Prognostic Significance of Growth Kinetics in Newly Diagnosed Glioblastomas Revealed by Combining Serial Imaging with a Novel Biomathematical Model

Abstract

Glioblastomas (GBMs) are the most aggressive primary brain tumors characterized by their rapid proliferation and diffuse infiltration of the brain tissue. Survival patterns in patients with GBM have been associated with a number of clinico-pathologic factors, including age and neurological status, yet a significant quantitative link to in vivo growth kinetics of each glioma has remained elusive. Exploiting a recently developed tool for quantifying glioma net proliferation and invasion rates in individual patients using routinely available magnetic resonance images (MRIs), we propose to link these patient-specific kinetic rates of biological aggressiveness to prognostic significance. Using our biologically-based mathematical model for glioma growth and invasion, examination of serial pre-treatment MRIs of 32 GBM patients allowed quantification of these rates for each patient’s tumor. Survival analyses revealed that even when controlling for standard clinical parameters (e.g., age, KPS) these model-defined parameters quantifying biologically aggressiveness (net proliferation and invasion rates) were significantly associated with prognosis. One hypothesis generated was that the ratio of the actual survival time after whatever therapies were employed to the duration of survival predicted (by the model) without any therapy would provide a “Therapeutic Response Index” (TRI) of the overall effectiveness of the therapies. The TRI may provided important information, not otherwise available, as to the effectiveness of the treatments in individual patients. To our knowledge, this is the first report indicating that dynamic insight from routinely obtained pre-treatment imaging may be quantitatively useful in characterizing survival of individual patients with GBM. Such a hybrid tool bridging mathematical modeling and clinical imaging may allow for statifying patients for clinical studies relative to their pretreatment biological aggressiveness.

A Novel, Patient-Specific Mathematical Pathology Approach for Assessment of Surgical Volume: Application to Ductal Carcinomain situof The Breast

“…Thus, for high grade tumors diagnosed on core biopsy, measurements of A and L could not only be feasible, but they might be used to predict tumor volume with better accuracy than current methods. 4 We can interpret these results as a biophysical explanation of how diffusion processes within the tumor tissue limit the maximum size that the tumor could achieve in an otherwise ideal environment with excess nutrients. Highly proliferative tumors with low apoptotic rates and with good penetration of nutrients will be larger; however, as the diffusion penetration length gets smaller then access to nutrients to support growth is negatively impacted and the expected tumor size decreases.…”

“…One aspect of surgical planning that has not been addressed here is how shape impacts the individ- 4 High grade when combined with presence of necrosis has been associated with an increased risk of invasion [57]. We note that the measured value for L tends to cluster at a range of lower values for the high-grade tumors (see Fig.…”

“…Furthermore, imaging data and mathematical models were used to predict glioma patient survival time and inform decisions on drug administration [3,4]. Using mathematical models, it was also demonstrated that the growth of U87 glioblastoma converges to a constant rate, which can be directly linked to tumor proliferation, apoptosis, and vascularization [5].…”

Modelling biological invasions: Individual to population scales at interfaces

“…In the patient data samples considered by Ellingson et al (2011), one has L D 4 1 mm, with substantially higher values for high grade gliomas. In the sample of 32 patients considered by Wang et al (2009), the average value of L D was 1.1 mm, though D dim ranged over three orders of magnitude in the estimates and ρ dim varied by two orders of magnitude. Nonetheless, for 28 out of the 32 patients, the imaging based estimates give L D 4 0:55 mm, corresponding to ϵ 2 ¼ 0:3.…”

A 3-dimensional DTI MRI-based model of GBM growth and response to radiation therapy

“…The trace of the diffusion tensor is scaled to a global D value which is similar to the one-dimensional model. For the current model, various values of D and ρ are used for simulations, drawn from the range of published values for GBM (16,20).…”