Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line–specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making.Publisher PDFPeer reviewe

Neural parameters estimation for brain tumor growth modeling

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personalize the model, i.e. find a relevant set of parameters, with respect to the tumor dynamics of a particular patient, the model is informed from empirical data, e.g., medical images obtained from diagnostic modalities, such as magnetic-resonance imaging. Existing model-observation coupling schemes require a large number of forward integrations of the biophysical model and rely on simplifying assumption on the functional form, linking the output of the model with the image information. In this work, we propose a learning-based technique for the estimation of tumor growth model parameters from medical scans. The technique allows for explicit evaluation of the posterior distribution of the parameters by sequentially training a mixture-density network, relaxing the constraint on the functional form and reducing the number of samples necessary to propagate through the forward model for the estimation. We test the method on synthetic and real scans of rats injected with brain tumors to calibrate the model and to predict tumor progression

Proteomics and mathematical modeling of longitudinal CSF differentiates fast versus slow ALS progression

Objective: Amyotrophic lateral sclerosis (ALS) is a heterogeneous disease with a complex etiology that lacks biomarkers predicting disease progression. The objective of this study was to use longitudinal cerebrospinal fluid (CSF) samples to identify biomarkers that distinguish fast progression (FP) from slow progression (SP) and assess their temporal response.Methods: We utilized mass spectrometry (MS)-based proteomics to identify candidate biomarkers using longitudinal CSF from a discovery cohort of SP and FP ALS patients. Immunoassays were used to quantify and validate levels of the top biomarkers. A state-transition mathematical model was created using the longitudinal MS data that also predicted FP versus SP.Results: We identified a total of 1148 proteins in the CSF of all ALS patients. Pathway analysis determined enrichment of pathways related to complement and coagulation cascades in FPs and synaptogenesis and glucose metabolism in SPs. Longitudinal analysis revealed a panel of 59 candidate markers that could segregate FP and SP ALS. Based on multivariate analysis, we identified three biomarkers (F12, RBP4, and SERPINA4) as top candidates that segregate ALS based on rate of disease progression. These proteins were validated in the discovery and a separate validation cohort. Our state-transition model determined that the overall variance of the proteome over time was predictive of the disease progression rate.Interpretation: We identified pathways and protein biomarkers that distinguish rate of ALS disease progression. A mathematical model of the CSF proteome determined that the change in entropy of the proteome over time was predictive of FP versus SP

Differentiating Peripherally-Located Small Cell Lung Cancer From Non-small Cell Lung Cancer Using a CT Radiomic Approach

Lung cancer can be classified into two main categories: small cell lung cancer (SCLC) and non-small cell lung cancer (NSCLC), which are different in treatment strategy and survival probability. The lung CT images of SCLC and NSCLC are similar such that their subtle differences are hardly visually discernible by the human eye through conventional imaging evaluation. We hypothesize that SCLC/NSCLC differentiation could be achieved via computerized image feature analysis and classification in feature space, as termed a radiomic model. The purpose of this study was to use CT radiomics to differentiate SCLC from NSCLC adenocarcinoma. Patients with primary lung cancer, either SCLC or NSCLC adenocarcinoma, were retrospectively identified. The post-diagnosis pre-treatment lung CT images were used to segment the lung cancers. Radiomic features were extracted from histogram-based statistics, textural analysis of tumor images and their wavelet transforms. A minimal-redundancy-maximal-relevance method was used for feature selection. The predictive model was constructed with a multilayer artificial neural network. The performance of the SCLC/NSCLC adenocarcinoma classifier was evaluated by the area under the receiver operating characteristic curve (AUC). Our study cohort consisted of 69 primary lung cancer patients with SCLC (n = 35; age mean ± SD = 66.91± 9.75 years), and NSCLC adenocarcinoma (n = 34; age mean ± SD = 58.55 ± 11.94 years). The SCLC group had more male patients and smokers than the NSCLC group (P \u3c 0.05). Our SCLC/NSCLC classifier achieved an overall performance of AUC of 0.93 (95% confidence interval = [0.85, 0.97]), sensitivity = 0.85, and specificity = 0.85). Adding clinical data such as smoking history could improve the performance slightly. The top ranking radiomic features were mostly textural features. Our results showed that CT radiomics could quantitatively represent tumor heterogeneity and therefore could be used to differentiate primary lung cancer subtypes with satisfying results. CT image processing with the wavelet transformation technique enhanced the radiomic features for SCLC/NSCLC classification. Our pilot study should motivate further investigation of radiomics as a non-invasive approach for early diagnosis and treatment of lung cancer

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

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

MultiCellDS : a community-developed standard for curating microenvironment-dependent multicellular data

Exchanging and understanding scientific data and their context represents a significant barrier to advancing research, especially with respect to information siloing. Maintaining information provenance and providing data curation and quality control help overcome common concerns and barriers to the effective sharing of scientific data. To address these problems in and the unique challenges of multicellular systems, we assembled a panel composed of investigators from several disciplines to create the MultiCellular Data Standard (MultiCellDS) with a use-case driven development process. The standard includes (1) digital cell lines, which are analogous to traditional biological cell lines, to record metadata, cellular microenvironment, and cellular phenotype variables of a biological cell line, (2) digital snapshots to consistently record simulation, experimental, and clinical data for multicellular systems, and (3) collections that can logically group digital cell lines and snapshots. We have created a MultiCellular DataBase (MultiCellDB) to store digital snapshots and the 200+ digital cell lines we have generated. MultiCellDS, by having a fixed standard, enables discoverability, extensibility, maintainability, searchability, and sustainability of data, creating biological applicability and clinical utility that permits us to identify upcoming challenges to uplift biology and strategies and therapies for improving human health

Patient-Specific Metrics of Invasiveness Reveal Significant Prognostic Benefit of Resection in a Predictable Subset of Gliomas

Object Malignant gliomas are incurable, primary brain neoplasms noted for their potential to extensively invade brain parenchyma. Current methods of clinical imaging do not elucidate the full extent of brain invasion, making it difficult to predict which, if any, patients are likely to benefit from gross total resection. Our goal was to apply a mathematical modeling approach to estimate the overall tumor invasiveness on a patient-by-patient basis and determine whether gross total resection would improve survival in patients with relatively less invasive gliomas. Methods In 243 patients presenting with contrast-enhancing gliomas, estimates of the relative invasiveness of each patient's tumor, in terms of the ratio of net proliferation rate of the glioma cells to their net dispersal rate, were derived by applying a patient-specific mathematical model to routine pretreatment MR imaging. The effect of varying degrees of extent of resection on overall survival was assessed for cohorts of patients grouped by tumor invasiveness. Results We demonstrate that patients with more diffuse tumors showed no survival benefit (P = 0.532) from gross total resection over subtotal/biopsy, while those with nodular (less diffuse) tumors showed a significant benefit (P = 0.00142) with a striking median survival benefit of over eight months compared to sub-totally resected tumors in the same cohort (an 80% improvement in survival time for GTR only seen for nodular tumors). Conclusions These results suggest that our patient-specific, model-based estimates of tumor invasiveness have clinical utility in surgical decision making. Quantification of relative invasiveness assessed from routinely obtained pre-operative imaging provides a practical predictor of the benefit of gross total resection

Mathematical Modeling of Human Glioma Growth Based on Brain Topological Structures: Study of Two Clinical Cases

Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor), and an advanced state when infiltration starts (malign tumor). Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality