Mathematical modeling identifies optimum lapatinib dosing schedules for the treatment of glioblastoma patients

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.

Dissecting sources of variability in patient response to targeted therapy: anti-HER2 therapies as a case study

BACKGROUND AND PURPOSE

Despite their use to treat cancers with specific genetic aberrations, targeted therapies elicit heterogeneous responses. Sources of variability are critical to targeted therapy drug development, yet there exists no method to discern their relative contribution to response heterogeneity.

EXPERIMENTAL APPROACH

We use HER2-amplified breast cancer and two agents, neratinib and lapatinib, to develop a platform for dissecting sources of variability in patient response. The platform comprises four components: pharmacokinetics, tumor burden and growth kinetics, clonal composition, and sensitivity to treatment. Pharmacokinetics are simulated using population models to capture variable systemic exposure. Tumor burden and growth kinetics are derived from clinical data comprising over 800,000 women. The fraction of sensitive and resistant tumor cells is informed by HER2 immunohistochemistry. Growth rate-corrected drug potency is used to predict response. We integrate these factors and simulate clinical outcomes for virtual patients. The relative contribution of these factors to response heterogeneity are compared.

KEY RESULTS

The platform was verified with clinical data, including response rate and progression-free survival (PFS). For both neratinib and lapatinib, the growth rate of resistant clones influenced PFS to a higher degree than systemic drug exposure. Variability in exposure at labeled doses did not significantly influence response. Sensitivity to drug strongly influenced responses to neratinib. Variability in patient HER2 immunohistochemistry scores influenced responses to lapatinib. Exploratory twice daily dosing improved PFS for neratinib but not lapatinib.

CONCLUSION AND IMPLICATIONS

The platform can dissect sources of variability in response to target therapy, which may facilitate decision-making during drug development.

Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology

BACKGROUND

To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data.

METHODS

We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves.

RESULTS

The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication.

CONCLUSIONS

A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Optimized scaling of translational factors in oncology: from xenografts to RECIST

Purpose

Tumor growth inhibition (TGI) models are regularly used to quantify the PK–PD relationship between drug concentration and in vivo efficacy in oncology. These models are typically calibrated with data from xenograft mice and before being used for clinical predictions, translational methods have to be applied. Currently, such methods are commonly based on replacing model components or scaling of model parameters. However, difficulties remain in how to accurately account for inter-species differences. Therefore, more research must be done before xenograft data can fully be utilized to predict clinical response.

Method

To contribute to this research, we have calibrated TGI models to xenograft data for three drug combinations using the nonlinear mixed effects framework. The models were translated by replacing mice exposure with human exposure and used to make predictions of clinical response. Furthermore, in search of a better way of translating these models, we estimated an optimal way of scaling model parameters given the available clinical data.

Results

The predictions were compared with clinical data and we found that clinical efficacy was overestimated. The estimated optimal scaling factors were similar to a standard allometric scaling exponent of − 0.25.

Conclusions

We believe that given more data, our methodology could contribute to increasing the translational capabilities of TGI models. More specifically, an appropriate translational method could be developed for drugs with the same mechanism of action, which would allow for all preclinical data to be leveraged for new drugs of the same class. This would ensure that fewer clinically inefficacious drugs are tested in clinical trials.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00280-022-04458-8.

Radiomic Deformation and Textural Heterogeneity (R-DepTH) Descriptor to Characterize Tumor Field Effect: Application to Survival Prediction in Glioblastoma

The concept of tumor field effect implies that cancer is a systemic disease with its impact way beyond the visible tumor confines. For instance, in Glioblastoma (GBM), an aggressive brain tumor, the increase in intracranial pressure due to tumor burden often leads to brain herniation and poor outcomes. Our work is based on the rationale that highly aggressive tumors tend to grow uncontrollably, leading to pronounced biomechanical tissue deformations in the normal parenchyma, which when combined with local morphological differences in the tumor confines on MRI scans, will comprehensively capture tumor field effect. Specifically, we present an integrated MRI-based descriptor, radiomic-Deformation and Textural Heterogeneity (r-DepTH). This descriptor comprises measurements of the subtle perturbations in tissue deformations throughout the surrounding normal parenchyma due to mass effect. This involves non-rigidly aligning the patients' MRI scans to a healthy atlas via diffeomorphic registration. The resulting inverse mapping is used to obtain the deformation field magnitudes in the normal parenchyma. These measurements are then combined with a 3D texture descriptor, Co-occurrence of Local Anisotropic Gradient Orientations (COLLAGE), which captures the morphological heterogeneity and infiltration within the tumor confines, on MRI scans. In this work, we extensively evaluated r-DepTH for survival risk-stratification on a total of 207 GBM cases from 3 different cohorts (Cohort 1 ( n1 = 53 ), Cohort 2 ( n2 = 75 ), and Cohort 3 ( n3 = 79 )), where each of these three cohorts was used as a training set for our model separately, and the other two cohorts were used for testing, independently, for each training experiment. When employing Cohort 1 for training, r-DepTH yielded Concordance indices (C-indices) of 0.7 and 0.65, hazard ratios (HR) and Confidence Intervals (CI) of 10 (6 - 19) and 5 (3 - 8) on Cohorts 2 and 3, respectively. Similarly, training on Cohort 2 yielded C-indices of 0.6 and 0.7, HR and CI of 1 (0.7 - 2) and 3 (2 - 5) on Cohorts 1 and 3, respectively. Finally, training on Cohort 3 yielded C-indices of 0.75 and 0.63, HR and CI of 24 (10 - 57) and 12 (6 - 21) on Cohorts 1 and 2, respectively. Our results show that r-DepTH descriptor may serve as a comprehensive and a robust MRI-based prognostic marker of disease aggressiveness and survival in solid tumors.

Extended transit compartment model to describe tumor delay using Coxian distribution

The measured response of cell population is often delayed relative to drug injection, and individuals in a population have a specific age distribution. Common approaches for describing the delay are to apply transit compartment models (TCMs). This model reflects that all damaged cells caused by drugs suffer transition processes, resulting in death. In this study, we present an extended TCM using Coxian distribution, one of the phase-type distributions. The cell population attacked by a drug is described via age-structured models. The mortality rate of the damaged cells is expressed by a convolution of drug rate and age density. Then applying to Erlang and Coxian distribution, we derive Erlang TCM, representing the existing model, and Coxian TCMs, reflecting sudden death at all ages. From published data of drug and tumor, delays are compared after parameter estimations in both models. We investigate the dynamical changes according to the number of the compartments. Model robustness and equilibrium analysis are also performed for model validation. Coxian TCM is an extended model considering a realistic case and captures more diverse delays.

Optimal Strategy and Benefit of Pulsed Therapy Depend On Tumor Heterogeneity and Aggressiveness at Time of Treatment Initiation

Therapeutic resistance is a fundamental obstacle in cancer treatment. Tumors that initially respond to treatment may have a preexisting resistant subclone or acquire resistance during treatment, making relapse theoretically inevitable. Here, we investigate treatment strategies that may delay relapse using mathematical modeling. We find that for a single-drug therapy, pulse treatment-short, elevated doses followed by a complete break from treatment-delays relapse compared with continuous treatment with the same total dose over a length of time. For tumors treated with more than one drug, continuous combination treatment is only sometimes better than sequential treatment, while pulsed combination treatment or simply alternating between the two therapies at defined intervals delays relapse the longest. These results are independent of the fitness cost or benefit of resistance, and are robust to noise. Machine-learning analysis of simulations shows that the initial tumor response and heterogeneity at the start of treatment suffice to determine the benefit of pulsed or alternating treatment strategies over continuous treatment. Analysis of eight tumor burden trajectories of breast cancer patients treated at Memorial Sloan Kettering Cancer Center shows the model can predict time to resistance using initial responses to treatment and estimated preexisting resistant populations. The model calculated that pulse treatment would delay relapse in all eight cases. Overall, our results support that pulsed treatments optimized by mathematical models could delay therapeutic resistance.

Optimizing the future: how mathematical models inform treatment schedules for cancer

For decades, mathematical models have influenced how we schedule chemotherapeutics. More recently, mathematical models have leveraged lessons from ecology, evolution, and game theory to advance predictions of optimal treatment schedules, often in a personalized medicine manner. We discuss both established and emerging therapeutic strategies that deviate from canonical standard-of-care regimens, and how mathematical models have contributed to the design of such schedules. We first examine scheduling options for single therapies and review the advantages and disadvantages of various treatment plans. We then consider the challenge of scheduling multiple therapies, and review the mathematical and clinical support for various conflicting treatment schedules. Finally, we propose how a consilience of mathematical and clinical knowledge can best determine the optimal treatment schedules for patients.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

In vitro biomimetic models for glioblastoma-a promising tool for drug response studies

The poor response of glioblastoma to current treatment protocols is a consequence of its intrinsic drug resistance. Resistance to chemotherapy is primarily associated with considerable cellular heterogeneity, and plasticity of glioblastoma cells, alterations in gene expression, presence of specific tumor microenvironment conditions and blood-brain barrier. In an attempt to successfully overcome chemoresistance and better understand the biological behavior of glioblastoma, numerous tri-dimensional (3D) biomimetic models were developed in the past decade. These novel advanced models are able to better recapitulate the spatial organization of glioblastoma in a real time, therefore providing more realistic and reliable evidence to the response of glioblastoma to therapy. Moreover, these models enable the fine-tuning of different tumor microenvironment conditions and facilitate studies on the effects of the tumor microenvironment on glioblastoma chemoresistance. This review outlines current knowledge on the essence of glioblastoma chemoresistance and describes the progress achieved by 3D biomimetic models. Moreover, comprehensive literature assessment regarding the influence of 3D culturing and microenvironment mimicking on glioblastoma gene expression and biological behavior is also provided. The contribution of the blood-brain barrier as well as the blood-tumor barrier to glioblastoma chemoresistance is also reviewed from the perspective of 3D biomimetic models. Finally, the role of mathematical models in predicting 3D glioblastoma behavior and drug response is elaborated. In the future, technological innovations along with mathematical simulations should create reliable 3D biomimetic systems for glioblastoma research that should facilitate the identification and possibly application in preclinical drug testing and precision medicine.

Updated Insights on EGFR Signaling Pathways in Glioma

Nowadays, due to recent advances in molecular biology, the pathogenesis of glioblastoma is better understood. For the newly diagnosed, the current standard of care is represented by resection followed by radiotherapy and temozolomide administration, but because median overall survival remains poor, new diagnosis and treatment strategies are needed. Due to the quick progression, even with aggressive multimodal treatment, glioblastoma remains almost incurable. It is known that epidermal growth factor receptor (EGFR) amplification is a characteristic of the classical subtype of glioma. However, targeted therapies against this type of receptor have not yet shown a clear clinical benefit. Many factors contribute to resistance, such as ineffective blood-brain barrier penetration, heterogeneity, mutations, as well as compensatory signaling pathways. A better understanding of the EGFR signaling network, and its interrelations with other pathways, are essential to clarify the mechanisms of resistance and create better therapeutic agents.

Quantifying Glioblastoma Drug Response Dynamics Incorporating Treatment Sensitivity and Blood Brain Barrier Penetrance From Experimental Data

Many drugs investigated for the treatment of glioblastoma (GBM) have had disappointing clinical trial results. Efficacy of these agents is dependent on adequate delivery to sensitive tumor cell populations, which is limited by the blood-brain barrier (BBB). Additionally, tumor heterogeneity can lead to subpopulations of cells with different sensitivities to anti-cancer drugs, further impacting therapeutic efficacy. Thus, it may be important to evaluate the extent to which BBB limitations and heterogeneous sensitivity each contribute to a drug's failure. To address this challenge, we developed a minimal mathematical model to characterize these elements of overall drug response, informed by time-series bioluminescence imaging data from a treated patient-derived xenograft (PDX) experimental model. By fitting this mathematical model to a preliminary dataset in a series of nonlinear regression steps, we estimated parameter values for individual PDX subjects that correspond to the dynamics seen in experimental data. Using these estimates as a guide for parameter ranges, we ran model simulations and performed a parameter sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients. Results from this analysis combined with simulations suggest that BBB permeability may play a slightly greater role in therapeutic efficacy than relative drug sensitivity. Additionally, we discuss recommendations for future experiments based on insights gained from this model. Further research in this area will be vital for improving the development of effective new therapies for glioblastoma patients.

Model-based optimization of combination protocols for irradiation-insensitive cancers

Alternations in the p53 regulatory network may render cancer cells resistant to the radiation-induced apoptosis. In this theoretical study we search for the best protocols combining targeted therapy with radiation to treat cancers with wild-type p53, but having downregulated expression of PTEN or overexpression of Wip1 resulting in resistance to radiation monotherapy. Instead of using the maximum tolerated dose paradigm, we exploit stochastic computational model of the p53 regulatory network to calculate apoptotic fractions for both normal and cancer cells. We consider combination protocols, with irradiations repeated every 12, 18, 24, or 36 h to find that timing between Mdm2 inhibitor delivery and irradiation significantly influences the apoptotic cell fractions. We assume that uptake of the inhibitor is higher by cancer than by normal cells and that cancer cells receive higher irradiation doses from intersecting beams. These two assumptions were found necessary for the existence of protocols inducing massive apoptosis in cancer cells without killing large fraction of normal cells neighboring tumor. The best found protocols have irradiations repeated every 24 or 36 h with two inhibitor doses per irradiation cycle, and allow to induce apoptosis in more than 95% of cancer cells, killing less than 10% of normal cells.

Towards standardization guidelines for in silico approaches in personalized medicine

Despite the ever-progressing technological advances in producing data in health and clinical research, the generation of new knowledge for medical benefits through advanced analytics still lags behind its full potential. Reasons for this obstacle are the inherent heterogeneity of data sources and the lack of broadly accepted standards. Further hurdles are associated with legal and ethical issues surrounding the use of personal/patient data across disciplines and borders. Consequently, there is a need for broadly applicable standards compliant with legal and ethical regulations that allow interpretation of heterogeneous health data through in silico methodologies to advance personalized medicine. To tackle these standardization challenges, the Horizon2020 Coordinating and Support Action EU-STANDS4PM initiated an EU-wide mapping process to evaluate strategies for data integration and data-driven in silico modelling approaches to develop standards, recommendations and guidelines for personalized medicine. A first step towards this goal is a broad stakeholder consultation process initiated by an EU-STANDS4PM workshop at the annual COMBINE meeting (COMBINE 2019 workshop report in same issue). This forum analysed the status quo of data and model standards and reflected on possibilities as well as challenges for cross-domain data integration to facilitate in silico modelling approaches for personalized medicine.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.

From cells to tissue: How cell scale heterogeneity impacts glioblastoma growth and treatment response

Glioblastomas are aggressive primary brain tumors known for their inter- and intratumor heterogeneity. This disease is uniformly fatal, with intratumor heterogeneity the major reason for treatment failure and recurrence. Just like the nature vs nurture debate, heterogeneity can arise from intrinsic or environmental influences. Whilst it is impossible to clinically separate observed behavior of cells from their environmental context, using a mathematical framework combined with multiscale data gives us insight into the relative roles of variation from different sources. To better understand the implications of intratumor heterogeneity on therapeutic outcomes, we created a hybrid agent-based mathematical model that captures both the overall tumor kinetics and the individual cellular behavior. We track single cells as agents, cell density on a coarser scale, and growth factor diffusion and dynamics on a finer scale over time and space. Our model parameters were fit utilizing serial MRI imaging and cell tracking data from ex vivo tissue slices acquired from a growth-factor driven glioblastoma murine model. When fitting our model to serial imaging only, there was a spectrum of equally-good parameter fits corresponding to a wide range of phenotypic behaviors. When fitting our model using imaging and cell scale data, we determined that environmental heterogeneity alone is insufficient to match the single cell data, and intrinsic heterogeneity is required to fully capture the migration behavior. The wide spectrum of in silico tumors also had a wide variety of responses to an application of an anti-proliferative treatment. Recurrent tumors were generally less proliferative than pre-treatment tumors as measured via the model simulations and validated from human GBM patient histology. Further, we found that all tumors continued to grow with an anti-migratory treatment alone, but the anti-proliferative/anti-migratory combination generally showed improvement over an anti-proliferative treatment alone. Together our results emphasize the need to better understand the underlying phenotypes and tumor heterogeneity present in a tumor when designing therapeutic regimens.

Opportunities for improving cancer treatment using systems biology

Current cancer therapies target a limited set of tumor features, rather than considering the tumor as a whole. Systems biology aims to reveal therapeutic targets associated with a variety of facets in an individual's tumor, such as genetic heterogeneity and its evolution, cancer cell-autonomous phenotypes, and microenvironmental signaling. These disparate characteristics can be reconciled using mathematical modeling that incorporates concepts from ecology and evolution. This provides an opportunity to predict tumor growth and response to therapy, to tailor patient-specific approaches in real time or even prospectively. Importantly, as data regarding patient tumors is often available from only limited time points during treatment, systems-based approaches can address this limitation by interpolating longitudinal events within a principled framework. This review outlines areas in medicine that could benefit from systems biology approaches to deconvolve the complexity of cancer.

System-based approaches as prognostic tools for glioblastoma

BACKGROUND

The evasion of apoptosis is a hallmark of cancer. Understanding this process holistically and overcoming apoptosis resistance is a goal of many research teams in order to develop better treatment options for cancer patients. Efforts are also ongoing to personalize the treatment of patients. Strategies to confirm the therapeutic efficacy of current treatments or indeed to identify potential novel additional options would be extremely beneficial to both clinicians and patients. In the past few years, system medicine approaches have been developed that model the biochemical pathways of apoptosis. These systems tools incorporate and analyse the complex biological networks involved. For their successful integration into clinical practice, it is mandatory to integrate systems approaches with routine clinical and histopathological practice to deliver personalized care for patients.

RESULTS

We review here the development of system medicine approaches that model apoptosis for the treatment of cancer with a specific emphasis on the aggressive brain cancer, glioblastoma.

CONCLUSIONS

We discuss the current understanding in the field and present new approaches that highlight the potential of system medicine approaches to influence how glioblastoma is diagnosed and treated in the future.

Optimization of Cancer Treatment in the Frequency Domain

Thorough exploration of alternative dosing frequencies is often not performed in conventional pharmacometrics approaches. Quantitative systems pharmacology (QSP) can provide novel insights into optimal dosing regimen and drug behaviors which could add a new dimension to the design of novel treatments. However, methods for such an approach are currently lacking. Recently, we illustrated the utility of frequency-domain response analysis (FdRA), an analytical method used in control engineering, using several generic pharmacokinetic-pharmacodynamic case studies. While FdRA is not applicable to models harboring ever increasing variables such as those describing tumor growth, studying such models in the frequency domain provides valuable insight into optimal dosing frequencies. Through the analysis of three distinct tumor growth models (cell cycle-specific, metronomic, and acquired resistance), we demonstrate the application of a simulation-based analysis in the frequency domain to optimize cancer treatments. We study the response of tumor growth to dosing frequencies while simultaneously examining treatment safety, and found for all three models that above a certain dosing frequency, tumor size is insensitive to an increase in dosing frequency, e.g., for the cell cycle-specific model, one dose per 3 days, and an hourly dose yield the same reduction of tumor size to 3% of the initial size after 1 year of treatment. Additionally, we explore the effect of drug elimination rate changes on the tumor growth response. In summary, we show that the frequency-domain view of three models of tumor growth dynamics can help in optimizing drug dosing regimen to improve treatment success.

Hyaluronic acid-functionalized gelatin hydrogels reveal extracellular matrix signals temper the efficacy of erlotinib against patient-derived glioblastoma specimens

Therapeutic options to treat primary glioblastoma (GBM) tumors are scarce. GBM tumors with epidermal growth factor receptor (EGFR) mutations, in particular a constitutively active EGFRvIII mutant, have extremely poor clinical outcomes. GBM tumors with concurrent EGFR amplification and active phosphatase and tensin homolog (PTEN) are sensitive to the tyrosine kinase inhibitor erlotinib, but the effect is not durable. A persistent challenge to improved treatment is the poorly understood role of cellular, metabolic, and biophysical signals from the GBM tumor microenvironment on therapeutic efficacy and acquired resistance. The intractable nature of studying GBM cell in vivo motivates tissue engineering approaches to replicate aspects of the complex GBM tumor microenvironment. Here, we profile the effect of erlotinib on two patient-derived GBM specimens: EGFR + GBM12 and EGFRvIII GBM6. We use a three-dimensional gelatin hydrogel to present brain-mimetic hyaluronic acid (HA) and evaluate the coordinated influence of extracellular matrix signals and EGFR mutation status on GBM cell migration, survival and proliferation, as well as signaling pathway activation in response to cyclic erlotinib exposure. Comparable to results observed in vivo for xenograft tumors, erlotinib exposure is not cytotoxic for GBM6 EGFRvIII specimens. We also identify a role of extracellular HA (via CD44) in altering the effect of erlotinib in GBM EGFR + cells by modifying STAT3 phosphorylation status. Taken together, we report an in vitro tissue engineered platform to monitor signaling associated with poor response to targeted inhibitors in GBM.

On the Impact of Chemo-Mechanically Induced Phenotypic Transitions in Gliomas

Tumor microenvironment is a critical player in glioma progression, and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work we analyze the effects of mechanical compression on migration and proliferation of glioma cells. We derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. Our results reveal a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these novel findings increase the current understanding of glioma/microenvironment interactions and can contribute to new strategies for improved therapeutic outcomes.

Serum‑derived hepatitis C virus can infect human glioblastoma cell line SF268 and activate the PI3K‑Akt pathway

Extra‑hepatic manifestations are frequently observed in hepatitis C virus (HCV)‑infected patients; however the underlying mechanisms remain largely unknown. In the present study, the human glioblastoma SF268 cell line (the precise origin of the cell type is not clear) was infected with HCV using HCV‑positive serum, and viral replication was assessed by immunofluorescence, reverse transcription‑polymerase chain reaction (PCR), quantitative PCR and western blotting following infection. HCV core protein and HCV RNA were detected in HCV‑positive serum‑infected SF268 cells at day 4 post‑infection, while no infection was observed in cells exposed to HCV‑negative serum. The mean HCV RNA levels at day 4 post‑infection were up to 5.00 IU/ml log10; however, HCV RNA and immunostaining for core protein were negative when cultured to day 6 or longer. The data suggest that human glioblastoma SF268 cells were transiently infected with HCV. AKT serine/threonine kinase phosphorylation was also detected in HCV‑infected SF268 cells at day 4 post‑infection. To the best of our knowledge, this is the first demonstration that a human glioblastoma cell line can be infected with serum‑derived HCV. The results provide evidence that HCV infection can occur in cells of the central nervous system. Neurological disorder‑associated phosphoinositide 3‑kinase‑AKT signaling pathway was activated in parallel with HCV infection, suggesting that SF268 may serve as an in vitro model for investigating HCV‑nervous system cell interactions.

Prediction of Optimal Drug Schedules for Controlling Autophagy

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.