Biophysical model-based parameters to classify tumor recurrence from radiation-induced necrosis for brain metastases

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach

Metastasis is the process through which cancer cells break away from a primary tumor, travel through the blood or lymph system, and form new tumors in distant tissues. One of the preferred sites for metastatic dissemination is the brain, affecting more than 20% of all cancer patients. This figure is increasing steadily due to improvements in treatments of primary tumors. Stereotactic radiosurgery (SRS) is one of the main treatment options for patients with a small or moderate number of brain metastases (BMs). A frequent adverse event of SRS is radiation necrosis (RN), an inflammatory condition caused by late normal tissue cell death. A major diagnostic problem is that RNs are difficult to distinguish from BM recurrences, due to their similarities on standard magnetic resonance images (MRIs). However, this distinction is key to choosing the best therapeutic approach since RNs resolve often without further interventions, while relapsing BMs may require open brain surgery. Recent research has shown that RNs have a faster growth dynamics than recurrent BMs, providing a way to differentiate the two entities, but no mechanistic explanation has been provided for those observations. In this study, computational frameworks were developed based on mathematical models of increasing complexity, providing mechanistic explanations for the differential growth dynamics of BMs relapse versus RN events and explaining the observed clinical phenomenology. Simulated tumor relapses were found to have growth exponents substantially smaller than the group in which there was inflammation due to damage induced by SRS to normal brain tissue adjacent to the BMs, thus leading to RN. ROC curves with the synthetic data had an optimal threshold that maximized the sensitivity and specificity values for a growth exponent β* = 1.05, very close to that observed in patient datasets.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Clinical assessment of a biophysical model for distinguishing tumor progression from radiation necrosis

PURPOSE

The efficacy of an imaging-driven mechanistic biophysical model of tumor growth for distinguishing radiation necrosis from tumor progression in patients with enhancing lesions following stereotactic radiosurgery (SRS) for brain metastasis is validated.

METHODS

We retrospectively assessed the model using 73 patients with 78 lesions and histologically confirmed radiation necrosis or tumor progression. Postcontrast T1-weighted MRI images were used to extract parameters for a mechanistic reaction-diffusion logistic growth model mechanically coupled to the surrounding tissue. The resulting model was then used to estimate mechanical stress fields, which were then compared with edema visualized on FLAIR imaging using DICE similarity coefficients. DICE, model, and standard radiographic morphometric analysis parameters were evaluated using a receiver operating characteristic (ROC) curve for prediction of radiation necrosis or tumor progression. Multivariate logistic regression models were then constructed using mechanistic model parameters or advanced radiomic features. An independent validation was performed to evaluate predictive performance.

RESULTS

Tumor cell proliferation rate resulted in ROC AUC = 0.86, 95% CI: 0.76-0.95, P < 0.0001, 74% sensitivity and 95% specificity) and DICE similarity coefficient associated with high stresses demonstrated an ROC AUC = 0.93, 95% CI: 0.86-0.99, P < 0.0001, 81% sensitivity and 95% specificity. In a multivariate logistic regression model using an independent validation dataset, mechanistic modeling parameters had an ROC AUC of 0.95, with 94% sensitivity and 96% specificity.

CONCLUSIONS

Imaging-driven biophysical modeling of tumor growth represents a novel method for accurately predicting clinically significant tumor behavior.

Characterization of multicellular breast tumor spheroids using image data-driven biophysical mathematical modeling

Multicellular tumor spheroid (MCTS) systems provide an in vitro cell culture model system which mimics many of the complexities of an in vivo solid tumor and tumor microenvironment, and are often used to study cancer cell growth and drug efficacy. Here, we present a coupled experimental-computational framework to estimate phenotypic growth and biophysical tumor microenvironment properties. This novel framework utilizes standard microscopy imaging of MCTS systems to drive a biophysical mathematical model of MCTS growth and mechanical interactions. By extending our previous in vivo mechanically-coupled reaction–diffusion modeling framework we developed a microscopy image processing framework capable of mechanistic characterization of MCTS systems. Using MDA-MB-231 breast cancer MCTS, we estimated biophysical parameters of cellular diffusion, rate of cellular proliferation, and cellular tractions forces. We found significant differences in these model-based biophysical parameters throughout the treatment time course between untreated and treated MCTS systems, whereas traditional size-based morphometric parameters were inconclusive. The proposed experimental-computational framework estimates mechanistic MCTS growth and invasion parameters with significant potential to assist in better and more precise assessment of in vitro drug efficacy through the development of computational analysis methodologies for three-dimensional cell culture systems to improve the development and evaluation of antineoplastic drugs.

Accounting for intraoperative brain shift ascribable to cavity collapse during intracranial tumor resection

Purpose: For many patients with intracranial tumors, accurate surgical resection is a mainstay of their treatment paradigm. During surgical resection, image guidance is used to aid in localization and resection. Intraoperative brain shift can invalidate these guidance systems. One cause of intraoperative brain shift is cavity collapse due to tumor resection, which will be referred to as "debulking." We developed an imaging-driven finite element model of debulking to create a comprehensive simulation data set to reflect possible intraoperative changes. The objective was to create a method to account for brain shift due to debulking for applications in image-guided neurosurgery. We hypothesized that accounting for tumor debulking in a deformation atlas data framework would improve brain shift predictions, which would enhance image-based surgical guidance. Approach: This was evaluated in a six-patient intracranial tumor resection intraoperative data set. The brain shift deformation atlas data framework consisted of n = 756 simulated deformations to account for effects due to gravity-induced and hyperosmotic drug-induced brain shift, which reflects previous developments. An additional complement of n = 84 deformations involving simulated tumor growth followed by debulking was created to capture observed intraoperative effects not previously included. Results: In five of six patient cases evaluated, inclusion of debulking mechanics improved brain shift correction by capturing global mass effects resulting from the resected tumor. Conclusions: These findings suggest imaging-driven brain shift models used to create a deformation simulation data framework of observed intraoperative events can be used to assist in more accurate image-guided surgical navigation in the brain.