - migration and net proliferation! This can be most efficiently done by mathematical modeling that allows for iterative comparisons between virtual and real situations providing direction for experimental designs in testing new hypotheses. We propose validating and extending our relatively simple mathematical model to define these two most basic characteristics, net proliferation and dispersal, in each patient. We have already successfully predicted the behavior of groups of patients, both low-grade and high-grade, and believe that the extension to individual patients would permit much more rapid identification of successful new therapies, conceivably also correlated with molecular analyses (genetic or proteomic) that can be expected to be practically unique for each patient.
Our model can be applied to an individual patient to calculate the two factors (proliferation and infiltrative potential) precisely enough to display the past, present and future distributions of tumor cell concentrations down to the individual cell, well beyond the "edge "of the tumor defined by current imaging. From the steepness of the gradient of glioma cells beyond the detectable tumor margin, the model provides information regarding the expected locations of potential recurrence, as well as the time scale on which we expect that regrowth to happen. These displays should provide guidance to surgeons, radiotherapists and neuro-oncologists as to where and when to expect recurrences. Not only should these predictions help them to define where to concentrate their respective treatments, but also comparison of the actual and predicted times to recurrence should also help to ascertain the effectiveness of treatments in individual patients, thereby, avoiding the necessity to use large groups of patients and averages as would be typical in most clinical trials.
Our modeling approach establishes a new way of thinking about gliomas and has many applications, in the clinic as well as in the laboratory. Clearly, it is necessary to develop better treatment protocols that more directly address the diffuse nature of gliomas. However, since standard imaging technologies cannot define the diffusiveness of gliomas, there is essentially no means of assessing the efficacy of such a diffuse treatment regime without a quantitative (complex systems) model to interpret the available patient data. With our model for the basic biological mechanisms involved in brain tumor progression, limited patient data can be combined to develop a more thorough picture of the tumor's past history and future behavior. Although this tool has eventual implications for clinical care, we see this as a necessary step to remedy the present bottleneck in the development of novel and effective treatments for gliomas.
With an easy-to-use computational interface, new strategies can be tested virtually (i.e. in the model) to assess their potential impact and either pursued more carefully or rejected. Eventually we hope that the modeling framework will be seen as so successful as to be used to test new treatment strategies in vivo, with fewer real test patients and on a shortened time scale than a standard clinical trial since each patient can serve as his/her own control.
We believe that this model will considerably improve the management of individual patients. Clinicians routinely question the efficacy of a given treatment at any given treatment and, to date, have very few tools for assessing treatment response in real time. Under the current treatment paradigm, glioma patients are considered to have failed a new treatment protocol if their imaging abnormality (T1gad for enhancing gliomas) has increased by at least 25%. In many GBM patients, this could translate to 3 months of practically untreated growth when an ineffective therapy is being administered. As new experimental therapies (radio and chemo) are introduced, an early and robust measure of effect is necessary in individual patients. These problems are compounded for those therapies that target molecular changes that only a subset of tumors will have and others not have, since tissue sampling may not be available in all.
Our mathematical model provides a means to enhance the interpretation of current imaging techniques using existing standard sequences (T1Gd and T2) without the necessity of developing new acquisition sequences. Although new imaging techniques are being developed continuously and can be incorporated into our model, it seems highly unlikely that any technique will reach to the level of the single invading cell in practice. It is for this reason that we feel mathematical modeling has a significant place in the analysis of present and future imaging techniques.
