Improved model prediction of glioma growth utilizing tissue-specific boundary effects

Kinetic parameter estimates for mathematical models of glioblastoma multiforme (GBM), derived from clinical scans, have been used to predict the occurrence of hypoxia, necrosis, response to radiation therapy, and overall survival. Modeling GBM growth in a cerebral model encounters anatomical boundaries that interfere with model calibration from clinical measurements.

METHODS

The effect of boundaries is examined on both spherically symmetric and anatomical models of tumor growth. This effect is incorporated into a method that updates kinetic parameters. The efficacy of this method in reproducing clinical image-derived subject data is evaluated.

RESULTS

Spherically symmetric simulations of tumor growth with simple boundaries behave predictably when in a linear phase of growth. Anatomic simulations of eleven out of twenty subjects demonstrated improved fit to subject data with the new method. When only subjects exhibiting linear growth are considered, eight out of nine subject demonstrate improved fit to the data.

CONCLUSION

Anatomical boundaries to tumor growth measurably deflect progression and affect estimates of kinetic parameters. The presented method reliably updates kinetic parameters to fit anatomic computational models to clinically derived subject data when those data are in a linear regime.

Mathematical model of perineural tumor spread: a pilot study

BACKGROUND

Perineural spread (PNS) of pelvic cancer along the lumbosacral plexus is an emerging explanation for neoplastic lumbosacral plexopathy (nLSP) and an underestimated source of patient morbidity and mortality. Despite the increased incidence of PNS, these patients are often times a clinical conundrum-to diagnose and to treat. Building on previous results in modeling glioblastoma multiforme (GBM), we present a mathematical model for predicting the course and extent of the PNS of recurrent tumors.

METHODS

We created three-dimensional models of perineurally spreading tumor along the lumbosacral plexus from consecutive magnetic resonance imaging scans of two patients (one each with prostate cancer and cervical cancer). We adapted and applied a previously reported mathematical model of GBM to progression of tumor growth along the nerves on an anatomical model obtained from a healthy subject.

RESULTS

We were able to successfully model and visualize perineurally spreading pelvic cancer in two patients; average growth rates were 60.7 mm/year for subject 1 and 129 mm/year for subject 2. The model correlated well with extent of PNS on MRI scans at given time points.

CONCLUSIONS

This is the first attempt to model perineural tumor spread and we believe that it provides a glimpse into the future of disease progression monitoring. Every tumor and every patient are different, and the possibility to report treatment response using a unified scale-as "days gained"-will be a necessity in the era of individualized medicine. We hope our work will serve as a springboard for future connections between mathematics and medicine.

Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric

Accurate clinical assessment of a patient's response to treatment for glioblastoma multiforme (GBM), the most malignant type of primary brain tumor, is undermined by the wide patient-to-patient variability in GBM dynamics and responsiveness to therapy. Using computational models that account for the unique geometry and kinetics of individual patients' tumors, we developed a method for assessing treatment response that discriminates progression-free and overall survival following therapy for GBM. Applying these models as untreated virtual controls, we generate a patient-specific “Days Gained” response metric that estimates the number of days a therapy delayed imageable tumor progression. We assessed treatment response in terms of Days Gained scores for 33 patients at the time of their first MRI scan following first-line radiation therapy. Based on Kaplan-Meier analyses, patients with Days Gained scores of 100 or more had improved progression-free survival, and patients with scores of 117 or more had improved overall survival. Our results demonstrate that the Days Gained response metric calculated at the routinely acquired first post-radiation treatment time point provides prognostic information regarding progression and survival outcomes. Applied prospectively, our model-based approach has the potential to improve GBM treatment by accounting for patient-to-patient heterogeneity in GBM dynamics and responses to therapy.